serious-discussion

[sleek wing]

What

[tribal talon]

how do you tell you're moving in space if you have nothing to compare it to against?

[sleek wing]

What the hell are you talking about

[toxic schooner]

u cant tell then

[sleek wing]

0/0?

[toxic schooner]

[bright hill]

ok, so I get what you're saying

...

[toxic schooner]

ryc is a known troll

[bright hill]

I think

but we can't have 0/0 be any value we want whenever we want

[tribal talon]

I know but it should be 1

[bright hill]

so we just say it's undefined

[tribal talon]

because it follows a pattern

same as the factorial

[deep mango]

It follows my pattern too

[bright hill]

you could believe that

[tribal talon]

😉

[bright hill]

but it's not useful

[deep mango]

Factorial is because of analytic continuation

[bright hill]

it does more harm than good

[neat lintel]

0/0 is defined to be an element which is not in R

Denoted by ⊥

[sleek wing]

Did you just have a stroke when ryc posted this or what #serious-discussion message

[deep mango]

🖕

[tribal talon]

do you guys disagree wiith the idea that zero to the power of zero is 1?

[sleek wing]

Yes

[bright hill]

yes

[deep mango]

I do disagree with that

Some people think it's 1 though

But you cant do that in analysis

[sleek wing]

“People”

[neat lintel]

0 is a natural number

[deep mango]

Those people are your algebraist brethern

[sleek wing]

Shaking my head, time for a schism

[neat lintel]

Powers are defined for natural numbers so, 0^0 is defined as mumber of functions from the 0-element set to a 0-element set

Which is precisely 1

[deep mango]

Empty function

[neat lintel]

Even in analysis the point is to extend the operations!

To real numbers

So 0^0 naturally should be 1

[sleek wing]

What you can say is that the limit of x^x as x approaches 0 from +infinity is 1 cope more I guess???????

[deep mango]

But the extension is ill defined

[sleek wing]

0^0 looks like a bird looking up

[neat lintel]

Why

[deep mango]

In analysis you extend functions by continuity

[rocky shuttle]

Is it?!

[bright hill]

math is just a creative art anyways

[sleek wing]

,w plot x^x

[bright hill]

humans can do whatever tf they want

[fathom swallow]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Wew Lads Tbh#0864

[neat lintel]

You don't need continuity, there are weaker notions which are ok too

[deep mango]

(x, y) mapsto x^y is not uniformly continuous in neighborhoods of (0, 0)

[sleek wing]

0^0 = 1 has far more going for it than 0/0 but it’s still not well defined

[tribal talon]

this might be the stupidest idea, but why haven't people looked into an undefined plane similar to the imagery plane

[neat lintel]

Just define 0/0 to be the set of all real numbers

[bright hill]

[sleek wing]

Because the complex numbers are a well defined field extension of R

[neat lintel]

We define square roots in complex analysis as sets too

[sleek wing]

Not some nebulous dream

[neat lintel]

sqrt(z) = {w : w^2 = z}

[surreal sapphire]

what would looking into undefined things entail

i think you have to define things to think about them

[sleek wing]

^

[neat lintel]

Wheel theory

[rocky shuttle]

1/0 is a number such that 0 • 1/0 = 1 and there is no such number (when talking about fields and not wheels)

[sleek wing]

If I see the word wheel im

[tribal talon]

if you guys could define 0/0, what would you choose

[sleek wing]

To leave it as it is

[torn willow]

Is there some funny way you can modify a Deterministic Finite Automata to simulate a Pushdown Automata?

[sleek wing]

So we get all of calculus

[surreal sapphire]

no?

pushdown automata are more powerful are they not

[torn willow]

How do you prove you can't

[surreal sapphire]

they have memory of some form

and there is a proof that this makes them computationally more powerful

[neat lintel]

1/0 = empty set

Just think of dividing as a multifunction

[torn willow]

Well, There's the TM = 2 PDAs thing

https://cs.stackexchange.com/questions/2832/is-a-push-down-automaton-with-two-stacks-equivalent-to-a-turing-machine

[bright hill]

tf is wheel theory

[tribal talon]

what makes this wrong?

[neat lintel]

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

[bright hill]

cos 0/0=1

[deep mango]

1/0 is not 0

[tribal talon]

since when?

[torn willow]

I learnt that a DFA can be thought of as a "PDA where you can't pop"

[tribal talon]

ugh nvm I stuffed up

[surreal sapphire]

ok?

you need to be able to pop to access your memory

[torn willow]

So maybe you can maintain like 2 DFAs and do something?

[sleek wing]

Once you pop you just can’t stop

[surreal sapphire]

i dont know what this is supposed to mean, if you cant pop, pushing is worthless

[torn willow]

Add special alphabets that can pop maybe

Like free word construction from free monoids where you construct an inverse set

[surreal sapphire]

with two stacks its kinda obvious that you can simulate a TM

[torn willow]

Ok,True

[surreal sapphire]

bcs you can shuffle around the stacks to get to wtv item

DFA dont have any memory

[rocky shuttle]

$\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}$

[fathom swallow]

Zanarcane

[foggy raft]

you can’t divide by 0

[cyan goblet]

how do you pronounce psi

sai or puh-sai

[hushed turret]

sai

i don't know if that's "correct", but it sounds nicer.

[cyan goblet]

agreed

[deep mango]

I say sai but there's a little more mouthiness to the s than usual

[bright hill]

puh-sai

[bright hill]

well, you probably don't want/can't pronounce it the correct way anyways

imagine if gamma was pronounced ghama

[sleek wing]

this

[fast ivy]

Whitney and induct

[tender tulip]

hm.
if z = ra for some irrational r, then there doesn't exist an (m,n) element of Z^2\{0} such that am + zn = 0, thus there is a minimum nonzero element, meaning modular forms could take in values on the real line but only for irrational inputs

for x,y real, x/y irrational

what is the minimum |mx+ny| if (m,n) is an element of Z^2\{0}

[sacred arch]

server logo is torus moment

[leaden torrent]

fascinating

[odd narwhal]

Server logo is a coffis cup

[neat lintel]

Florida education just banned 54 math books

[dire mulch]

why?

