#serious-discussion | Mathematics | Page 490

neat lintel Dec 24, 2021, 5:11 AM

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none of this talks about curvature

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but if you use imagination, one of the examples she gives can help you think of whats going on

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I see

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like

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you know how earth is round

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Yeah

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and thats not completely obvious from when you are born

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Correct

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this is only the case because you are so small compared to earth

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so you cant really see the obvious curve that exists when you zoom out

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And this is analogous to the universe in general and our observations about it?

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kinda

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but we can do math

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to see what curvature looks like locally

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and estimate what that means about global curvature

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creatures like ants (if they were intilligent) would have no chance of verifying these things.

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because of how small they are in comparison to the earth

mortal igloo Dec 24, 2021, 5:14 AM

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One way you can detect curvature is to parallel transport a vector around a large loop (or around a loop many times)

neat lintel Dec 24, 2021, 5:14 AM

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also because their vision is shit

mortal igloo Dec 24, 2021, 5:15 AM

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If the resulting vector is rotated compared to the original vector, your space is curved

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One day I hope to parallel transport myself around a room without changing my facing direction many times until my facing direction changes

neat lintel Dec 24, 2021, 5:15 AM

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So they(ants) say this hill is kinda steep and conclude a vague idea how the planet actually is?

mortal igloo Dec 24, 2021, 5:15 AM

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Intuitively this shouldn't work but the math says it will...

neat lintel Dec 24, 2021, 5:16 AM

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neat lintel So they(ants) say this hill is kinda steep and conclude a vague idea how the pla...

ye

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ill give you honest opinion

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idk why anyone gives a shit

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It's math for the sake of math I guess

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catshrug

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And physicists with way too much free time

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what

mortal igloo Dec 24, 2021, 5:18 AM

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Are you lampooning theoretical physics

neat lintel Dec 24, 2021, 5:18 AM

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neat lintel And physicists with way too much free time

bruh math is worse

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bro

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the curvature of the earth is not calculated 'for fun'

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Mr. Icy001

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whats last cool NT thing you learned

neat lintel Dec 24, 2021, 5:19 AM

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neat lintel the curvature of the earth is not calculated 'for fun'

we talking about universe

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not earth

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even so

coarse grotto Dec 24, 2021, 5:19 AM

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uhhhh

neat lintel Dec 24, 2021, 5:20 AM

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it has no forseeable practicality

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you are coping otherwise

mortal igloo Dec 24, 2021, 5:20 AM

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neat lintel whats last cool NT thing you learned

Arthur packets correspond to perverse sheaves

neat lintel Dec 24, 2021, 5:20 AM

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is arthur packets a type of food

mortal igloo Dec 24, 2021, 5:20 AM

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If you define food correctly, yes

neat lintel Dec 24, 2021, 5:21 AM

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langlands 😵‍💫

mortal igloo Dec 24, 2021, 5:21 AM

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Did you google it? lol

neat lintel Dec 24, 2021, 5:21 AM

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yeah

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Modern Gps systems rely on relativity theories for their accuracy (lagtime due to speeds), and the idea that mass curves space time is applicable in how light bends around stars so that their postion is altered, and we have observed altered positions of stars that would not be predicted by newton's laws of gravitations otherwise

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It is viewable on a cosmic scale

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honestly langlands program sounds like one of those things i would like if i had enough background

mortal igloo Dec 24, 2021, 5:22 AM

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I'm under the impression no one in the world would say they have enough background on Langlands currently

neat lintel Dec 24, 2021, 5:22 AM

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the purpose sounds cool, but idk if it is as cool as it seems

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how do people even get into that

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i am still a silly undergrad and im naive about who knows what

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how many advisors are doing langlands

mortal igloo Dec 24, 2021, 5:23 AM

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linear algebra -> commutative algebra -> algebraic geometry + representation theory -> graduate school -> pick an advisor working on Langlands, probably

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Or read a lot

neat lintel Dec 24, 2021, 5:24 AM

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oh shit!

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im in the pipeline

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barely in step 2: commutative alg

mortal igloo Dec 24, 2021, 5:24 AM

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but expository material on Langlands is extremely unfriendly

neat lintel Dec 24, 2021, 5:24 AM

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reading sucks sometimes ngl

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feels lonely

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and i am already lonely enough irl

mortal igloo Dec 24, 2021, 5:25 AM

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Are you lonely right now?

neat lintel Dec 24, 2021, 5:25 AM

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anyways

mortal igloo Dec 24, 2021, 5:25 AM

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Trick question

neat lintel Dec 24, 2021, 5:25 AM

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is your advisor working on langlands

mortal igloo Dec 24, 2021, 5:25 AM

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An off-shoot of it, I'd say

neat lintel Dec 24, 2021, 5:25 AM

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what in the sam harris

mortal igloo Dec 24, 2021, 5:26 AM

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what's up with Sam Harris nowadays

neat lintel Dec 24, 2021, 5:26 AM

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idk

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just sounds like a funny name

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i want to learn more about number theory connections to other fields

mortal igloo Dec 24, 2021, 5:27 AM

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I feel the sudden urge to calculate how many times I need to walk around my room to feel the curvature of the Earth

neat lintel Dec 24, 2021, 5:27 AM

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i dont have enough examples though

mortal igloo Dec 24, 2021, 5:27 AM

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Basically the principle is this

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If you start at the north pole, go all the way to the equator, then go a quarter circle around the equator, then go back to the north pole, all while "facing" the same direction, your rotation is 90 degrees off from where you started

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This means that parallel transport around a loop with the area of 1/8 of the Earth's surface area causes a 90 degree vector rotation

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On a surface with constant curvature, the amount a vector is rotated when parallel transported around a loop is directly proportional to the area enclosed by the loop

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Ok so 1/8 of the surface area of the earth is 24.6 million square miles

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divide that by the area of my room which is on the order of 500 square feet

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1.4 x 10^12 😔

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So a vector parallel transported around my room will be rotated by like 0.00000000009 degrees

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will need to repeat that 11 billion times to rotate it by 1 degree

velvet dagger Dec 24, 2021, 5:31 AM

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Did someone say Langlands

neat lintel Dec 24, 2021, 5:31 AM

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bronze pelican Dec 24, 2021, 5:31 AM

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lan glands

mortal igloo Dec 24, 2021, 5:32 AM

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So basically for all intents and purposes the section of Earth covered by my room is flat

neat lintel Dec 24, 2021, 5:32 AM

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mortal igloo will need to repeat that 11 billion times to rotate it by 1 degree

what is smallest amount of percivable rotation of our head

mortal igloo Dec 24, 2021, 5:32 AM

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🕵️

neat lintel Dec 24, 2021, 5:32 AM

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how do you spell that word

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percievable

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persevable

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precievable

mortal igloo Dec 24, 2021, 5:32 AM

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pregananant

neat lintel Dec 24, 2021, 5:33 AM

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perceivable

velvet dagger Dec 24, 2021, 5:33 AM

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@mortal igloo I didn't realize you were near the langlands program

neat lintel Dec 24, 2021, 5:33 AM

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cant spell perceivable without a perc 30

velvet dagger Dec 24, 2021, 5:33 AM

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What kinda stuff do you do (or your advisor does if you're not there yet)

mortal igloo Dec 24, 2021, 5:33 AM

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hehe

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My thesis was related to automorphic representations over function fields, and right now I'm trying to fill myself in on the theta correspondence and Shimura variety stuff

velvet dagger Dec 24, 2021, 5:36 AM

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Wait are you a postdoc? I thought you were a grad student lol

mortal igloo Dec 24, 2021, 5:36 AM

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Yep

narrow rock Dec 24, 2021, 5:37 AM

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langlands stare

velvet dagger Dec 24, 2021, 5:37 AM

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But yeah that's good stuff. Covers 2 of the 4 research projects in AWS this semester

mortal igloo Dec 24, 2021, 5:37 AM

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You may have heard of my adventure this semester which is teaching Calc II students for the first time

neat lintel Dec 24, 2021, 5:37 AM

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narrow rock langlands <:stare:826920038623346729>

thats what im saying

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amazon web services

velvet dagger Dec 24, 2021, 5:37 AM

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Lmao

mortal igloo Dec 24, 2021, 5:37 AM

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Are you going to AWS?

velvet dagger Dec 24, 2021, 5:37 AM

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I applied yeah

neat lintel Dec 24, 2021, 5:37 AM

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oh wtf

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arizona winter sem

mortal igloo Dec 24, 2021, 5:37 AM

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We might see each other then!

neat lintel Dec 24, 2021, 5:37 AM

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right?

velvet dagger Dec 24, 2021, 5:38 AM

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That'd be pretty dope! I'm looking especially at the project about quaternionic modular forms

mortal igloo Dec 24, 2021, 5:38 AM

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I was invited as one of the assistants but I'm not sure if they are following up

velvet dagger Dec 24, 2021, 5:39 AM

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Or possibly the one about constructing vector-valued automorphic forms from scalar-valued ones

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Tbh I haven't thought enough about anything beyond GL2 to really get the point of the second project

mortal igloo Dec 24, 2021, 5:39 AM

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That sounds like theta correspondence

neat lintel Dec 24, 2021, 5:39 AM

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https://www.math.arizona.edu/~swc/

velvet dagger Dec 24, 2021, 5:39 AM

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Yup that Mahael

neat lintel Dec 24, 2021, 5:40 AM

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lol

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i think i applied to this

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or some version of it

velvet dagger Dec 24, 2021, 5:40 AM

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Basically I'm thinking Pollack, followed by just doing rep theory psets at night, followed by Eischen's project

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Gan's stuff was a bit scary and I've never really thought about function fields

mortal igloo Dec 24, 2021, 5:41 AM

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Is rep theory psets part of this AWS?

narrow rock Dec 24, 2021, 5:41 AM

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I should apply next year catThin4K

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the projects look pretty cool

velvet dagger Dec 24, 2021, 5:43 AM

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Yeah basically the way it seems to work is, there are lectures and associated projects. You can either sign up to do the projects, you can sign up to be in study groups which review the lecture content in the evenings, or you can sign up for "problem sessions" which just do a bunch of psets in the evenings

pure sun Dec 24, 2021, 5:43 AM

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thats about right, yeah

narrow rock Dec 24, 2021, 5:43 AM

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is it online this year

pure sun Dec 24, 2021, 5:43 AM

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but for the projects it's not really a sign up

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it's more of an application

velvet dagger Dec 24, 2021, 5:43 AM

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There were 2 problem sessions, one was on "Rep theoretic aspects of automorphic forms" and the other is "Geometric aspects of automorphic forms"

mortal igloo Dec 24, 2021, 5:43 AM

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Oh so you were saying your top 3 choices for what to do basically?

pure sun Dec 24, 2021, 5:44 AM

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you can sign up for the problem sessions and the study groups but you typically have to apply for the project groups

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also in my experience nobody really monitored the attendance at the problem sessions and study groups and so you could basically move between them freely

velvet dagger Dec 24, 2021, 5:44 AM

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So yeah I put Pollack's project as my top choice, second choice is rep theory problem session, third was Eischen's project

mortal igloo Dec 24, 2021, 5:45 AM

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nice

pure sun Dec 24, 2021, 5:45 AM

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good luck

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AWS is fun

velvet dagger Dec 24, 2021, 5:46 AM

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Was considering geometric problem session since I don't really get what's happening in Eischen's project but when talking to my advisor, we weren't really sure if geometric means AG or hyperbolic geometry

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And when he went over Eischen's thing he was like yeah this could be cool I'd go with this over the geometry problem session

velvet dagger Dec 24, 2021, 5:47 AM

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pure sun good luck

Thanks fam

mortal igloo Dec 24, 2021, 5:48 AM

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I can't find information on the geometric problem session

velvet dagger Dec 24, 2021, 5:50 AM

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Yeah they don't seem to have it anywhere

neat lintel Dec 24, 2021, 5:58 AM

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random question

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why do deserts have sand wave patterns?