[neat lintel]

That apparently have critical race theory

Nobody puts that in a math book

[dire mulch]

race theory?

[neat lintel]

Yea

[sleek wing]

....lol?

[dire mulch]

just looked it up, didn’t realize that was a thing.

[neat lintel]

Yea it became mainstream recently

[dire mulch]

Yeah I agree, I don’t see why that should be in a math book.

[neat lintel]

Apparently the board is going over social studies books next and I bet their wiping out 3/4 of all books

Poor math teachers

[leaden torrent]

this is entirely a political stunt

they dont actually care about the books, they just know voters want to see "republicans taking action against CRT in schools"

even if that's an absolutely stupid talking point that makes no sense

[alpine kindle]

crt?

[brave hollow]

critical race theory

[frozen merlin]

when they don't teach chinese remainder theorem 🙁

[alpine kindle]

is this just
anti racism?

[brave hollow]

yep

[alpine kindle]

i hate the usa

[fair mural]

lol

[brave hollow]

well critical race theory is also a usa thing so

[fair mural]

usa has things i don’t like = usa bad

[brave hollow]

what you should hate is probably the people that want these policies

[alpine kindle]

yeah

[autumn nymph]

Me2

[alpine kindle]

I don't hate everything in the usa

but overall i do

[delicate knoll]

I ve got sully

Noo

[fair mural]

black scholes hmm

wait no

that’s not black scholes

[delicate knoll]

what?

[deep mango]

That's the spherical form of laplace's equation I think

Idk

[sleek wing]

it is, ryc

[delicate knoll]

did you not get it?

My God

@sleek wing why do you sully me?

[light needle]

No one knows what ur memes are suppose to mean man

[sleek wing]

because it's just not funny

the second one was funnier than the first I'll give you that

at this rate is should only take 2 more iterations

[delicate knoll]

maybe their are too high level

super lol

sorry guys, i dont know how to make jokes

[sleek wing]

lemme show you how it's done

[fair mural]

[deep mango]

I thought the meme was funny

[delicate knoll]

here the templete

@sleek wing uses it

[deep mango]

Maybe Wew and John don't know much about PDEs?

[light needle]

True…. Ur right

I’m just not a pre guy sorry for insulting

[fair mural]

wew didn’t you plan on doing something with pdes at one point?

or am i remembering wrong

[light needle]

I never did research on the heat eqn for a yr In hs with a prof either

So I wouldn’t know anything about this

[delicate knoll]

really?

[deep mango]

Yes

[delicate knoll]

the first or the second?

[sleek wing]

ok thanks

[sleek wing]

fluid dynamics

[deep mango]

The second

[bronze pelican]

Wew is an expert memer

[deep mango]

This is pretty good I guess...

[brave hollow]

hits the gen z audience

[light needle]

Lol

[sleek wing]

I'm in one of those moods chat you have to bear with me

[deep mango]

the 219 + 10 thing is like

[light needle]

Seizure pls stop

[deep mango]

i feel like i'm going crazy

[light needle]

Delet

[sleek wing]

I really don't that's the sad part

and you're meant to feel like you're going crazy

that's the... joke?

[delicate knoll]

@sleek wing

[sleek wing]

wait a minuite

[sleek wing]

ok NOW you're getting it

I need to plot another PDE solution for my next pfp

[light needle]

Understanding wew is more like when grodd got ejected to space

[thorn brook]

lmao

[sleek wing]

I don't get the ref

[light needle]

The gorilla there is gorilla grodd

A dc villain

[thorn brook]

lol same I was lolling to the meme

[sleek wing]

I see

[light needle]

It’s from justice league the tv show

[deep mango]

woah

how did you know that?

did you have a little brother or something?

[light needle]

U know I’m a big dc nerd smh

I rewatch the series often

Cause it’s saur good

[deep mango]

[delicate knoll]

yeah he makes those strange faces

[sleek wing]

dc more ac more like acdc beow bow bow beow wow

[deep mango]

everyone knows i'm a shameless marvel fanboy

[light needle]

Also wow why not sister

[sleek wing]

whomever has not reacted to the first rectify this at once

[light needle]

Sexism within moderators

[sleek wing]

thanks ;)

[delicate knoll]

lol

[thorn brook]

understanding wew be like

[deep mango]

That was poor form of me and I apologize. Next time I'll own you more equitably

[light needle]

Indeed

[sleek wing]

pwn'd

[delicate knoll]

in one pitcure he is thinking, in another he is disturbed/perturbed

[sleek wing]

no I meant JohnDS's ref

[deep mango]

me when i'm forced to watch 5 seconds of a superhero movie ad

[light needle]

Oh well I guess spoiler but I described grodd last appearance in the dcau lol

[sleek wing]

ryc are you telling me you're not part of the #morbiussweep

[deep mango]

Idk who morbius is

is he the vampire

[sleek wing]

https://tenor.com/view/morbius-morbius-sweep-fries-venomverse-morbiusbeans-gif-23652959

[deep mango]

That's scary

[thorn brook]

sotue

[sleek wing]

https://cdn.discordapp.com/attachments/961920176062889994/962018715002622052/20220331_201707.jpg the movie did pretty well

[sleek wing]

ok last meme in discussion I promise (hahahahahha)
https://cdn.discordapp.com/attachments/546135409495769088/962679335964270622/IMG_1409.png

[thorn brook]

oh lol I didn't even know it was a movie, I thought it was just nonense

[sleek wing]

it was just nonsense

it literally did not have a second act

well

actually no

the first act was like 5 minuites and then the rest of the film was the 2nd act

[sleek wing]

[Noun] [Related Noun]

[delicate knoll]

...

[sleek wing]

now we're cooking with [REDACTED]

[delicate knoll]

pardon?