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they don't

clever knot Dec 24, 2021, 6:26 AM

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neat lintel why do deserts have sand wave patterns?

you mean something like this

neat lintel Dec 24, 2021, 6:26 AM

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yeah

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i know sand movement is caused by wind mostly

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but why is this always so orderly

clever knot Dec 24, 2021, 6:28 AM

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https://en.wikipedia.org/wiki/Dune

Dune

A dune is a landform composed of wind- or water-driven sand. It typically takes the form of a mound, ridge, or hill. An area with dunes is called a dune system or a dune complex. A large dune complex is called a dune field, while broad, flat regions covered with wind-swept sand or dunes with little or no vegetation are called ergs or sand seas....

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catshrug

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i assume the large wind gusts pick up a large line of sand and throw it up slightly over

neat lintel Dec 24, 2021, 6:30 AM

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shit is cool ngl

jolly token Dec 24, 2021, 11:42 AM

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Does anyone of you have any experience self teaching himself relatively "advance topics"(linear algebra I&II, optimization, group theory, etc) in mathematics as a high school student? What would recommend to your back then self after having gained experience later on your career? What are some interesting topics to study?
Thank you in advance!

honest veldt Dec 24, 2021, 11:43 AM

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i don't think i qualify here

brave hollow Dec 24, 2021, 11:43 AM

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jolly token Does anyone of you have any experience self teaching himself relatively "advance...

I am not experienced but I learned group theory in high school, but I wanted to say
study groups with weekly discussions work

honest veldt Dec 24, 2021, 11:44 AM

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study groups bleak

brave hollow Dec 24, 2021, 11:44 AM

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group theory sotrue its in the name

honest veldt Dec 24, 2021, 11:44 AM

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maybe one day I'll meet someone who knows what algebra is, that'd be a day

fair mural Dec 24, 2021, 11:45 AM

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jolly token Does anyone of you have any experience self teaching himself relatively "advance...

i’m in high school and self learning learning odes, i just learn when i feel like it

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to be fair, when i feel like it is quite often lol

light needle Dec 24, 2021, 11:45 AM

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jolly token Does anyone of you have any experience self teaching himself relatively "advance...

I did a lot of stuff in hs, my advice would probably be to not get bogged down in the detail as I do now

somber musk Dec 24, 2021, 11:46 AM

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fair mural i’m in high school and self learning learning odes, i just learn when i feel lik...

Same, almost

fair mural Dec 24, 2021, 11:46 AM

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wait i don’t think i really answered your question now that i think about it

light needle Dec 24, 2021, 11:46 AM

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But also when i think about it, maybe getting bogged down in the details is important when ur new to math and the topics

icy forge Dec 24, 2021, 11:46 AM

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fair mural i’m in high school and self learning learning odes, i just learn when i feel lik...

Highschool isn't very far from ODEs considering many around the same age globally learn it as part of required syllabus

fair mural Dec 24, 2021, 11:46 AM

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oof

honest veldt Dec 24, 2021, 11:47 AM

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In any case, I found starting with linear algebra to be really helpful, it was a nice transition from computational stuff like calculus to the more abstract side of maths (I did abstract linear algebra, not the one that mostly focuses on R^n and C^n and stuff)

light needle Dec 24, 2021, 11:47 AM

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Oh yeah also that do LA with rigor

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Rather than with like mitocw

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Or w/e

honest veldt Dec 24, 2021, 11:47 AM

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Yeah, it was real nice

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I used Axler's Linear Algebra Done Right, but there might be better books out there

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Ask around

light needle Dec 24, 2021, 11:48 AM

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Like i was around 15 when i did LA but like, mostly computationally, definately wish i did it rigorously it would open up more math for me

ancient flame Dec 24, 2021, 2:12 PM

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15???? damnnnn

rotund steppe Dec 24, 2021, 3:33 PM

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bleak

solemn sequoia Dec 24, 2021, 6:21 PM

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When did RIT start offering a PhD in Mathematical Modeling?!

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First I've heard of a program specific to modeling.

sharp mulch Dec 24, 2021, 6:23 PM

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Suspicious

coarse grotto Dec 24, 2021, 6:24 PM

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RIT attempted to guilt trip me for not applying

sharp mulch Dec 24, 2021, 6:26 PM

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I mean I looked at the website and it isn't like a scam I guess

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I'm a bit concerned about the coursework requirements though

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Do they not have any pure math? It looks like their department is entirely applied math

coarse grotto Dec 24, 2021, 6:29 PM

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yeah, and it looks like their only math phd option is the mathematical modeling program

frozen venture Dec 24, 2021, 6:40 PM

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Is there a way to define the limit of a sequence of groups?

sharp mulch Dec 24, 2021, 6:41 PM

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What ambient space are you working in

unborn trellis Dec 24, 2021, 6:41 PM

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that's a loaded question

mortal igloo Dec 24, 2021, 6:41 PM

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There’s category theoretical limits

unborn trellis Dec 24, 2021, 6:41 PM

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depends on whether you ask an algebraist or analyst

mortal igloo Dec 24, 2021, 6:41 PM

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Inductive and projective limits

sharp mulch Dec 24, 2021, 6:41 PM

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You can consider all the groups as just sets and take the intersection of all of them

frozen venture Dec 24, 2021, 6:43 PM

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sharp mulch What ambient space are you working in

I'm trying to come up with a way to naturally show that the sequence of dihedral groups D_n approaches the circle group.

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My thinking was that we would first need to define a metric on this set of groups.

sharp mulch Dec 24, 2021, 6:45 PM

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Do they though

frozen venture Dec 24, 2021, 6:45 PM

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Intuitively yeah

sharp mulch Dec 24, 2021, 6:45 PM

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D_n is generally not abelian whereas the circle group is

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I'd believe it if you said that Z_n approached the circle group as n->infinity

frozen venture Dec 24, 2021, 6:46 PM

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Hmm, I think I used the wrong terminology sorry

mortal igloo Dec 24, 2021, 6:47 PM

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The corresponding thing for dihedral groups should be O(2)

frozen venture Dec 24, 2021, 6:47 PM

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I mean the group of reflections and rotations of circle

sharp mulch Dec 24, 2021, 6:47 PM

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Ok the orthogonal group

frozen venture Dec 24, 2021, 6:47 PM

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Yeah

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So how would you define limits in this setting in order to capture this intuition?

sharp mulch Dec 24, 2021, 6:48 PM

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Well you'll need to be careful because you want D_n to approach O(2) and not the infinite dihedral group

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But I think I would argue that a n-gon approaches a circle as n goes to infinity

frozen venture Dec 24, 2021, 6:49 PM

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Wouldn't you need to define a metric on this set of groups?

pure sun Dec 24, 2021, 6:50 PM

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there are more general notions of "limits" than just metric spaces

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for example, you can talk about direct limits of directed sets of groups

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though you need to be careful about how you would apply that in this case

mortal igloo Dec 24, 2021, 6:51 PM

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If for each $n\mid N$ you embed $D_n$ into $D_N$ and take the inductive limit, I believe you will get the subgroup of $O(2)$ consisting of reflections and rational angle rotations

pure sun Dec 24, 2021, 6:51 PM

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also as ange wrote, how do you anticipate being able to distinguish the group you're considering from the infinite dihedral group?

fathom swallowBOT Dec 24, 2021, 6:51 PM

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Icy001

mortal igloo Dec 24, 2021, 6:51 PM

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This is probably the best you can do, and to get all of $O(2)$ you need to take some sort of completion

fathom swallowBOT Dec 24, 2021, 6:51 PM

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Icy001

pure sun Dec 24, 2021, 6:51 PM

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which to me looks equally well like the "limit" of the dihedral groups

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(i concur with icy, btw)

bronze pelican Dec 24, 2021, 6:52 PM

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Letts gooooo

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I'm mentoring an undergrad research project next semester

pure sun Dec 24, 2021, 6:52 PM

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cool!

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those are fun

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what topic?

bronze pelican Dec 24, 2021, 6:52 PM

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On something called the Log-Rank conjecture and its connection to incidence geometry

sharp mulch Dec 24, 2021, 6:53 PM

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I wonder when I'll hear back about the thing I applied to mentor

neat lintel Dec 24, 2021, 7:06 PM

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isnt direct limit most general notion

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because afaik you just need index set and a partial order

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directed set*

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in one word i think its a directed set

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and a maximal element?

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or maybe not

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probably not

pure sun Dec 24, 2021, 7:08 PM

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if you take the direct limit of a directed set with a maximal element you will just get the maximal element back

frozen merlin Dec 24, 2021, 7:34 PM

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bronze pelican I'm mentoring an undergrad research project next semester

a project supervisor at my uni told me he'd get back to my application after he waits "a few days" for everyone to apply

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but it's been 3 weeks

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if you were him, would you appreciate a follow up email or would it just annoy you

bronze pelican Dec 24, 2021, 7:35 PM

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Follow up

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Sometimes people forget

bronze pelican Dec 24, 2021, 8:01 PM

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I'm taking a diff geo final oral exam in 1 hour

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😬

fair mural Dec 24, 2021, 8:01 PM

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good luck

mortal igloo Dec 24, 2021, 8:08 PM

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Good luck!

somber musk Dec 24, 2021, 8:09 PM

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bronze pelican I'm taking a diff geo final oral exam in 1 hour

Good luck

bronze pelican Dec 24, 2021, 8:11 PM

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Ty

neat lintel Dec 24, 2021, 8:12 PM

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pure sun if you take the direct limit of a directed set with a maximal element you will j...

ig question is what are weakest conditions for the directed limit to exist?

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or does it always exist?

pure sun Dec 24, 2021, 8:13 PM

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Depends on the category

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In a category of modules it will always exist because you can construct it explicitly

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(Assuming no set theory nonsense gets in the way but i dont think that should really be an issue)

velvet dagger Dec 24, 2021, 8:14 PM

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@bronze pelican remember if you have something equal to zero take a derivative, you'll be just fine

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(Jokes aside good luck fam)

neat lintel Dec 24, 2021, 8:19 PM

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cool is cool

bronze pelican Dec 24, 2021, 10:01 PM

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Finished the oral exma

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Bro wtf was that

fair mural Dec 24, 2021, 10:01 PM

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did you do good

mortal igloo Dec 24, 2021, 10:02 PM

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How hard was it?

bronze pelican Dec 24, 2021, 10:03 PM

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It was fine

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Being on the spot is kind of nerve wracking

mortal igloo Dec 24, 2021, 10:04 PM

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I can imagine

narrow rock Dec 24, 2021, 10:54 PM

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icy honorable stare

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hype

sharp mulch Dec 24, 2021, 10:57 PM

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Brofib it's stopped raining so you can go outside now

swift sinew Dec 24, 2021, 11:42 PM

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figured id drop back into the server for christmas (eve), hows everyone doing?

fair mural Dec 24, 2021, 11:43 PM

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i think i remember you, i’m doing pretty good, what about you?

swift sinew Dec 24, 2021, 11:44 PM

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doing well! are finals done for you?

fair mural Dec 24, 2021, 11:46 PM

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i’m not actually in college so i’m not doing those lol

swift sinew Dec 24, 2021, 11:47 PM

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haha well i hope the holidays are going well, nice to hear from you again

fair mural Dec 24, 2021, 11:50 PM

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same to you

ancient flame Dec 24, 2021, 11:50 PM

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fuck the holidays

swift sinew Dec 24, 2021, 11:50 PM

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nice to see this server hasnt changed

ancient flame Dec 24, 2021, 11:51 PM

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LOL

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dw it's just me

velvet dagger Dec 24, 2021, 11:51 PM

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It has now we have another nerd here named justAlex smh

fair mural Dec 24, 2021, 11:52 PM

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sad

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no meanies allowed

ancient flame Dec 24, 2021, 11:52 PM

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beaned

swift sinew Dec 24, 2021, 11:52 PM

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mod privileges revoked

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rip

ancient flame Dec 24, 2021, 11:52 PM

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rip

stone valve Dec 25, 2021, 12:04 AM

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wait what

rotund steppe Dec 25, 2021, 3:46 AM

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Why is real analysis a prerequisite of differential equations

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i thought it was like right after calc and linear algebra

devout nacelle Dec 25, 2021, 4:11 AM

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rotund steppe Why is real analysis a prerequisite of differential equations

It depends on the kind of differential equations class you're taking. Cookbook courses that emphasise methods to solve usually only have calculus (and possibly linear algebra) as a prerequisite; more theoretical courses that emphasise the qualitative analysis of equations, existence/uniqueness of solutions, etc. require a first course in real analysis.

coarse grotto Dec 25, 2021, 4:12 AM

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yeah, a look at the syllabus will be a better descriptor of the expectations

bright hill Dec 25, 2021, 12:57 PM

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What do you guys do when you absolutely have NO IDEA how to solve a problem?

neat lintel Dec 25, 2021, 12:58 PM

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ask here

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in the help channels

bright hill Dec 25, 2021, 1:01 PM

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Well, I'm asking but no one is answering

leaden skiff Dec 25, 2021, 1:02 PM

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bright hill What do you guys do when you absolutely have *NO IDEA* how to solve a problem?

well it's rare that i have 0 idea

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usually there's something you can try

leaden skiff Dec 25, 2021, 1:02 PM

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bright hill What do you guys do when you absolutely have *NO IDEA* how to solve a problem?

do you have a specific problem in mind?

bright hill Dec 25, 2021, 1:03 PM

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For example

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All of those 3 are monsters on their own

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But man, the last one

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All I could do since yesterday was blankly stare at the wall trying to find something to try

leaden skiff Dec 25, 2021, 1:05 PM

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ok well i don't really know real analysis, but like if i had to do it i'd ust try playing around with the problems first

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just make random guesses and see what happens

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like my first instinct for 6.7 is trying to interleave digits

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like if one element of R^2 is (0.1111...,0.222...) then the corresponding element in R might be 0.121212...

bright hill Dec 25, 2021, 1:08 PM

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Yeah I tried that

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But there is still a problem with numbers who end in all 0s or all 9s

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I sort've found a clue for 0.6.8 too but it has a similar caveat

solid yoke Dec 25, 2021, 1:13 PM

#

if its any help (0,1) is isomorphic to R, so you can show the powerset of N has same cardinality as (0,1)

bright hill Dec 25, 2021, 1:14 PM

#

Yeah I tried that too

#

I then considered them in binary

#

So for every real number x in (0,1) and start with the empty set; if x has 1 in its 1st digit after decimal add the number 1

#

If it has 1 in its 2nd digit, add the number 2

#

And so on

solid yoke Dec 25, 2021, 1:19 PM

#

hmm

bright hill Dec 25, 2021, 1:20 PM

#

But that would map 0.011111111... and 0.1000... to different sets

#

Although they're the same number

solid yoke Dec 25, 2021, 1:20 PM

#

why dont you try if you have 0.1

#

map it to 1

#

0.01

#

map it to 10

#

and 0.11 = 11

#

so you have an injective function

bright hill Dec 25, 2021, 1:23 PM

#

But I need a bijective function to determine cardinality

#

I think the shröder-bernstein theorem can help me but I still haven't understood it will enough yet

#

I asked on #calculus but no one answered

solid yoke Dec 25, 2021, 1:25 PM

#

you can use the bernstein theorem

#

show AlessthanorequalB and BlessthanorequalA

#

then AtildaB

bright hill Dec 25, 2021, 1:27 PM

#

Yeah, yeah

#

I understand that part

river linden Dec 25, 2021, 1:27 PM

#

If you show A injective to B and vise versa you get A ~ B. so the .99... issue doesn't matter

bright hill Dec 25, 2021, 1:28 PM

#

But there's an exercise which serves as a proof sketch

river linden Dec 25, 2021, 1:28 PM

#

river linden If you show A injective to B and vise versa you get A ~ B. so the .99... issue d...

I think you only lose onto but not injectivity (I did a similar problem in real anal)

solid yoke Dec 25, 2021, 1:29 PM

#

I did this question a bit back in set theory

bright hill Dec 25, 2021, 1:29 PM

#

Anyways

#

My original question was about the last one

#

How do you approach such a problem?

river linden Dec 25, 2021, 1:30 PM

#

try and list Q st the diag is zeros? then the diag would be rational

#

not sure if Q grows "too fast" for you to do that though

bright hill Dec 25, 2021, 1:31 PM

#

There are rational which don't have any 0 on them

river linden Dec 25, 2021, 1:31 PM

#

ah right

bright hill Dec 25, 2021, 1:31 PM

#

So you won't be listing all rationals like that

river linden Dec 25, 2021, 1:31 PM

#

then try to get a repeating decimal like x/9 somehow? intuitively it should be possible

#

but maybe it isn't

#

maybe base 2 is easier then bsse 10

bright hill Dec 25, 2021, 1:37 PM

#

Both of these are things I thought about

river linden Dec 25, 2021, 1:39 PM

#

idk then, mb look for a contradiction. I gtg

bright hill Dec 25, 2021, 1:39 PM

#

K then

#

Thanks anyways

wispy dune Dec 25, 2021, 2:04 PM

#

bright hill For example

i think this works: ||We claim that the answer is no. Assume to the contrary, that the diagonal element is rational. Note that incrementing the digits of a rational (the increment of 9 is 0 in this case) still yields a rational. Now incrementing this diagonal element yields us a rational which is not on our list (by similar logic as in the standard diagonalization argument), which is a contradiction with the fact that our list contains every rational||

bright hill Dec 25, 2021, 2:05 PM

#

I don't want an answer, sry pacman

wispy dune Dec 25, 2021, 2:06 PM

#

if you want a hint ||consider using the diagonalization argument||

jovial ember Dec 25, 2021, 4:01 PM

#

I feel like you can solve this

deep mango Dec 25, 2021, 4:01 PM

#

Wowie

#

Good morning!

jovial ember Dec 25, 2021, 4:02 PM

#

deep mango Good morning!

Good morning!

#

@wispy dune I think you can solve it. ||Take a bijection x_n of N with the rationals in [0,1]. Then consider the specific bijection of N with N^2 where you do the zigzag. Then the diagonal elements are a specific fixed subsequence n_i, so just swap x_n_k in order with the numbers 0.1,0.11,0.111,… this gives you a way to list all of the rationals such that the diagonal elements are 0.1,0.11,0.111,…||

#

tiny marten Dec 25, 2021, 4:13 PM

#

Classic zigzag thingy

wispy dune Dec 25, 2021, 4:14 PM

#

jovial ember <@226715564050087936> I think you can solve it. ||Take a bijection x_n of N with...

what is x_n

#

an enumeration of the rationals?

jovial ember Dec 25, 2021, 4:21 PM

#

Right

#

Or maybe I misinterpreted what the problem meant tbh

#

Idk wtf “the diagonal” meant

#

Maybe you don’t even need to list them in this 2-dimensional way lol

#

Actually

#

I re-read the problem and think I understand what it actually is asking

#

And I no longer think it’s possible

#

opencry

#

Whoops

deep mango Dec 25, 2021, 4:25 PM

#

bleak

#

Is this "list all the rationals so that the diagonal gives another rational"?

jovial ember Dec 25, 2021, 4:26 PM

#

Yes

deep mango Dec 25, 2021, 4:26 PM

#

What if you do 1-it

#

Do you get a different rational from everything on the list

#

Idk

jovial ember Dec 25, 2021, 4:27 PM

#

I think this is the idea or something

deep mango Dec 25, 2021, 4:27 PM

#

Lots of edge cases

jovial ember Dec 25, 2021, 4:27 PM

#

Pappa’s solution was to add 1 to every digit

deep mango Dec 25, 2021, 4:27 PM

#

I see

#

I guess rational means it repeats so its ok

jovial ember Dec 25, 2021, 4:28 PM

#

I mean

#

You don’t even need that

#

You make 9 roll over to a 0

#

Without carrying a 1

toxic schooner Dec 25, 2021, 4:28 PM

#

deep mango I guess rational means it repeats so its ok

catThin4K

jovial ember Dec 25, 2021, 4:28 PM

#

So if you can represent any number as an infinite sequence you can just add 1 to each thing

toxic schooner Dec 25, 2021, 4:29 PM

#

not really? it can probably mean terminating or non terminating repeating

toxic schooner Dec 25, 2021, 4:29 PM

#

jovial ember So if you can represent any number as an infinite sequence you can just add 1 to...

and 9 goes to 0? that thing?

jovial ember Dec 25, 2021, 4:29 PM

#

Or maybe there is an issue idk

sonic ether Dec 25, 2021, 4:42 PM

#

https://media.discordapp.net/attachments/846220156316680197/924168045214175242/IMG_3118.png

somber musk Dec 25, 2021, 4:44 PM

#

I'm seeing this 4th time today

scarlet lichen Dec 25, 2021, 5:39 PM

#

same

neat lintel Dec 25, 2021, 5:51 PM

#

why wasn't it "as" from the beginning?

fair mural Dec 25, 2021, 6:10 PM

#

that’s what i said before

ancient flame Dec 25, 2021, 6:45 PM

#

why aren't you "as" smart as me???

distant mason Dec 25, 2021, 6:57 PM

#

Merry Christmas!
https://youtu.be/3K9HSCtTXHE

YouTube

Math Solving Channel

Bad Math! Merry Christmas 2021

Math Special ~ Merry Christmas 2021

▶ Play video

sick kite Dec 25, 2021, 7:36 PM

#

This is the 5th time I've seen this today

bronze pelican Dec 25, 2021, 10:11 PM

#

https://youtu.be/r4gOlttnJ_E

YouTube

Mathologer 2

A cute visual proof with a great punchline (xpost from my Instagram)

Here is the next chapter in my Instagram adventure.
Enjoy.
P.S.: If you use Instagram please drop by the Mathologer testing ground at https://www.instagram.com/the_real_mathologer/. Also if you like the proof in this video, definitely check out this Mathologer video https://youtu.be/p-0SOWbzUYI were I showed this proof for the first time.