[fair mural]

[REDACTED]

[delicate knoll]

what it have to do with the meme

[brave hollow]

idk how you managed to not improve this meme a single bit in all this time

[rustic wraith]

https://cdn.discordapp.com/attachments/465969813769158666/777457652191723550/video0.mp4

[fair mural]

they do be triangles

[deep mango]

lol

[rustic wraith]

The trailer for school geometry looks pretty nice

[deep mango]

blo introduced me to lagtrain triangle one and that one is very good

[delicate knoll]

man, how says i have a degree on meme making hum?

here do it better

@terse flax show me you meme knowlegde!

[sleek wing]

Perhaps the problem lies in the antiquated concept of a “meme format”

Post-ironic schools of thought believe that memes should be more of a general allusion or a thematic element to a work rather than a rigid framework for structure

[fervent pebble]

i will post ironize ur mum

[sleek wing]

This guy gets it

[fervent pebble]

^^^

[delicate knoll]

@terse flax

[sleek wing]

Now we must subvert the genre

[brave hollow]

hahahaha

[fervent pebble]

wew r u drunk

[brave hollow]

fractal cauhgt up

because of me lmao

funniest thing about this meme

[sleek wing]

Put three of your previous memes as the captions

[sleek wing]

Quite the opposite

I am in the undrunk state of mind

[thorn brook]

I love how it's the same template all the time

[delicate knoll]

meme lession humm

[delicate knoll]

i could use the same tool for several jobs, lol

[sleek wing]

Hate it when the lighting of a room changes but it won’t tell you how

[swift sinew]

This is also slightly more in-line with the original definition of meme as a unit of culture

[delicate knoll]

what?

[sleek wing]

Put the memes. As the captions

[delicate knoll]

how could use this to make meme?

[torn willow]

Based JLU memes

[sick burrow]

I have made the terrible mistake of going on Twitter

Never again

[torn willow]

There are some good memes

Like how speedrunning is a exhibition of a new kind of radical left sexuality

https://youtu.be/Cegk0QYJu-M

[limber thunder]

https://www.youtube.com/watch?v=n__GJuqLb00

[toxic schooner]

i dont get this meme but its funny

[toxic schooner]

ludwig? based

[torn willow]

Well It's literally the same tweet

[limber thunder]

yes

it's just some channel that dubs viral tweets and memes as if they were Sonic cutscenes

[toxic schooner]

Ooo

i dont get what the tweet means either

i will see the ludwig vid for that ig

[limber thunder]

alt-right nonsense

[inner finch]

lmao

those tweets

i am adding

"in a petersonian sense"

to everything

[toxic schooner]

ah lmao

[inner finch]

in a petersonian sense

my balls fat

[torn willow]

In a petersonian sense,you are just insecure

In layman terms,you will never be balling

[inner finch]

lolol

[torn willow]

In a petersonian sense,You are fighting the hydra to reclaim the treasure that is yourself

I will let you ponder on the meaning of this life changing claim

And yes That's something Peterson would say. 1/14

[compact tartan]

"weebs" "fuckin weeb" "other weebs"

[delicate knoll]

What?

[sick burrow]

As Godel proved

[frigid lark]

@lime sorrel ..

[lime sorrel]

??

[frigid lark]

Can IPhone do this 😂

I can almost count the people.

[lime sorrel]

How come when you search for the best cellphone camera and sensors , you never get Huawei as a result from any expert

[frigid lark]

😔If you are using google in the first place you do sth wrong.

Huawei and Google have some problems... specially with the p40...

[brave hollow]

where are these photos from

[lime sorrel]

https://www.techradar.com/news/we-need-to-talk-about-samsung-galaxy-s22-ultra-zoom

Also it's not only about zoom

Sensor quality is not only zoom

Plus Huawei is literally banned from Google

Why buying it anyways, it's trash company and they deserve the ban.

[frigid lark]

The first pics are from near Cologne today. The other one is from Kirchheim towards Heidelberg. The towers are in HD.

😔For me the only important thing about an camera is the low light photo.

The zoom is just fun.

[brave hollow]

I swear I have seen a french village with the same church tower like the second picture

[frigid lark]

If there is absolutely no power

We had no electricity once so I took a pic. It was super dark...

The pic above is when you have some light sources. Bottom one is only moon light.

[lime sorrel]

I took this with my shitty cellphone

[frigid lark]

I like such buildings. I hope they have a organ.

[lime sorrel]

Of course

All churches in Italy have one almost

[fair mural]

this phone honestly looks like one of those portable battery supplies

[lime sorrel]

I recommend you to visit Florence

(if you can)

[frigid lark]

Holy

[vivid halo]

oh wow nice zoom

too bad Huawei is kinda out of the question

[thorn brook]

Wow this looks so cozy

[frigid lark]

Quite some pain to get the apks. There is even apps that are synchronized with Google Play... You can forget them.

So I have 2 phones sadly.

[sleek wing]

this is a dreamcore image

very nice photography lol

[deep mango]

these are gorgeous photos

[deep mango]

this is incredible

[hushed turret]

yeah i love that

[hybrid rune]

If I’m applying to math grad school, do the courses I take actually matter? I finished all the courses that are usually considered preparation for the QR exams and will taking like algebraic geometry or algebraic topology 2 strengthen my application?

[fresh oriole]

the courses you take matter

taking those and doing well in them sure couldn't hurt

[hybrid rune]

Yeah but if they dont help that much then id rather just self study them and take more stats and comp sci courses

[fresh oriole]

ah sure. Go after what interests you most

[deep mango]

If you're applying to math grad school it's probably wise to have those officially on your transcript, especially if you're interested in them.

Many people applying will have a good amount more than the minimum.

[hybrid rune]

Damn guess I’ll just stick with physics then

[loud iris]

rash

[primal seal]

If I have a system of equations as such:

[frozen venture]

How do you guys get intuition for abstract algebra?

[primal seal]

Consider e)

And the solution is presented as such:

[sleek wing]

stick em in a matrix

[primal seal]

Is it to indicate that the set of solutions forms a coset of the subspace generated by the span of the two vectors?

[brave hollow]

my neck hurts

[sleek wing]

that's what that set is, yes

[brave hollow]

there's no context tho, what book is this what was the question etc.