▶ Play video

main monolith Dec 26, 2021, 1:59 AM

#

bronze pelican https://youtu.be/r4gOlttnJ_E

Thats actually really good!

jovial ember Dec 26, 2021, 4:11 AM

#

Guys wish RYC a happy birthday!

narrow rock Dec 26, 2021, 4:14 AM

#

Happhtithdy dryc

primal crater Dec 26, 2021, 4:30 AM

#

Happy Birthday @ryc

agile wedge Dec 26, 2021, 5:00 AM

#

Happy Birthday Ryc ! catThumbsUp

deep mango Dec 26, 2021, 5:02 AM

#

sully

ancient flame Dec 26, 2021, 5:04 AM

#

happy bday rychalkboard

bronze pelican Dec 26, 2021, 5:06 AM

#

happy ryc day

toxic schooner Dec 26, 2021, 6:12 AM

#

deep mango <:sully:651816820122189834>

is it really ur bday? catThin4K

agile wedge Dec 26, 2021, 7:30 AM

#

Who cares about that

#

Just say Happy Birthday and stop asking questions

devout nacelle Dec 26, 2021, 7:33 AM

#

My birthday's tomorrow 🥳

stone valve Dec 26, 2021, 7:33 AM

#

happy birthday

#

future u

#

😄

devout nacelle Dec 26, 2021, 7:34 AM

#

AWOOKEN

stone valve Dec 26, 2021, 7:34 AM

#

awoogenzoom

fringe needle Dec 26, 2021, 9:42 AM

#

Bappy hday ryc

toxic schooner Dec 26, 2021, 10:11 AM

#

agile wedge Just say Happy Birthday and stop asking questions

Ok then

#

Happy bday ryc!

toxic schooner Dec 26, 2021, 10:11 AM

#

devout nacelle My birthday's tomorrow 🥳

hype

spring wyvern Dec 26, 2021, 11:18 AM

#

devout nacelle My birthday's tomorrow 🥳

happy n-th $\mid$ $n \equiv 0.99726027397$ (mod 1) birthday!

fathom swallowBOT Dec 26, 2021, 11:18 AM

#

just sаm

devout nacelle Dec 26, 2021, 11:18 AM

#

stareFlushed

#

Thanks

toxic schooner Dec 26, 2021, 11:44 AM

#

spring wyvern happy n-th $\mid$ $n \equiv 0.99726027397$ (mod 1) birthday!

explain what does this mean? catThin4K

#

i kinda get it but also dont, really dont understand mod notation pensivebread

primal crater Dec 26, 2021, 12:11 PM

#

stare

dry pasture Dec 26, 2021, 12:20 PM

#

#

Help

toxic schooner Dec 26, 2021, 12:37 PM

#

primal crater <:stare:826920038623346729>

catThin4K

#

whats there to stare at catThin4K

neat lintel Dec 26, 2021, 12:39 PM

#

everything 😳

#

kekw

deep mango Dec 26, 2021, 12:39 PM

#

uhhhh

toxic schooner Dec 26, 2021, 12:43 PM

#

neat lintel everything 😳

stare

somber musk Dec 26, 2021, 12:43 PM

#

stare

ashen bison Dec 26, 2021, 6:10 PM

#

dry pasture

HCF? Highest common factor?

#

That’s the first time I’ve seen HCF used lol

woven grotto Dec 26, 2021, 7:03 PM

#

Hello. What do you think is the best approach to solve such a task:
You need to invent some integral equivalent of sum of some function.
In other words you need somehow map discrete space to continuous one. I know that gamma function doing something familiar, but not exactly what I need to do.

#

I just need a hint in which direction to move. This is not kinda math "help to solve" question so I asked it here instead of help

#

or do I need to ask it in advance chat...

sick burrow Dec 26, 2021, 7:05 PM

#

Here is fine

#

Not quite sure what the question is though

honest veldt Dec 26, 2021, 7:07 PM

#

So you need the integral and the sum to produce equal results when given equal inputs?

woven grotto Dec 26, 2021, 7:07 PM

#

yes

#

but integral would produce results in between as well

honest veldt Dec 26, 2021, 7:07 PM

#

I see

woven grotto Dec 26, 2021, 7:08 PM

#

And it must work for any function(in theory)

honest veldt Dec 26, 2021, 7:08 PM

#

Now I'm lost again

woven grotto Dec 26, 2021, 7:08 PM

#

I am managed to make it work for several polynomials but it is not following some pattern that I could detect

honest veldt Dec 26, 2021, 7:09 PM

#

So you're trying to invent some new type of integral, rather than look for some function where this holds

woven grotto Dec 26, 2021, 7:09 PM

#

honest veldt So you're trying to invent some new type of integral, rather than look for some ...

kinda

#

Not new exactly. Just some modification that will do the trick

honest veldt Dec 26, 2021, 7:10 PM

#

I get it

woven grotto Dec 26, 2021, 8:01 PM

#

@honest veldt
I am managed to get the same results again with x^2 function. Still it is not working with all functions, but maybe this will help you.

woven grotto Dec 26, 2021, 8:36 PM

#

What I found so far:

https://www.desmos.com/calculator/v0wo0orryu

Desmos

doin' research

crystal stream Dec 26, 2021, 9:05 PM

#

are you trying to get integral representations of sums?

modern oasis Dec 27, 2021, 12:27 AM

#

I found this paradox very interesting
https://www.youtube.com/watch?v=Uj3_KqkI9Zo

YouTube

TED-Ed

The Infinite Hotel Paradox - Jeff Dekofsky

Sign up for our newsletter and never miss an animation: http://bit.ly/TEDEdNewsletter

View full lesson: http://ed.ted.com/lessons/the-infinite-hotel-paradox-jeff-dekofsky

Want more? Try to solve the buried treasure riddle: https://www.youtube.com/watch?v=tCeklW2e6_E

The Infinite Hotel, a thought experiment created by German mathematician Davi...

▶ Play video

#

the lesson is

#

dont play with infinity

deep mango Dec 27, 2021, 12:29 AM

#

Im having trouble understanding what the paradox is

#

Or

#

What's paradoxical about it

coarse grotto Dec 27, 2021, 12:37 AM

#

Ah yes, the TED-ed version of Hilbert’s Hotel, idk why they put paradox next to it
maybe to get more views bc paradoxes are whimsical

sly vale Dec 27, 2021, 1:01 AM

#

deep mango Im having trouble understanding what the paradox is

"paradox" as in the fact you can have both infinitely many rooms full yet still put more people in a room

#

since paradoxes are just "seemingly absurd statements that end up being true upon further inspection"

deep mango Dec 27, 2021, 1:01 AM

#

well, if i had all the even rooms full, i would have infinitely many rooms full but i could put someone in room 1

#

❓

sly vale Dec 27, 2021, 1:02 AM

#

To the layman it's a paradox sully

#

Worse "math paradox" is the interesting number paradox

cinder zephyr Dec 27, 2021, 1:07 AM

#

Nah

#

The worst "math paradox" is anything anyone tries to justify with Godel's stuff

stone valve Dec 27, 2021, 1:07 AM

#

does anyone know how to makee the DI tabel in latex?

cinder zephyr Dec 27, 2021, 1:08 AM

#

Like the whole "Math has a gaping hole" or whatever that video is

#

That's annoying

cinder zephyr Dec 27, 2021, 1:08 AM

#

stone valve does anyone know how to makee the DI tabel in latex?

The what?

stone valve Dec 27, 2021, 1:08 AM

#

DI table when u integrat by parts

cinder zephyr Dec 27, 2021, 1:08 AM

#

Oh

#

Any table thing should do

stone valve Dec 27, 2021, 1:08 AM

#

cinder zephyr Dec 27, 2021, 1:08 AM

#

https://www.tablesgenerator.com/

stone valve Dec 27, 2021, 1:08 AM

#

something lik this

cinder zephyr Dec 27, 2021, 1:08 AM

#

This makes life easier lol

stone valve Dec 27, 2021, 1:09 AM

#

ok

sly vale Dec 27, 2021, 1:09 AM

#

stone valve ok

https://www.overleaf.com/learn/latex/Tables

Tables

An online LaTeX editor that’s easy to use. No installation, real-time collaboration, version control, hundreds of LaTeX templates, and more.

sly vale Dec 27, 2021, 1:10 AM

#

cinder zephyr The worst "math paradox" is anything anyone tries to justify with Godel's stuff

🤨

#

Godel's stuff is perfectly fine

stone valve Dec 27, 2021, 1:10 AM

#

sly vale https://www.overleaf.com/learn/latex/Tables

yep ill have a look

cinder zephyr Dec 27, 2021, 1:10 AM

#

No I know

#

I'm talking like

hushed iron Dec 27, 2021, 1:10 AM

#

Veritasium's video was fine

cinder zephyr Dec 27, 2021, 1:10 AM

#

Pop math stuff

hushed iron Dec 27, 2021, 1:10 AM

#

Except his lies about Kronecker

sly vale Dec 27, 2021, 1:10 AM

#

That's completely different than "Godel's stuff"

cinder zephyr Dec 27, 2021, 1:10 AM

#

About how "Math will never be right" or some other shit I see

hushed iron Dec 27, 2021, 1:11 AM

#

Veritasium didn't claim this

#

You're making things up

cinder zephyr Dec 27, 2021, 1:11 AM

#

Right but people try to justify those "paradox's" with that video

sly vale Dec 27, 2021, 1:11 AM

#

Derek presented the history of it

cinder zephyr Dec 27, 2021, 1:11 AM

#

Veritasium's video is fine

hushed iron Dec 27, 2021, 1:11 AM

#

The highly redacted history

cinder zephyr Dec 27, 2021, 1:11 AM

#

People watching it draw the wrong conclusions

#

And that's the part that's annoying

#

I've had people tell me "why do u study math when this is a thing"

#

His video is fine I should have worded it better

sly vale Dec 27, 2021, 1:12 AM

#

Yeah you should have lol

#

Given you started with a completely different thing

brittle jay Dec 27, 2021, 4:06 AM

#

Hello,

#

I dont know if this is the right place to post this, but it is math related.

#

https://github.com/RylanYancey/temp-rusty-noise/issues/1

GitHub

Looking for help with improperly implemented FBM on Simplex Noise ·...

The Problem(s): Unsure how to implement a seed for Simplex Noise algorithm. Unsure how to increase octaves without flattening. Unsure how to make a more robust FBM implementation. References: https...

#

This is a question over Fractal Brownian Motion

#

I'm askingg specifically about section 2 of this post

#

It asks about how to reverse the effects of large amounts of Octaves, that is, the flattening that comes from it.

#

If anybody knows anything about how to solve this issue, I would be very thankful.

spring wyvern Dec 27, 2021, 4:41 AM

#

cinder zephyr Like the whole "Math has a gaping hole" or whatever that video is

imo veritasium kinda screwed up something

young wagon Dec 27, 2021, 9:03 AM

#

spring wyvern imo veritasium kinda screwed up something

Isn't he a physics major. He just thinks like a physicist

fading hull Dec 27, 2021, 10:49 AM

#

You know who else has a gaping hole?

woven grotto Dec 27, 2021, 1:15 PM

#

crystal stream are you trying to get integral representations of sums?

Yes. This is what I am trying to do.

#

Integral itself is a sum, but continues one, and it somehow follows how discrete sum works. If you try to apply integral and discrete sum to the same function you may see they kinda follow each other, and with some manipulations you can force integral to give same exact values as discrete sum do. So I trying to figure out some generalisation of this.

woven grotto Dec 27, 2021, 1:21 PM

#

woven grotto <@!305064722225692674> I am managed to get the same results again with x^2 func...

Here is an example of fine tuning that works for x^2

woven grotto Dec 27, 2021, 1:22 PM

#

woven grotto What I found so far: https://www.desmos.com/calculator/v0wo0orryu

You may see what I found out so far

crystal stream Dec 27, 2021, 1:34 PM

#

#

there's also another formula from ramanujan

woven grotto Dec 27, 2021, 2:40 PM

#

crystal stream

You are my saviour

crystal stream Dec 27, 2021, 4:01 PM

#

#

This one is nastier and doesn't let you pick bounds for the sum

woven grotto Dec 27, 2021, 4:07 PM

#

that's a shame that I am still very bad at complex numbers

woven grotto Dec 27, 2021, 4:07 PM

#

crystal stream

thanks

#

and this is really bad that desmos does not support complex numbers, nor 3d dimension drawing

#

I think I need to find a new tool for math visualisation

#

it's time to learn geogebra

livid gulch Dec 27, 2021, 7:27 PM

#

Let a, b positive real numbers. Given a rectangle with sides a and b, is there a way to fill it only by using squares not necessarily of the same size?

static loom Dec 27, 2021, 7:29 PM

#

my guess is yes if they're algebraic, no if they're not

#

and I suppose if they are both transcendental but can have it scaled out to be algebraic as a kind of corner case where the transcendental one technically has a solution

#

idk lol

hushed iron Dec 27, 2021, 7:30 PM

#

Finitely many squares?

livid gulch Dec 27, 2021, 7:31 PM

#

Yes

hushed iron Dec 27, 2021, 7:35 PM

#

I suspect 1xsqrt(2) can't be covered by squares

#

More generally 1xa for a irrational cannot

static loom Dec 27, 2021, 7:47 PM

#

you can kind of do a euclidean algorithm type reduction to look at equivalence classes of rectangles, for instance if you have a 5x13 rectangle you could make two 5x5 squares and cut them out to get a 5x3 rectangle. Generally speaking we could write the sides as a tuple (a,b) ~ (a,b-na) when b>na for positive integer n

#

additionally you have scaling (a,b) ~ (1, b/a)

#

but we don't have to cut a rectangle up into squares necessarily in this kind of way

#

but there might be a way to show that this is sufficient and other ways of cutting down rectangles doesn't matter

#

like suppose you have a rectangle cut into squares of varying sizes, then you can cut down the squares into a finer mesh of squares where they are all equal size, then on this grid recut it into the algorithm I describe, something like that

fair mural Dec 27, 2021, 7:54 PM

#

flonshed

bronze pelican Dec 27, 2021, 8:21 PM

#

Filling a rectangle with sides a and b using the greedy algorithm is basically performing the Euclidean algorithms on the pair (a,b) to get the gcd

#

The greedy algorithm is choosing the largest square that will fit in the rectangle

#

And if there's an ambiguity, always choose the square with the largest area that is most bottom and most left

#

The Euclidean algorithm/ greedy algorithm terminates in finitwly many steps when the side lengths are commensurable, that is the side lengths have ratio a/b which is rational

#

As Merosity said, if you have any partition of a rectangle into finitely many squares then you can get a finer partition consisting of equally sized squares, which shows that any such rectangle has side lengths which are commensurable

#

Partitioning a rectangle into squares is very much related to approximating real number by rationals

#

And continued fraction expansion

static loom Dec 27, 2021, 8:47 PM

#

bronze pelican As Merosity said, if you have any partition of a rectangle into finitely many sq...

I didn't actually say that

#

I only suggested it might be true

#

I don't have a proof for that

bronze pelican Dec 27, 2021, 8:49 PM

#

Now that I'm thinking about it, I don't know if it's true

static loom Dec 27, 2021, 8:50 PM

#

yeah, when cutting up a rectangle with irrational side lengths, it's possible that the squares you put with irrational side lengths to fill it up might end up not having some finer mesh of all smaller squares, the same problem with the gcd not terminating

late anchor Dec 27, 2021, 9:05 PM

#

Hey there. I sort of made up a problem for myself... here it is.

#

The computer makes up a natural number (with no limitations on its value). You can ask it about some number - and the computer will tell you if it's greater than its number, less, or equal

#

How fast can you get to the number made up by the computer?

sharp mulch Dec 27, 2021, 9:07 PM

#

~log_2N steps I would guess

late anchor Dec 27, 2021, 9:08 PM

#

I was trying to formalize "fast", and my best attempt so far is
Algorithm A is faster than algorithm B if for the worst case the function describing the growth of the number of iterations for A is at some point always lower than that of B

late anchor Dec 27, 2021, 9:08 PM

#

sharp mulch ~log_2N steps I would guess

Yeah, that's my best result so far too

sharp mulch Dec 27, 2021, 9:09 PM

#

Algorithm speed is using formalized with big O notation

#

And constants on the leading order terms if you're being fancy

late anchor Dec 27, 2021, 9:09 PM

#

There are faster ways to get the upper bound - e. g. by using towers or by squaring - but searching within lower/upper would still be log

late anchor Dec 27, 2021, 9:09 PM

#

sharp mulch Algorithm speed is using formalized with big O notation

That won't work in this case I'm afraid

wild lantern Dec 27, 2021, 9:10 PM

#

late anchor I was trying to formalize "fast", and my best attempt so far is Algorithm A is f...

Is big O not basically what you were already headed towards when you said this?

#

(Sans multiplicative constant or whatever)

simple raven Dec 27, 2021, 9:10 PM

#

late anchor I was trying to formalize "fast", and my best attempt so far is Algorithm A is f...

That's exactly how we compare algorithms in computer science ! With big O as said above

late anchor Dec 27, 2021, 9:10 PM

#

Well, maybe in naive understanding

#

But it's not exactly big O

simple raven Dec 27, 2021, 9:10 PM

#

But yeah you need some constants usually

wild lantern Dec 27, 2021, 9:11 PM

#

You probably would have wound up at big O after a while lol.

late anchor Dec 27, 2021, 9:11 PM

#

The thing is, it's infinite thing

#

Big O is described for finite cases

#

Now the "average" of naturals is not a finite number

#

For any finite number the prob that a random number is greater than that is 1

#

So Big O would be simply infinity

simple raven Dec 27, 2021, 9:12 PM

#

Well, your computer has a finite amount of memory so you have to bound your random number

late anchor Dec 27, 2021, 9:12 PM

#

That's why I was trying to formalize

late anchor Dec 27, 2021, 9:12 PM

#

simple raven Well, your computer has a finite amount of memory so you have to bound your rand...

It doesn't

wild lantern Dec 27, 2021, 9:12 PM

#

What do you mean by "finite/infinite things" here?

sharp mulch Dec 27, 2021, 9:12 PM

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It doesn't matter that the numbers can be large

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We're considering how the number of steps grows as the number grows

late anchor Dec 27, 2021, 9:12 PM

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The computer can make up any natural number and it's key in this problem

static loom Dec 27, 2021, 9:12 PM

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interesting thing to consider is there's no uniform probability distribution you can put on the natural numbers

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and so your algorithm will depend on this choice

late anchor Dec 27, 2021, 9:13 PM

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You can think of a non-uniform one 😉

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E. g. round of a sigmoid

wild lantern Dec 27, 2021, 9:13 PM

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late anchor The computer can make up *any* natural number and it's key in this problem

Why would that matter?

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Can't you compute big O of any function T from N to R?

static loom Dec 27, 2021, 9:14 PM

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the best strategy is to chop it so that you get the most information content

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for the probability distribution there's a number that you can look at which is at the halfway point

simple raven Dec 27, 2021, 9:15 PM

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Well, if your random number is N you can find an algorithm which find the number in O(log N) steps, so we could quantify a solution to the problem with this

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In algorithm analysis we always think like this, quantify the number of steps depending of the size of the entry, and the entry can be as big as we want

late anchor Dec 27, 2021, 9:17 PM

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wild lantern Why would that matter?

Actually maybe you folks are right...
I'm just not sure if Big O can cover this thing fully

static loom Dec 27, 2021, 9:18 PM

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I don't think big O is appropriate for this because this hypothetical computer has infinite memory

wild lantern Dec 27, 2021, 9:18 PM

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Well I don't know. I'm just asking because I don't fully understand your problem and it sounds interesting lol.

static loom Dec 27, 2021, 9:18 PM

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but instead of doing binary search on numbers, you're doing binary search based on the sets which split the probabilities

simple raven Dec 27, 2021, 9:18 PM

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Yes, but he choose a finite number

late anchor Dec 27, 2021, 9:19 PM

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static loom but instead of doing binary search on numbers, you're doing binary search based ...

Like for example?

simple raven Dec 27, 2021, 9:19 PM

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So we need to analyse how we find the number according to the size of the number

late anchor Dec 27, 2021, 9:19 PM

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To the value of the number itself actually*

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it's a matter of log10, but still 😛

static loom Dec 27, 2021, 9:20 PM

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for instance, there's a 51% chance the number is less than 192932 and a 49% the number is greater than or equal to 192932

late anchor Dec 27, 2021, 9:20 PM

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static loom for instance, there's a 51% chance the number is less than 192932 and a 49% the ...

There's no middle point though

static loom Dec 27, 2021, 9:20 PM

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you get approximately one bit of information asking this

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there is

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because of what I said earlier

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there's no uniform probability distribution on the naturals

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so you must be picking from a non uniform distribution

wild lantern Dec 27, 2021, 9:21 PM

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The amount of steps for the given number n will at least always be bounded above by f(x)=x right?

static loom Dec 27, 2021, 9:21 PM

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this has a median

late anchor Dec 27, 2021, 9:21 PM

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Can we even talk about distribution at this point?

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If we, say, play this game once

static loom Dec 27, 2021, 9:21 PM

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at a finite number

late anchor Dec 27, 2021, 9:21 PM

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And actually distribution won't help you

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We aren't talking about average case, but about worst one

wild lantern Dec 27, 2021, 9:22 PM

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Since you can simply ask whether the number is greater or less than 0 and iterate one at a time in whichever direction til you reach it?

late anchor Dec 27, 2021, 9:22 PM

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For average case I agree you'd need to know how the computer makes up that number - but we don't know its rules, and our algorithm should be optimal for the worst case

simple raven Dec 27, 2021, 9:22 PM

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late anchor it's a matter of log10, but still 😛

Depends of conventions ^^ you can look at how fast your algorithm is according to the value of the number, how the size of the number when we see it as a string of bits (so yeah it's just taking the log)

late anchor Dec 27, 2021, 9:23 PM

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wild lantern Since you can simply ask whether the number is greater or less than 0 and iterat...