[sleek wing]

assuming your vector space is over R

[brave hollow]

nvm I thought they were talking about the circled answers

[primal seal]

It’s friedberg; I’m mostly curious why he isn’t writing the solution in the more standard way

[brave hollow]

which made no sense

[primal seal]

E.g., one solution vector with the components containing the “free” variables

I don’t know if he’s trying to make a point by writing them the way they are above or if he’s just strange

[sleek wing]

ok lemme

think

nah I'm not seeing any obvious linear dependence but I'll assume there is some

it's just expressing the solution space as an element of the quotient space very explicitly ig

[primal seal]

Ok so it is involving a coset

[sleek wing]

looks like it

[primal seal]

Interesting

Thank you!

So not only is the vector we’re investigating a member of the subspace (linear combinations) generated by the other vectors in the “columns” of the system; but the solution set of all such vectors is a coset- which in turn is an element of the vector space of the quotient

So in terms of this example, what does the quotient space represent?

[fresh oriole]

do many problems and learn many theorems

[frozen venture]

So far I've only had classes where I already had an intuition for the subject, like analysis

I've come to rely on using intuition to problem solve and don't know how else to do it

[fresh oriole]

fail to solve problems, get help and learn

[sleek wing]

step 1: what properties does the object you're working with have
step 2: which one of those properties might be useful to exploit for your problem
step 3: try it

[fresh oriole]

you could take the quotient of the space by the subspace consisting of those linear combos without (-4,3,0,0,5) added on

the points of that quotient space are all planes parallel to that subspace

[primal seal]

Ahh i see, so that point just selects which parallel plane were “on”

[fresh oriole]

yeah

[primal seal]

Jeez

He tried to pack all that in just by how he expressed a solution?

Lol

Guess it worked though

[sleek wing]

yeah this is what a coset of a quotient space is

[fresh oriole]

well, you don't really need to mention the quotient space in giving the solution

[sleek wing]

they're a series of spaces "parallel" to the kernel space

[fresh oriole]

and they didnt

[primal seal]

True, but maybe he’s just use to that way. For me it’s much easier to just write all the components’ dependencies in one vector

That’s why I thought maybe it was an attempt to make a point

Even in the text the solutions aren’t really laid out like that

[brave hollow]

after reading through that section

the question has contextr

which says solve using the method introduced in this section

[brave hollow]

which looks like the usual row reduction algorithm

[primal seal]

Yeah I noticed, snd that’s how I did; it’s just in the text he doesn’t have his final form expressed the same way

[brave hollow]

and he wants this, which I presume leads to solution ending up that way

[primal seal]

Yeah these are all steps to obtain the solution set

Which I understand

It’s just the way he expresses the solutions set in the solutions section

Doesn’t match the way he expressed them in the text or examples

I understand what he did, I just wanted to know if maybe there was a deeper reason for doing so than preference

Like if you look maybe a paragraph or so below the photo you sent

He finished an example of doing the same; but his final solution is simply expressed as a single solution vector, or explicitly as the linear combo of the other vectors with the discovered coefficients

[fresh oriole]

it displays the solutions as an affine plane

which is a nice way of seeing them

[primal seal]

Ok

That can be the end of that

[ancient flame]

who remembers this song https://youtu.be/rY-FJvRqK0E

[fair mural]

good song

[primal seal]

So there’s some discussion above about solutions of systems of equations and their structure. I looked into things some more and came up with some of these tentative findings:

• if a vector can be expressed as a linear combination of vectors of a subset S of the parent vector space, the solution set of coefficients has a parameter for each number of “extra” vectors in S over the dimension of the vector space; this appears to “scale” the vectors of the solution set accordingly confined to some line/plane/etc…
  -in Euclidean 2-space, for fixed S, vectors for which the difference of components is a fixed constant appear to have solution sets (i.e. be cosets) in the same quotient space

Are these theoretical concepts that eventually get covered? It feels like there’s something here

[fresh oriole]

I feel like it's something you kind of just eventually grok as you absorb more LA

I don't think it came up as a specific topic in my classes

though it may have when we were talking about systems of linear equations and their solutions

we barely talked about quotient spaces at all

[primal seal]

Thanks for you response. I see; just forcing myself to work from cover to cover- not sure if I’m making useful connections or trying to make some of the early material more exciting

[fresh oriole]

sure

which book are you using?

[primal seal]

Friedberg as the primary source but I have halmos on deck too

[fresh oriole]

I used friedberg too, good stuff

[primal seal]

I think you were right though

Some of the stuff I mentioned seems to be touched in ch3.3

Theorem 3.9 specifically looks like the coset idea

[fresh oriole]

oh, yeah

so it is

K_H is a subspace, {s} + K_H is a coset of that

[primal seal]

Yup

Good to know though; I’ve always wanted to work through a text like this, just never had the time

[ripe wasp]

kkb

[waxen lily]

ye

[worldly shadow]

Hi, do you think self studying math on a master level would be doable?

I don’t think I’ll have the funds to be in the city where my faculty will be

[calm frost]

does anybody here view textbooks or slides on ipad?

[surreal sapphire]

probably with enough free time (and maybe some basic education in math)

there are people who do math as a hobby

[worldly shadow]

Yeah i have bsc in math and full free time if I stay home so I guess ill be fine

[surreal sapphire]

ye, i think the hardest part is knowing how mathematics is "supposed to be learned"

with a bsc you should know this and a masters degree is a lot of self study anyway

dont expect to do research level stuff tho and ofc it will be hard to convince others of your knowledge

[neat lintel]

I mean, that's even hard to do in person undergrad 🤣

[lean moon]

I’m doing this right now with the same level of formal training as you. However, I’ve forgotten a lot of my undergrad level math so I’m rebuilding the foundations by reading textbooks, watching lectures, and going through the practices

The hardest part is not having a prof, or other peers, to help you with questions and intuition

I think the best way to supplement self study is to either find a study group or a general purpose tutor for the categories of math you’re studying. That’s what I’m looking to find now

[worldly shadow]

Actually, I never asked my professor, or my peers a question so far I think (maybe in my first years)