Well, that's the baseline

wild lantern Dec 27, 2021, 9:23 PM

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I see thonk

late anchor Dec 27, 2021, 9:23 PM

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You still can do worse if you want 😛

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But yeah, that's the naive impl

wild lantern Dec 27, 2021, 9:24 PM

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Do it over NU{omega} and do a "normal" binary search that way kekw

late anchor Dec 27, 2021, 9:24 PM

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Finding a and 2a such that a < x < 2a and then do bin search between a and 2a would be the second "baseline"

simple raven Dec 27, 2021, 9:26 PM

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late anchor But yeah, that's the naive impl

That's O(N)
We can do O(log N) by comparing with 2^k as k grows, and then find it in [2^k, 2^{k+1}] by dividing by 2 the size of the intervals at each step
You get 2.O(log N)=O(log N) !

wild lantern Dec 27, 2021, 9:27 PM

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Interesting thonk

late anchor Dec 27, 2021, 9:27 PM

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That's exactly what I described in my previous message 😉

late anchor Dec 27, 2021, 9:27 PM

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late anchor Finding `a` and `2a` such that `a < x < 2a` and then do bin search between `a` a...

^

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I wonder if there's a better algorithm

simple raven Dec 27, 2021, 9:27 PM

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Are you sure that's the same to look at 2k vs 2^k ?

late anchor Dec 27, 2021, 9:27 PM

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Or how we can prove that there's no

late anchor Dec 27, 2021, 9:28 PM

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simple raven Are you sure that's the same to look at 2k vs 2^k ?

a = 2^k
2a = 2^(k + 1)

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Maybe I wasn't 100% clear, my bad then

sharp mulch Dec 27, 2021, 9:28 PM

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You might also want to ask in the CS server linked in network if you don't get a satisfactory answer here

simple raven Dec 27, 2021, 9:29 PM

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Oh ok, I thought a was a fixed number 😛

wild lantern Dec 27, 2021, 9:29 PM

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Can you do roughly the same trick with a faster growing function than b^x? For ex can you also do the same trick using k!?

late anchor Dec 27, 2021, 9:29 PM

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That's what I was thinking of

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You can use faster growing functions to find the upper bound

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However then the search between the lower and upper bound becomes harder?

simple raven Dec 27, 2021, 9:30 PM

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late anchor Or how we can prove that there's no

Maybe you can have a lower bound by looking at the best algorithm for searching in a fixed interval (once you have an upper bound for your number)

simple raven Dec 27, 2021, 9:31 PM

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late anchor However then the search between the lower and upper bound becomes harder?

Yeah it's harder but maybe it's not a problem if you have a really efficient algorithm for searching

late anchor Dec 27, 2021, 9:31 PM

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I think that searching in a fixed interval can't be faster than log2

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So if an algo uses lower - upper bound search, then we can probably easily prove that log2 is the answer.
But what if it does not?

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or am I actually wrong about my assumption?

simple raven Dec 27, 2021, 9:33 PM

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Yeah we could imagine an other algorithm which doesn't use bounding the number then searching, then I have no clue

late anchor Dec 27, 2021, 9:34 PM

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Yeah, same XD

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Alright... thanks for the convo, it's after midnight for me already... guess time to sleep

simple raven Dec 27, 2021, 9:35 PM

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Like picking random numbers or something

simple raven Dec 27, 2021, 9:35 PM

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late anchor Alright... thanks for the convo, it's after midnight for me already... guess tim...

Good night !

bronze pelican Dec 27, 2021, 11:20 PM

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Still thinking about a rectangle whose ratio of side lengths is not rational but can be tiled by squares

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Does such a rectangle exist?

sly vale Dec 27, 2021, 11:21 PM

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I'd think no..?

bronze pelican Dec 27, 2021, 11:21 PM

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Proof?

sly vale Dec 27, 2021, 11:21 PM

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Cause you'd require one of the side lengths to be irrational

bronze pelican Dec 27, 2021, 11:22 PM

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Why?

sly vale Dec 27, 2021, 11:22 PM

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How else do you get a/b to be irrational?

bronze pelican Dec 27, 2021, 11:22 PM

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Okay , but then why can't it be tiled by square s?

sly vale Dec 27, 2021, 11:23 PM

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oh wait

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yeah it'd be tilable

bronze pelican Dec 27, 2021, 11:23 PM

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Example?

sly vale Dec 27, 2021, 11:24 PM

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so if I take a rectangle 1 by sqrt(2), I make squares with side lengths of each decimal place of sqrt(2) then just fill in the rest with those squares I'd think?

static loom Dec 27, 2021, 11:24 PM

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finitely many squares

sly vale Dec 27, 2021, 11:24 PM

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Oh

static loom Dec 27, 2021, 11:26 PM

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maybe we can work backwards, start by arbitrarily putting squares together and show that the resulting rectangle has width/length always rational

bronze pelican Dec 27, 2021, 11:26 PM

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Yes I forgot to mention the finitely many tiles part

static loom Dec 27, 2021, 11:26 PM

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might be doable by an induction argument

sharp mulch Dec 27, 2021, 11:27 PM

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Finite sum of rationals is rational

static loom Dec 27, 2021, 11:29 PM

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that's not a false statement

bronze pelican Dec 27, 2021, 11:30 PM

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Why is this hard? I've been thinking about this for hours opencry

static loom Dec 27, 2021, 11:31 PM

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lol they joys of math

sly vale Dec 27, 2021, 11:31 PM

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sharp mulch Finite sum of rationals is rational

almost like Q is closed KEK

sharp mulch Dec 27, 2021, 11:32 PM

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giggle

dense belfry Dec 27, 2021, 11:36 PM

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sly vale almost like Q is closed <:KEK:586240877358350341>

this statement makes me uncomfortable

sly vale Dec 27, 2021, 11:36 PM

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not enough info to answer what 8-4 is

fair mural Dec 27, 2021, 11:37 PM

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banned

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#diff-geo-diff-top

bronze pelican Dec 27, 2021, 11:37 PM

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I gave u one

bronze pelican Dec 27, 2021, 11:37 PM

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bronze pelican Still thinking about a rectangle whose ratio of side lengths is not rational but...

This

fair mural Dec 27, 2021, 11:38 PM

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stop spewing nonsense

dense belfry Dec 27, 2021, 11:39 PM

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show that there is an algorithm that tells you whether a polyonomial in any finite number of variables with rational coefficients has a rational solution, or show that no such algorithm exists

fair mural Dec 27, 2021, 11:39 PM

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dense belfry show that there is an algorithm that tells you whether a polyonomial in any fini...

this sounds like the rational root theorem

dense belfry Dec 27, 2021, 11:39 PM

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that's for 1 variable

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this is hilberts 10th problem for Q

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KEK

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grad school or advanced undergrad usually

bronze pelican Dec 27, 2021, 11:42 PM

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Rational root test works for all polynomials of 1 variable regardless of degree

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Thats nice

dense belfry Dec 27, 2021, 11:42 PM

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anyway I was just trolling you with an open problem

ancient flame Dec 27, 2021, 11:43 PM

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#❓how-to-get-help

dense belfry Dec 27, 2021, 11:43 PM

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KEK

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I need to assign grades to my students today but a lot of them are actually going to fail

fair mural Dec 27, 2021, 11:44 PM

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liquid is a teacher?

dense belfry Dec 27, 2021, 11:44 PM

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yeah I teach

fair mural Dec 27, 2021, 11:44 PM

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lol

dense belfry Dec 27, 2021, 11:45 PM

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and now I have to give a bunch of F's out

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😢

fair mural Dec 27, 2021, 11:45 PM

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what’s the class on

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liquid is getting bombarded by questions

dense belfry Dec 27, 2021, 11:45 PM

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I taught 2 college classes, college algebra and basic probability and stats

static loom Dec 27, 2021, 11:45 PM

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I used to have trouble with remembering how the rational root test went until I learned newton polygons lol

fair mural Dec 27, 2021, 11:46 PM

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ok i’ve seen that a few times, what in the world is college algebra

static loom Dec 27, 2021, 11:46 PM

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but then I came up with a stupider trick that I should have learned a long time ago after that

dense belfry Dec 27, 2021, 11:46 PM

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its algebra for college students

static loom Dec 27, 2021, 11:46 PM

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just look at ax+b=0 and see that x=-b/a so you just think "oh yeah leading coeff divisors in denom, etc etc)

tall badge Dec 27, 2021, 11:47 PM

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they all joined at the same time. its a raid

fair mural Dec 27, 2021, 11:48 PM

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i was a bit suspicious of that at first

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but nothing seemed wrong so i ignored it

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it was quite weird that 3 new people came in chat all at the same time

static loom Dec 27, 2021, 11:49 PM

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lol

ancient flame Dec 27, 2021, 11:53 PM

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college algebra is like algebra 2 / precalc

dense belfry Dec 27, 2021, 11:55 PM

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no it's not

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it is like algebra 1

fair mural Dec 27, 2021, 11:57 PM

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flonshed

ancient flame Dec 28, 2021, 12:00 AM

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idk

bronze pelican Dec 28, 2021, 12:02 AM

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If you take the multiplicative inverse of sqrt2 and double it, you get sqrt2 back again

sharp mulch Dec 28, 2021, 12:03 AM

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Right

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2*1/sqrt(2)=sqrt(2)

bronze pelican Dec 28, 2021, 12:03 AM

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Sqrt2 is a fixed point of x\mapsto 2/x

sharp mulch Dec 28, 2021, 12:04 AM

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Right

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sqrt(3) is a fixed point of x -> 3/x

static loom Dec 28, 2021, 12:07 AM

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here's an approach I'm thinking about, but is sort of only looking at a special case when all the real numbers that appear are algebraic.