I just use internet or this discord for thay

That

Or i think longer

[lean moon]

That’s interesting! We used to do study groups for each assignment and we would go about explaining the process for our proofs. It was a lot of fun and made it collaborative

Also, going to see professors is a good way to get references for graduate level studies

[worldly shadow]

Yeah definitely I just don't like to force my actions

[charred mortar]

In my experience profs seem pretty happy to just talk about what math you're doing

your mileage may vary admittedly

[lucid berry]

Just used Fourier series to show that humming produces a sawtooth wave. I looked at my humming in an FFT graph and saw something like this:

The peaks lie on n*f with f the basis frequency and amplitude 1/n

This then gives this sum:

which is the Fourier series of a sawtooth

And here a test to show that indeed it is correct, the upper side are the lines from a sawtooth generator, and below is humming

[primal seal]

Interesting

[lucid berry]

First time i've used Fourier stuff for something real 😅

[primal seal]

If I recall correctly humming has all partials at 1/n amplitudes?

[lucid berry]

It does

Fascinating that our voice produces this nearly perfect mathematical pattern

Only in the really high overtones does it start to diverge

[primal seal]

So they produce the same timbre, but at different pitches (I.e. the first overtone varies)

[lucid berry]

What does timbre mean?

[primal seal]

Timbre means like texture of sound; ie sawtooth vs triangle waves

They can have the save fundamental but they “sound” different

Different spectra

[lucid berry]

Yes, humming and whisteling give different results for example

[primal seal]

Very cool

What work are you doing?

[lucid berry]

I look at whisteling with the same basis frequency, and the overtones were negligable

And with humming it produces a nearly perfect sawtooth

[primal seal]

So whistling is sine wave?

[lucid berry]

I'm a uni student doing engineering

[lucid berry]

Here is whisteling

You can see there is only one peak with (nearly) no overtones

[primal seal]

Yeah mostly one around 1k

Probably transforms to close to sine

[lucid berry]

Extremely close, I suspect the difference is that whistling doesn't use voice glands

[primal seal]

The red spectrum has a second hump though

[lucid berry]

And that voice glands and throat vibrates like a sawtooth

[lucid berry]

The red spectrum is a persistent type graph I think

[primal seal]

Yeah you could be right, whistling is more of a lip-driven action

[lucid berry]

Yep, I always find things like this satisfying

Getting an idea or suspicion, doing the math, and seeing a beautiful answer pop out

[primal seal]

Good stuff

You’re recording into a mic and using a spectrum analyzer?

[lucid berry]

Yes, using the spectroid app

and using maple math software for the fourier stuff

[primal seal]

Not bad for those results

If you had dedicated hardware/software it’d probably be even closer

[lucid berry]

Well, I didn't use the real data points to make the graph. I looked at the pattern and extrapolated a model

Then I checked with different basis frequencies, and humming always gets close

[primal seal]

Oh wow

Cool work 👍

[lucid berry]

Thanks

[dry yacht]

hey guys, i'm trying to calculate some gacha rates, is my calculation correct?
the probability of getting character A is 0.301% while the probability of getting character B is 0.069%
so the probability of getting A thrice and B once in 10 trials is
(9 choose 3) * 0.00301^3 * 0.99699^6 * 10 * 0.00069

[lime sorrel]

what about the money required

I don't have time to pull out my calculator, but that is pretty much 0%

[dry yacht]

yes i am aware but i just want to know if the method i am using is correct

[lime sorrel]

Are the events independent?

like A and B are not influenced by each other

[dry yacht]

yup

[fervent pebble]

guess who just got prescribed amphetamines 😎

hint

me

i did

i can't wait to see what i feel like 👀

[fair mural]

[lime sorrel]

Guess who just got prescribed heroin 😎

😎 not me

[bright hill]

you ok?

[fervent pebble]

yeah it's for adhd lmao

[bright hill]

oh

I was thinking something far more sinister

lol

ok now that sounds fun

[lime sorrel]

Did u know someone told me I actually have a weak ADHD too

But I don't take anything rn, although I probably should

[neat frost]

No I didn’t know

[neat frost]

I don’t know if everyone who has adhd takes or has to take something

[lime sorrel]

Its probably the reason I always do shit at math test lmao

Tbh I should go see my doctor because this year I studied a shit ton for math test and physics but never getting any decent result and I believe it might be because of things like adhd

[primal seal]

Here’s another from friedberg:

It’s interesting to note that a sufficient condition for the equality to hold is either subset being a subset of the other; however, it’s not a necessary condition of the equality

[swift sinew]

What you said sounds wrong. Two sets are equal if and only if both are subsets of the other - making it a necessary and sufficient condition.

[primal seal]

No, I was probably unclear because I used “subset” in two ways. I meant “…equality to hold is either S_1 or S_2 being a subset of the other”

[swift sinew]

Ah, neat indeed.

[primal seal]

Probably should’ve made it part of the problem

[fresh oriole]

that problem should be a fairly straightforward "follow your nose"

take $v \in \mbox{span}(S_1 \cap S_2)$

[fathom swallow]

ManifoldCuriosity

[fresh oriole]

consider what it means to be in the span of that intersection

and show v is in the intersection of spans

i.e. it's in span(S_1) and span(S_2)

[primal seal]

Yeah the problem wasn’t bad i just wanted to point out the interesting bit about the sufficient condition for equality not being a necessary consequence of it

Problem didn’t ask for it but just was messing investigating it a bit

[fresh oriole]

word

[primal seal]

Should S be restricted to nonempty subsets?