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take all the squares that appear and index them by their side lengths, then wlog we can say the width of the rectangle is 1 and the height is some real number r

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the sides are $s_i$ and now take two straight lines horizontal and vertical, then it cuts thorugh some squares of some side length some number of times, that gets us two equations

fathom swallowBOT Dec 28, 2021, 12:08 AM

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Merosity

static loom Dec 28, 2021, 12:09 AM

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the $f_i$ and $g_i$ are non negative integers $$1=\sum_{i=1}^n f_i s_i$$ $$r = \sum_{i=1}^n g_i s_i$$

fathom swallowBOT Dec 28, 2021, 12:09 AM

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Merosity

static loom Dec 28, 2021, 12:10 AM

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now we look at some automorphism of Q(r) that doesn't fix r and apply it

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$$1=\sum_{i=1}^n f_i \sigma(s_i)$$ $$\sigma(r)=\sum_{i=1}^n g_i \sigma(s_i)$$

fathom swallowBOT Dec 28, 2021, 12:10 AM

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Merosity

static loom Dec 28, 2021, 12:11 AM

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that's as far as I've gotten, seems like it'd be possible to break something this way, maybe take more lines and build up multiple more equations and looka t more automorphisms simultaneously to help that

bronze pelican Dec 28, 2021, 12:15 AM

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I'm imagining a horizontal line sweeping up across the rectangle

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This gives you a sequence of partitions of the width of the rectangle

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Where the parts are coming from the multiset of sidelengths of squares

static loom Dec 28, 2021, 12:17 AM

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yeah exactly, those are the equations I'm referring to

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might help to think of it as a matrix equation like $$F \begin{bmatrix}s_1 \ s_2 \ \vdots \ s_n \end{bmatrix} = \begin{bmatrix}r \r \ \vdots \r \ 1 \ 1 \\vdots \ 1 \end{bmatrix} $$

fathom swallowBOT Dec 28, 2021, 12:19 AM

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Merosity

static loom Dec 28, 2021, 12:20 AM

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s_i being all the distinct side lengths that can occur, then the F is the matrix of non negative integers of their frequencies that add up to either the real number r or 1

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because wlog we can pick one side to be 1 by scaling

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maybe some kind of matrix rank argument can be made idk

bronze pelican Dec 28, 2021, 12:22 AM

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fathom swallow **Merosity**

Or u can allow the s_i's to repeat and have F be a {0,1} matrix

static loom Dec 28, 2021, 12:23 AM

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you could, but I feel like that would be too isolating

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I don't know, whatever works

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in particular if we take F and augment with the vector of rs and 1s and do row operations, we still have rational number coefficients, which seems nice

bronze pelican Dec 28, 2021, 12:27 AM

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One thing to notice is that if you count the s_i's with multiplicity then the n-tuple (s_i) is a point on the n-sphere of radius r

static loom Dec 28, 2021, 12:29 AM

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hmm interesting, I guess the weird thing is n is not a constant now

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or I guess it can be a constant you just have lots of 0 components

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wait wait no that doesn't quite work

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cause even though the lengths match up, the areas won't match up

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wait I think I misunderstood but I understand now

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you want $s_1^2+...+s_n^2 = r*1$ so it's radius $\sqrt{r}$ though

fathom swallowBOT Dec 28, 2021, 12:32 AM

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Merosity

bronze pelican Dec 28, 2021, 12:33 AM

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Oh right

static loom Dec 28, 2021, 12:46 AM

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if we glue the ends together to make it a torus, does the problem get easier?

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suppose a rectangle is tilable iff a torus is with squares, does that open up some kind of elliptic curve memery lmao

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modularity theorem => ??? => you can tile ur square 😎

dense belfry Dec 28, 2021, 12:48 AM

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opencry

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okay I'm giving out 9 F's for my basic probability and stats class

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can we get an F in the chat

static loom Dec 28, 2021, 12:54 AM

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lol did they deserve it though

dense belfry Dec 28, 2021, 12:54 AM

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I mean from the pov of not doing work yeah

static loom Dec 28, 2021, 12:55 AM

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good enough for me lol

bronze pelican Dec 28, 2021, 1:03 AM

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I thought I was gonna fail complex analysis and then got a B

mortal igloo Dec 28, 2021, 1:16 AM

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9 out of how many students?

dense belfry Dec 28, 2021, 1:19 AM

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38

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To be fair they are remedial math students

bronze pelican Dec 28, 2021, 1:21 AM

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@static loom if the greedy algorithm terminates in finitely many steps, is it true that the side lengths are commensurable ?

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Yes I think this is true

static loom Dec 28, 2021, 1:23 AM

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yeah pretty sure because the steps are the euclidean algorithm, so you're computing the gcd

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in particular if we start with one side as a rational number, then we're getting a bunch of equations that relate things together through more integers and rational numbers with a finite number of operations

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kinda like I wrote earlier if we use (a,b) to be a symbol that is 1 if there is a solution and -1 if there is no solution, then we have a handful of properties like (a,b)=(b,a), (a,b)=(1,b/a), and especially: (a,b)=(a,b-na) for integer n such that b>=an which is part of our algorithm that should boil down in finitely many steps

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finitely many steps means eventually we end up with (1,1) (up to scaling) for a square

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so we can walk back up the finitely many subtractions we did to show a,b are also rational multiples of some real number, kind of like we do usually with the euclidean algorithm when getting solutions to bezout's eqn

bronze pelican Dec 28, 2021, 1:30 AM

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👍

main monolith Dec 28, 2021, 3:14 AM

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Question, is it true that as the collatz conjecture starting numbers get larger, generally speaking (not strictly, but generally), the sequence steps to hit 4, 2, 1 also increase?

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I've done a bit of playing on a calculator and while there are many exceptions, it seems fairly true.

cinder zephyr Dec 28, 2021, 4:02 AM

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I think it must but not in a meaningful way

vast surge Dec 28, 2021, 4:03 AM

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I mean, it's trivial to find a starting point of arbitrary length n to reach the 4,2,1 part in a Collatz conjecture sequence.

cinder zephyr Dec 28, 2021, 4:03 AM

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and also there is no general trend

vast surge Dec 28, 2021, 4:03 AM

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Just do 2^n and you get n steps

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I don't know if that quite answers your question, but at least to an extent, it's really just "when numbers are bigger you need to divide by 2 more to get to 4", or if you want something fancier-sounding, the logarithm is an increasing function.

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If the number of steps required tended to require significantly more than k*log(n) steps to reach 4,2,1 for appropriate choice of constant k that would be notable, but I've never heard about anything like that.

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That said I don't even know how you would define that rigorously, the collatz algorithm behaves very chaotically.

vast surge Dec 28, 2021, 4:10 AM

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main monolith Question, is it true that as the collatz conjecture starting numbers get larger,...

^

bronze pelican Dec 28, 2021, 4:41 AM

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@static loom i googled the rectangle problem. Don't click if you don't want to read a solution:
||https://math.stackexchange.com/questions/1010070/partition-rectangle-into-finite-number-of-squares||

Mathematics Stack Exchange

Partition rectangle into finite number of squares

For what positive real numbers $x,y$ can an $x\times y$ rectangle be partitioned into a finite number of squares?

When $\dfrac{x}{y}$ is a rational number, it is not hard to see that we can partit...

dense belfry Dec 28, 2021, 4:43 AM

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That's a nice proof

static loom Dec 28, 2021, 4:43 AM

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bronze pelican <@622029249053982720> i googled the rectangle problem. Don't click if you don't ...

fancy

dense belfry Dec 28, 2021, 4:44 AM

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Tbh this problem did make me think of the Dehn invariant talk I went to a while ago

spring wyvern Dec 28, 2021, 11:57 AM

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static loom fancy

merosity left the server??

gentle bay Dec 28, 2021, 12:13 PM

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He keeps doing that.

bronze pelican Dec 28, 2021, 12:20 PM

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He's a mere curiosity

gentle bay Dec 28, 2021, 12:37 PM

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Mhm?

spring wyvern Dec 28, 2021, 2:26 PM

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bronze pelican He's a mere curiosity

what's his monero address?

bronze pelican Dec 28, 2021, 2:27 PM

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whyare you asking me

spring wyvern Dec 28, 2021, 2:27 PM

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bc it was in his status and i forgot it and (i think you can still see his status)

bronze pelican Dec 28, 2021, 2:33 PM

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not my issue

bronze pelican Dec 28, 2021, 3:08 PM

#

https://youtu.be/NoRjwZomUK0

YouTube

Numberphile

Squared Squares - Numberphile

Featuring Dr James Grime.
More links & stuff in full description below ↓↓↓

Extra footage from this interview: https://youtu.be/I0peG_kRE-4
Blog post about the old photo: http://www.bradyharanblog.com/blog/the-squared-square

Check out http://www.squaring.net for loads of great info.

Objectivity: https://www.youtube.com/c/ObjectivityVideos

Jam...

▶ Play video

tiny marten Dec 28, 2021, 3:23 PM

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Squared squares

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Interesting

bronze pelican Dec 28, 2021, 3:24 PM

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Its really interesting to me that this simple condition of being tilable by squares forces rationality

tiny marten Dec 28, 2021, 3:24 PM

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Aww I lost my blue name!

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Not enough chatting I guess

bronze pelican Dec 28, 2021, 3:24 PM

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I wonder if similar rationality results hold in higher dimensions

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Like say you have a rectangular prism. And suppose you are able to partition the prism into finitely many cubes. Can you conclude a rationality result, such as tha ratio of the sidelengths of the prism are rational

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LolDongs if you missed it, yesterday we were talking about rectangles being partitioned into finitely many squares

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And how that forces the ratio of the sidelengths of the rectangle to be rational

tiny marten Dec 28, 2021, 3:48 PM

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Oh really?

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That's weird I wouldnt just immediately think something like that is true

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Or I guess it makes sense now that I think about it actually

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Yeah because they are squares it actually makes sense

rotund steppe Dec 28, 2021, 3:53 PM

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thank god my calc final was curved happy

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I barely knew how to apply uniform convergence LMFAO

deep mango Dec 28, 2021, 4:16 PM

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holoYay

ancient flame Dec 28, 2021, 4:43 PM

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wouldn't that be an analysis class

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or an analysis-based calc class

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idk

neat lintel Dec 28, 2021, 6:15 PM

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rotund steppe thank god my calc final was curved <:happy:908558103992225822>

what was the slope of that curve?

rotund steppe Dec 28, 2021, 6:16 PM

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No idea o.O it was based on how well you did relative to the class

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based on your standard deviation or w/e

analog salmon Dec 28, 2021, 7:16 PM

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is it true that a monotonically increasing function and a monotonically decreasing function intersect at most once 🤔

bronze pelican Dec 28, 2021, 7:18 PM

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I have a question. Say you are given a partition of a rectangle into finitely many squares. We know that the side lengths of the rectangle must have ratio which is a rational number. Can we conclude that the sidelengths of each of the squares are commensurable with the side lengths of the rectangle?

peak tide Dec 28, 2021, 7:47 PM

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analog salmon is it true that a monotonically increasing function and a monotonically decreasi...

Yes, if they are strictly monotone. To see it, note that if f is increasing and g is decreasing, then f-g is increasing, so it can't be zero at more than one point.

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If you don't mean strictly monotone, then f=g=0 is a simple counterexample.

real sigil Dec 28, 2021, 9:12 PM

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is it true that when combining ceil and floor function symbols you get the rounding symbol

#

?

bronze pelican Dec 28, 2021, 9:30 PM

#

TilingBySquares.pdf

📎 TilingBySquares.pdf

bronze pelican Dec 28, 2021, 9:31 PM

#

bronze pelican I have a question. Say you are given a partition of a rectangle into finitely ma...

The above pdf has a proof of this

#

#

Now we've learned that given any tiling of a rectangle by finitley many squares, we can always scale the whole configuration such that all the side length of every square is a natural number.