It would seem they forgot to mention that if you follow the convention that the span of the empty set is the zero subspace

[fresh oriole]

that is a convention, but it doesn't conflict here

if S is empty, you can't form the linear combo equaling 0

[modest rune]

Uh

It might conflict

[primal seal]

No

It does

[modest rune]

oh well

[primal seal]

It’s the zero subspace

[modest rune]

this happens all the time

i wouldnt worry about it

[primal seal]

Ah ok

[modest rune]

its good to know how to correct this stuff, but its nbd in practice

[fresh oriole]

oh I see the issue, the last sentence

you are right

[modest rune]

there are a few times this stuff matters but normally you can kind of brush this off

[primal seal]

Ok cool thanks

[primal seal]

Thanks

[karmic zealot]

oh i didn't realise that when i was doing that problem

that's neat

[waxen lily]

im not sure ur allowed here but i hope someone helps u

read #❓how-to-get-help

[karmic zealot]

did someone get banned

[neat lintel]

I think there was an 11 yo here

[marsh robin]

How could u tell? I didn’t see the message

[neat lintel]

Because he got banned

[karmic zealot]

because 11 year-old usually go around saying "hey i'm 11 btw"

i don't know why kids do it

[marsh robin]

Ah lol

[karmic zealot]

they always preface or conclude a message with i'm 13 btw or something like that

[neat lintel]

He wanted to look more helpless so someone helps him, I think

[marsh robin]

Very true

Smh

While simultaneously doxxing himself

[waxen lily]

when i was that young id always lie about my age

[karmic zealot]

me too

i'd make myself look older

[neat lintel]

Why though

When I was that young I didn't have a reason to lie

We didn't really use internet

I didn't have social media

[karmic zealot]

just to blend in i guess

yea i didn't have internet when i was that age

[surreal sapphire]

its funny when i was younger i pretended to be older on the internet bcs everyone was older and kids didnt really use the internet (that much) yet

[marsh robin]

100% it’s the smart thing to do. The benefits of the internet.

[surreal sapphire]

now im old 👵

[marsh robin]

Well “smart” idk

[karmic zealot]

how is it like being old

[surreal sapphire]

but also the average age of internet users went down a lot

[karmic zealot]

true

[surreal sapphire]

well, "internet"

most kids use the same 3-5 social media apps only

[marsh robin]

Well I mean every middle school gets Snapchat. It’s almost like a right of passage to the tween/teen years.

Most at least

[sleek wing]

Children online.... u hate to see it

[karmic zealot]

children anywhere you hate to see it

i'm only halfjoking

[surreal sapphire]

ye, everyone uses snapchat and instagram

i know some teachers and they had to get into this stuff during the pandemic

[sleek wing]

People still use Instagram?

[surreal sapphire]

because their students were unable to receive emails

and the only way to get a hold of them is via snapchat

[karmic zealot]

bruh

[sleek wing]

Freaky world

[karmic zealot]

don't you need an email to make said accounts

[surreal sapphire]

snapchat etc is also a really big social issue in school here

[sleek wing]

Don’t you have a school email?

[surreal sapphire]

its used for a lot of bad things

not in middle and highschools

[marsh robin]

I have never fully understood the point of it

[surreal sapphire]

i mean you generally want the parents to be reachable by email

but especially immigrants dont have this

and when the kids are like 13-14+, it might be better to reach them directly

but many dont have computers, only phones

and they dont really want to use email

and never check it

[marsh robin]

True, but just Snapchat as a social media. Like the point as a social media thing is just a little pointless to me.

[sleek wing]

the iphone and it’s consequences have been a disaster for the human race

[surreal sapphire]

so if you want to send them homework or remind them of something, its better to do snapchat

[shut anvil]

Do the people in this server consider philosophy of maths relevant to this server?

If so, can I please have some recommendations of things I should read about that?

[devout nacelle]

#book-recommendations might be a fine place to ask

There are no dedicated channels for philosophy of math but constructive discussion is welcome in any of the discussion channels

[shut anvil]

Noted! Thank you

[hushed turret]

lol wtf id be so creeped out if my teachers contacted me on snapchat

i mean maybe it's better than zero contact but that feels extremely inappropriate

[surreal sapphire]

oh well in this case its teacher trying to contact them via email, they dont respond

so they ask how they can stay in contact otherwise

and students suggest snapchat

[hushed turret]

that makes more sense but tbh i would have expected students to just say nothing and enjoy not being bothered

[surreal sapphire]

they have to go to school though

[swift sinew]

Well at the start of covid, one of my professors attempted to teach the class via snail mail. Albeit I don’t think he still works at the university but it was an earnest attempt.

[deep mango]

What the hell lmao

[neat lintel]

this sounds like an obscure reference to something

[ripe wasp]

💀

[surreal sapphire]

one of my profs published his home phone number so we can call him with problems

[neat lintel]

Not really, I can just stare at discord and ignore people I don’t like irl 🤔

[sleek wing]

yup hence a disaster

[frigid lark]

@surreal sapphire 9mg

Omg

Hab ne 2.3 geschafft in theoretische Krypto

Themen waren PRG, PRF, CPA CCA MAC fujisaki okamoto und nen komisches Beispiel

Ob man nicht CCA erreicht indem man Digitale Signatur um einen CPA sicheren PKE verwenden kann. Was falsch sein sollte

Srr for German.

[sleek wing]

Ich liebe Krypto !!! Alles mein Geld auf der Blockchain!!!!!

[neat frost]

You’re a disaster

[sleek wing]

disaster from "dis" and "aster" meaning "ill star"

I am not a sickly child, slurp

[neat frost]

No… you’re a sickly adult

[sleek wing]

s-s.... s-s-s..tt... stfffff STFU!!

[neat frost]

Sick sick man

[frigid lark]

😔Krypto nix gut tun fur Geldbeutel

Kauf Gold

[surreal sapphire]

interesting topic selection

you should invest all your money in crypto (me)

[bright hill]

based

[primal seal]

Thank you

[hushed turret]

did he get a lot of calls

[surreal sapphire]

i doubt it

[marsh robin]

True, but if you have to be 13 to be on the server it wouldn’t make sense to explicitly state you’re underage.

[leaden torrent]

it's almost like young children aren't always entirely rational on the internet

[marsh robin]

🤯

Idk. It’s pretty easy to lie or act older on the internet.

[pale orchid]

yeah, we do, since it's a public server

we have to follow the discord ToS

[bronze pelican]

Bro

There's an elliptic function called dn

[neat frost]

too... many... wews....

[fair mural]

dn theory perhaps

[neat frost]

oh im starting dn theory next semester!

with professor Joe Candice

[fair mural]

i don’t get the joke

[neat frost]

its not a joke...

[neat frost]

i donut believe my eyes

[fair mural]

dn um

[bronze pelican]

Lmao

But its literally called dn

The Jacobi elliptic function dn

[rocky shuttle]

And the ante meridiem function am

[light needle]

its a fancy theta i think

$\vartheta$

[fathom swallow]

JohnDS

[bronze pelican]

dn is periodic

Doubly periodic

dn is elliptic

19th century mathematicians were wild

I was reading the wiki page for lemniscate

[rocky shuttle]

The lemniscate constant: ∞

[bronze pelican]

No its transcendental

Like pi

Arithmeic-geometric mean is so weird

You start with 2 numbers, and take thir average and sqrt of product. Then you do the same thing with those two numbers. And you keep doing this to get two sequences. These two sequences converge to the same number, and its called the arithmetic-geometric mean of the two you started with.

The last formula of the above screenshot is saying if you form the arithmetic geometric mean of 1 and sqrt2, you get pi/lemniscate constant

[deep mango]

wtf

varpi

[fair mural]

does that constant pop up anywhere

or is it just a name for an absolutely random number

makes sense then

[bronze pelican]

It comes up when you study elliptic functions

Like special values of the weirstrauss p function

This is where I encountered it initially

[light needle]

oh wow

[bronze pelican]

Just like cyclotomic polynomials, you can consider lenmatomic polynomials, where you divide the lemniscate into n equal length pieces

Yes

I don't understand ur question

Yeah the roots of the n'th cyclotomic polynomial are the n'th primitive roots of unity

So nth roots which are not m'th roots for m<n

Compare

[alpine kindle]

@sleek wing your new album slaps

also i finally beat 8c

[sleek wing]

ty boss and the c in 8c stands for "cool"

[alpine kindle]

it is cool

[fair mural]

wew “pde” tbh

[alpine kindle]

if you don't try and hyper at the start

[sleek wing]

oh I fucking ultra at the start

[alpine kindle]

well you're in another league

[sleek wing]

I don't actually

well sometimes I do but I die immediately

[alpine kindle]

i have a habit of accidentally ultraing when i want to wavedash

[sleek wing]

are you sure lol

[alpine kindle]

when it's from air

yes

[sleek wing]

an ultra is a hyper/wavedash and then a downright+non-buffered jump

[alpine kindle]

i mean
the second part of an ultra

[sleek wing]

ah ok lol

anyway is that you done with the game?

[alpine kindle]

i mean

I'm playing custom maps

[sleek wing]

spring collab?

[alpine kindle]

but yeah I've finished the base game

[alpine kindle]

yeah

[sleek wing]

very good mod

[alpine kindle]

i might try some other maps

arphi's d-sides maybe

[sleek wing]

I might try the same map on repeat for another 150 hours

[alpine kindle]

farewell golden moment

[sleek wing]

yur

nearly gotten to the heart gate

i.e. the start of farewell lol

[alpine kindle]

wow

[alpine kindle]

remembered can be brutal ngl

[sleek wing]

remembered is awful

all the rooms are just slightly too hard to be free except rm-5 lol

[alpine kindle]

yeah

[sleek wing]

oh I'm also doing power source skip

probably doesn't help lol

[alpine kindle]

yeah

i managed to get it second try ever

[sleek wing]

I'm like

2/3rds consistent at it now

[alpine kindle]

I've become more consistent at jellyvators

[sleek wing]

there's a setup for the 2nd part of power source skip (the part I actually do) that means you don't have to jellyvator

just make sure you're facing towards whatever wall you're closest to when you throw and then regrab it after it bounces

[alpine kindle]

also today i watched the farewell and farewell superdash tases
they are amazing

[sleek wing]

the reason you usually have to jelly vator in general is that throwing jellies gives you a little boost sideways but if your far from the wall it doesn't matter

also yes they are incredible

superdash is art

[alpine kindle]

yep

the part i like the most is that both of them use the kevins in eh final room

which is very funny

[sleek wing]

it's mainly the last checkpoint of super dash that stands out to me

you just do not see madeline at all lmfao

[alpine kindle]

yeah

[sleek wing]

every frame is a screen transition

also speaking of power source skip brb

[alpine kindle]

you just get freezeframes

it's a slideshow

and then suddenly you're at the end of fwfw

[sleek wing]

cock

[fair mural]

[sleek wing]

and yeah it's so funny when they hit the badeline orb and you're like "oh. oh we're here apparently"

[alpine kindle]

it's amazing

also that was made before oil skip was discovered

[sleek wing]

oil skip
doesn't skip the oil

[alpine kindle]

i think that's what it's called

[fair mural]

what are the prerequisites to reading loring tus “an introduction to manifolds”? i know you need at least topology, real analysis, and LA, but what about multi variable analysis, or anything else?

[bronze pelican]

Multivariable analysis is essentially smooth manifolds

Different words for the same thing

[fair mural]

would smooth manifolds basically just be DG

[bronze pelican]

No

Smooth manifolds is a prereq for dg

Riemannian manifolds is dg

[fair mural]

well

the book i was talking about is called an intro to manifolds

so

i might have just gotten them confused honestly

but basically i just wanna know all the prerequisites for that book

[bronze pelican]

Yeah, try reading it and see if u can follow

[fair mural]

i don’t know analysis yet

or topology

[bronze pelican]

Oof

[swift sinew]

At least during my first attempt at it, it felt like you didn't need a lot of specifc prereqs, just fluency with math
The appendix on topology is a really nice onramp as well

[fair mural]

did you read that book alex?

[swift sinew]

I got through about the first half then other responsibilities took over

hence, > attempt
(aka, i have very little authority on the matter and am just here to provide a bit of anec-data)

[fair mural]

so, after i finish LA and real analysis, do you think i should just try it?

[fresh oriole]

you don't need much analysis at all

LA is a must

and basic topology

[fair mural]

you don’t need analysis…. for something that’s literally an extension of calculus?