#

holoYay

humble storm Dec 28, 2021, 9:56 PM

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Fuck you guys

sharp mulch Dec 28, 2021, 9:56 PM

#

?

sly vale Dec 28, 2021, 9:58 PM

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You too 🥰

real sigil Dec 28, 2021, 9:59 PM

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xDDDD

mystic mountain Dec 28, 2021, 10:04 PM

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rude

fair mural Dec 28, 2021, 10:05 PM

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my feelings are hurt

real sigil Dec 28, 2021, 10:05 PM

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mystic mountain rude

wild lantern Dec 28, 2021, 10:05 PM

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humble storm Fuck you guys

kekw

fair mural Dec 28, 2021, 10:05 PM

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hi doot

wild lantern Dec 28, 2021, 10:05 PM

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Hello quantum

bright hill Dec 28, 2021, 11:26 PM

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bright hill For example

I have found it!

fair mural Dec 28, 2021, 11:26 PM

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@bright hill you remember how you somehow found that one anime yesterday right

bright hill Dec 28, 2021, 11:26 PM

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Yeah?

fair mural Dec 28, 2021, 11:27 PM

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https://tenor.com/view/sad-sad-anime-sad-anime-girl-thinking-anime-girl-gif-19553755

Tenor

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can you do the same to this

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i’m sure you just reverse image searched it

sly vale Dec 28, 2021, 11:27 PM

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Yeah, that's from One Piece

fair mural Dec 28, 2021, 11:27 PM

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but just in case

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oh nice

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thanks

sly vale Dec 28, 2021, 11:27 PM

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oh I was right??

bright hill Dec 28, 2021, 11:27 PM

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sly vale Yeah, that's from One Piece

No way

fair mural Dec 28, 2021, 11:27 PM

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don’t know

sly vale Dec 28, 2021, 11:27 PM

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I just guessed a random anime

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KEK

fair mural Dec 28, 2021, 11:27 PM

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mosh mean

bright hill Dec 28, 2021, 11:27 PM

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Lol

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One piece has waaay different art style

sly vale Dec 28, 2021, 11:28 PM

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catshrug

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all weebs for me

bright hill Dec 28, 2021, 11:31 PM

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fair mural Dec 28, 2021, 11:32 PM

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we have done it

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thanks

bright hill Dec 28, 2021, 11:33 PM

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It's nothing

fair mural Dec 28, 2021, 11:33 PM

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huh

bright hill Dec 28, 2021, 11:33 PM

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What?

bright hill Dec 28, 2021, 11:36 PM

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fair mural we have done it

I just used Google and searched by image

fair mural Dec 28, 2021, 11:36 PM

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oh lol

bright hill Dec 28, 2021, 11:36 PM

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And between the alternative images it gives you look for any keywords

rotund steppe Dec 29, 2021, 12:55 AM

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weebs catAngery

fair mural Dec 29, 2021, 12:56 AM

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anime pfp

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and username is neko

stone valve Dec 29, 2021, 2:33 AM

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the irony

fair mural Dec 29, 2021, 2:33 AM

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when you respond to someone almost instantly but they don’t respond to you at all sad

spring wyvern Dec 29, 2021, 2:40 AM

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hi
anybody know merosity's monero address?

frigid lark Dec 29, 2021, 2:48 AM

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new member. First some hours already saying "fuck you".

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🤔I cant tell if its someone who was banned previously here, but why not only allowing phone verified users.

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omg quantum has new avatar.

fair mural Dec 29, 2021, 2:52 AM

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that happens often

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me getting nitro has kinda ruined it though

rotund steppe Dec 29, 2021, 5:28 AM

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fair mural when you respond to someone almost instantly but they don’t respond to you at al...

sadcat

fair mural Dec 29, 2021, 5:29 AM

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once again i instantly respond sad

rotund steppe Dec 29, 2021, 5:29 AM

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i was reading a book sad

fair mural Dec 29, 2021, 5:29 AM

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understandable sad

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https://tenor.com/view/anime-bookworm-book-reading-eyeglasses-gif-17661630

Tenor

mint patio Dec 29, 2021, 7:13 AM

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Do y’all see any reason why a MVC class would be a prerequisite for single variable real analysis

toxic schooner Dec 29, 2021, 7:13 AM

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catThin4K

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wait MVC is a pre req for analysis?

mint patio Dec 29, 2021, 7:14 AM

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Because I’ve given up on self studying

toxic schooner Dec 29, 2021, 7:14 AM

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Oh class?

mint patio Dec 29, 2021, 7:14 AM

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I am so bad at it

toxic schooner Dec 29, 2021, 7:14 AM

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i dont see any apparent reason

fair mural Dec 29, 2021, 7:14 AM

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as someone that knows nothing about analysis

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i don’t see a reason for it

mint patio Dec 29, 2021, 7:14 AM

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hehe

toxic schooner Dec 29, 2021, 7:14 AM

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as someone who knows 3 chapters worth of an analysis text

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i see no reason either

mint patio Dec 29, 2021, 7:15 AM

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Right

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Cause like

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Ok so my school has an “advanced” MVC class

toxic schooner Dec 29, 2021, 7:15 AM

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hmmCat

mint patio Dec 29, 2021, 7:15 AM

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The standard MVC here is pretty dogshit to be honest

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Like it’s just a typical sophomore plug chug calc class

toxic schooner Dec 29, 2021, 7:16 AM

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catThin4K

mint patio Dec 29, 2021, 7:16 AM

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The “advanced” one is a lot more interesting and abstract, a lot deeper connection to linear algebra

toxic schooner Dec 29, 2021, 7:16 AM

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ah so like plugging given stuff into formulae and all that?

mint patio Dec 29, 2021, 7:16 AM

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And I want to take it

mint patio Dec 29, 2021, 7:16 AM

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toxic schooner ah so like plugging given stuff into formulae and all that?

Well like

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You took a standard gened calc 1, 2 class right

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It’s just like that but multivariable

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Idk how else to describe it

toxic schooner Dec 29, 2021, 7:17 AM

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Understood

mint patio Dec 29, 2021, 7:17 AM

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Yeah exactly

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So this one’s a lot more interesting

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And I want to take it this summer

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But the thing is it’s a prereq for the single variable real analysis 1 class

toxic schooner Dec 29, 2021, 7:18 AM

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thonk

mint patio Dec 29, 2021, 7:18 AM

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but I’m so excited for that and I don’t want to wait till next fucking fall to take it

fair mural Dec 29, 2021, 7:18 AM

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weird

toxic schooner Dec 29, 2021, 7:18 AM

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that doesnt seem to make much sense

mint patio Dec 29, 2021, 7:18 AM

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I agree

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Maybe it’s just bc the class is hard

toxic schooner Dec 29, 2021, 7:18 AM

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do they use apostol?

mint patio Dec 29, 2021, 7:18 AM

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It’s a weedout class I guess

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The analysis class does not

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It uses some random text I’ve never heard of

toxic schooner Dec 29, 2021, 7:18 AM

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catThin4K

mint patio Dec 29, 2021, 7:18 AM

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But idrc I have people here to explain and I am good at learning on my own

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Just not good at discipline

toxic schooner Dec 29, 2021, 7:19 AM

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coz like, apostol does do both single and multi variable analysis

mint patio Dec 29, 2021, 7:19 AM

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Which is why I can’t self study

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Yup so does this one

toxic schooner Dec 29, 2021, 7:19 AM

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a little less of the latter, but yeah

mint patio Dec 29, 2021, 7:19 AM

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The follow up class Analysis 2 does multivariable analysis

toxic schooner Dec 29, 2021, 7:19 AM

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mint patio But idrc I have people here to explain and I am good at learning on my own

😌

mint patio Dec 29, 2021, 7:19 AM

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And with an intro to Fourier series and some other cool stuff

toxic schooner Dec 29, 2021, 7:19 AM

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mint patio The follow up class Analysis 2 does multivariable analysis

I see catThin4K

toxic schooner Dec 29, 2021, 7:19 AM

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mint patio And with an intro to Fourier series and some other cool stuff

noice!

mint patio Dec 29, 2021, 7:20 AM

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Also covers basic stuff on measures which also interests me but I don’t think we get to any Lebesgue integration

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Anyways irrelevant

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My question was

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if I like just emailed one of the two profs for it

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and asked why

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would they mind

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or ask why and say would u waive it for me or let me do it as a corequisite this summer

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so I can take both at once

toxic schooner Dec 29, 2021, 7:20 AM

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That probably depends on who the profs are/what they are like

mint patio Dec 29, 2021, 7:21 AM

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I know one of them, I had him for my intro analysis class and he was chill

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He’s like a 30-40 year old Indian teenager fuckboy

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but in an adult’s body

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He looks like a surfer

toxic schooner Dec 29, 2021, 7:21 AM

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mint patio He’s like a 30-40 year old Indian teenager fuckboy

stare

mint patio Dec 29, 2021, 7:21 AM

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He’s cool

toxic schooner Dec 29, 2021, 7:21 AM

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amazing description lmao

mint patio Dec 29, 2021, 7:22 AM

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The other professor is his best friend and all I know about her is she’s Russian

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They teach like half of the upper division undergrad math classes

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💀

toxic schooner Dec 29, 2021, 7:22 AM

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so yeah try asking him ig,
most probably wont mind

toxic schooner Dec 29, 2021, 7:22 AM

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mint patio They teach like half of the upper division undergrad math classes

Damn

mint patio Dec 29, 2021, 7:22 AM

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Yuhhh if I remember maybe I’ll shoot my shot

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But uh we’re in winter break now so they probably won’t respond for a while yeah?

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sadge

toxic schooner Dec 29, 2021, 7:23 AM

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mint patio But uh we’re in winter break now so they probably won’t respond for a while yeah...

yeah
profs probably would like to chill

mint patio Dec 29, 2021, 7:23 AM

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I’m going to go read through the syllabi just to hype myself up

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can I dm sammy

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hehe

toxic schooner Dec 29, 2021, 7:23 AM

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sure

mint patio Dec 29, 2021, 7:41 AM

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how it started

#

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how it’s going

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toxic schooner Dec 29, 2021, 7:42 AM

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lmaoo

coarse grotto Dec 29, 2021, 7:44 AM

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uhhhh

fair mural Dec 29, 2021, 7:52 AM

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flonshed

gentle bay Dec 29, 2021, 7:53 AM

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mint patio

bleakkekw

bright hill Dec 29, 2021, 11:05 AM

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bright hill For example

Finally!

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I found the answer to 0.6.9

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And it only took 5 days

fair mural Dec 29, 2021, 11:06 AM

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i would have given up after 5 minutes

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that’s not a joke either

gentle bay Dec 29, 2021, 11:07 AM

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bright hill And it only took 5 days

stare

gentle bay Dec 29, 2021, 11:07 AM

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fair mural i would have given up after 5 minutes

Me too.

bright hill Dec 29, 2021, 11:08 AM

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Then how would you know you understood the material?

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If you don't do the exercises?

gentle bay Dec 29, 2021, 11:09 AM

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Skip it or directly see the solution.

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uhhhh

fair mural Dec 29, 2021, 11:09 AM

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obviously i do the exercises

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i’m just saying i probably wouldn’t spend a week on a single problem

gentle bay Dec 29, 2021, 11:10 AM

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fair mural obviously i do the exercises

Now I know why I suck at Mathematics.

bright hill Dec 29, 2021, 11:10 AM

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fair mural i’m just saying i probably wouldn’t spend a week on a single problem

Ofc

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I just have 2 or 3 that I juggle around until I solve them

fair mural Dec 29, 2021, 11:11 AM

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gentle bay Now I know why I suck at Mathematics.

if you only read how to do something but never use it, the chances of you remembering it are 0

gentle bay Dec 29, 2021, 11:12 AM

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It would be the biggest achievement in life if I spent that much time in a prolem.

gentle bay Dec 29, 2021, 11:12 AM

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fair mural if you only read how to do something but never use it, the chances of you rememb...

I am scared.