[swift sinew]

I concur, but RA will definitely give you a bit more experience with handling that style of textbook

[fresh oriole]

you need multivariable calc

but you don't need much that a rigorous analysis course covers

[primal seal]

Is this a fair analogy?

[fresh oriole]

if you know what a topological space is and when a map from R^n to R^m is smooth, you're ready to know what a smooth manifold is

[primal seal]

Real analysis is to analysis what matrices are to linear algebra

[zenith forge]

no

[bronze pelican]

No

[zenith forge]

nomegalol

hey yamin

[bronze pelican]

Hi gabe

[zenith forge]

hello los angeles

[primal seal]

Ok i see

@zenith forge whatup bro

[bronze pelican]

Gabegabegabegabge

[fresh oriole]

Real analysis and analysis are the same thing

[zenith forge]

🤔

[primal seal]

I meant more as the general subject

Complex analysis, functional analysis, abstract analysis, harmonic analysis

[fresh oriole]

Ah

Well, complex analysis is its own thing. Functional analysis is LA + real analysis. Abstract analysis I've never heard of. Harmonic analysis is a subfield of real analysis

Roughly

[primal seal]

I see

[fresh oriole]

Harmonic analysis also overlaps with functional analysis

[deep mango]

I would say that real analysis is about continuous / differentiable / integrable functions on R / R^n, complex analysis is about differentiable functions on C / C^n, functional analysis is about vector spaces with a metric (a norm / an inner product), and harmonic analysis is about the Fourier transform and its extensions.

[fresh oriole]

But anyway, analytic type arguments aren't really used in Tu's book much

^ well said

[ancient flame]

harmonic anal ;)

[fresh oriole]

by analytic arguments I mean lots of reasoning with inequalities and limits

[bronze pelican]

Limits can be removed entirely from real analysis

[flat harbor]

reject limits, finite real analysis is the future

[ancient flame]

discrete real analysis

makes so much sense

only considers the real numbers with fractional part 0

[bronze pelican]

There's a limit free definition of derivative

[deep mango]

[flat harbor]

discorder challenge : make an original joke

[deep mango]

READ MY ABOUT ME!!!!

[ancient flame]

I have a mental discorder

WAIT YOU ADDED IT TOO LMAO

[flat harbor]

thank you ryc

[fervent pebble]

ryc is gay and also not into real anal

this tells me ryc is a top

👀

[flat harbor]

all the ppl desperate for low hanging fruit have already made the anal joke

[deep mango]

[flat harbor]

so they wont read ur abt me and join the mindless mob

[deep mango]

My favorite field of math is probably real analysis

whatever that means

[ancient flame]

my favorite is calculus

lol

ik im basic

[fervent pebble]

who said anything abt real analysis?

[modest rune]

My favorite is counting burritos

[ancient flame]

oh

that's too applied

[flat harbor]

my favourite field of math is quotient field on Z_p[x] :)

[fair mural]

[deep mango]

Which p??? which quotient field?!?

[fair mural]

blo what’s the joke i don’t get it

[fresh oriole]

the field Z_p(x)?

[flat harbor]

do ppl call it the fraction field

[flat harbor]

ye its this one

[deep mango]

Oh

yeah

"quotient field" makes me think you're quotienting Z_p[x] by a maximal ideal

[zenith forge]

i think it usually means field of fractions

[primal seal]

Anyone else go through mad amounts of chewing gum when doing math?

I must be averaging half a pack a day

[sick burrow]

do the perpendicular bisectors of a triangle always meet on a sphere?

[bronze pelican]

?

Triangle is 2d

Where's the sphere

Oh you mean spherical geometry?

[sick burrow]

yes

should have clarified

[bronze pelican]

I recall a proof of this

Involving reflections

BTW you are only asking about geodesic triangles, right?

[sick burrow]

triangles as take 3 points and take the lines joining them

[bronze pelican]

But there are many lines joining them

[sick burrow]

I don't know what a geodesic triangle is but I assume it's the same thing

[light needle]

geodesic is shortest path between two points

[bronze pelican]

The geodesics on the sphere are the great circles

[sick burrow]

right that's what I thought

[light needle]

cause u dont have "lines" on a sphere right

[bronze pelican]

Intersectthe sphere with a plane passing through the center. Thats a great circle. Any arc segment of that is a geodesic path

[sick burrow]

right right

yeah I just wasn't aware this was called a geodesic

[light needle]

now you are :)

[sick burrow]

anyways

the perpendicular bisectors do all meet at a point, right?

Found a proof

https://math.stackexchange.com/questions/834877/intersection-of-perpendicular-bisectors-of-a-spherical-triangle

[lost moon]

hi im looking for cs side projects does anyone have any ideas for math related cs projects or want to work together on one?

[sick burrow]

solve P=NP

[lost moon]

that is too hard

[limber thunder]

rendering fractals can be fun

you could e.g. learn some basic complex analysis, enough to understand and render a Mandelbrot set

[lost moon]

any other ideas? more like pure math

[wild lantern]

Ever fool around with computer graphics stuff?

Fundamentals of Computer Graphics has some cool stuff.

[waxen lily]

o hell ya

[ancient flame]

for anyone who has tutored, you will relate to this video a lot: https://youtu.be/2MjRk5q710k

[toxic schooner]

this video was nice

zach star is nice

[neat frost]

Hewwo shyshy

Good mornin

[toxic schooner]

hello slurp

good morning

[bright hill]

Slurp, were you still alive at 7am or did you sleep then wake up again?

[deep mango]

Slurp is an early bird

[neat frost]

I don’t understand the q
I woke up at 8 today (I had to wake up early cuz we went out)

[neat frost]

I’m neither early nor a bird. You are though

[static loom]

more worms 4 me

[deep mango]

Why are you uwu now

If you're going to have a silly name at least have it be a wew name

[bright hill]

[neat frost]

I’ve been for like a while now

[neat frost]

No. Why would I do that

I am more than just wew

Wew should be me tbh

[neat frost]

What have I told you about ing me, DarQ?

[deep mango]

Shuri is "wew uwu tbh" which is so silly

[neat frost]