serious-discussion

[sharp lake]

Pretty

[pastel bolt]

Strang’s linear algebra and Stewart’s calculus are classic picks

I personally have learned the most calculus through doing Paul’s online notes and practicing a lot. If you get comfortable with calculus you can try to do some diff eq which let you apply a lot of calculus while applying methods and a lot of recognition.

Linear is just linear

[near vapor]

have any of you taken ap lang

[brittle socket]

Hana!

[quick beacon]

@crystal linden square roots of real numbers cannot be negative.

That being said, there is a concept of non-principal roots

[crystal linden]

look#help-29

[quick beacon]

Ah complex numbers

[crystal linden]

so complex numbers can be negative sq roots?

[quick beacon]

Not principal roots

Principal roots can only have arg (-pi/2, pi/2]

[crystal linden]

oh

[timid bronze]

i have

[bitter lance]

Does 1=0.9999...?

[agile fiber]

yes

[stable charm]

1 = -1/12. found it on youtube. no clue how they got there

[nimble moss]

yes

[strong gorge]

yes

[neat lintel]

yes

[small dust]

yes

[fresh comet]

yes

[pure hollow]

yes

[limber thunder]

yes https://www.youtube.com/watch?v=cPCLFtxpadE

[brisk pasture]

yes

[cobalt verge]

Türk var mı ?

[noble silo]

I am turk yes

8% turk blood

[neat lintel]

https://youtu.be/NyxjfIdKpwo?si=nl3R2MthW441lsDZ

eeee

[lament bramble]

русские есть?

[quasi parrot]

Would a dimension with shifting constants have a roadmap or just a shifting mirage?

[halcyon dune]

dsk

Ok

ok

[dense cairn]

Ok

[proud olive]

I forgot to mention this but there might be some people in #probability-statistics who could to teach you more about distributions, if you're curious, @lament bramble

[lament bramble]

oh

[wooden wasp]

Who knows what a bimodal distrubution is

[jagged forge]

a distribution with two peaks

[lusty jungle]

shrek and biden are the same ppl but one is in a costume

[timid bronze]

oh sorry for not responding to ur initial msg yes clau did

[neat lintel]

What’s y divided by y

[robust brook]

Any number divided by itself is 1

y can't be 0 though

[vast wraith]

i’ve been frequently craving and eating some salt by itself for some weeks now is this normal

[shrewd loom]

WHAT

[north topaz]

go to the doctor

maybe you're iron deficient

[vast wraith]

hmm

[north topaz]

oh wait not iron but

[vast wraith]

why do all my friends take one look at me and say “go to the doctor”

[surreal sapphire]

my gf eats like bouillon cubes

this isnt normal

but at least its not harmful if you drink enough water and dont have any health issues

[empty mirage]

!worms

[quasi jetty]

[empty mirage]

Yay

!ducks

[quasi jetty]

[empty mirage]

Yayyyyy

[neat lintel]

It is true that each area of ​​mathematics is so specialized that sometimes people from other areas sometimes don't understand each other?
I mean to the point that a major could be created just for that area, like engineers who are separated by area

and in the end you have to choose one to be good at

[cursive lantern]

i wish there were a way to learn math primarily through listening

it seems though that the only way to learn math is to read a textbook and practice the content

it would be cool if there were a way to learn math mainly through listening and thinking, that way i could do it while going for a walk

[jagged forge]

there is no free lunch sadly

though going for a walk and thinking is actually a good idea from time to time

provided that you've built up a good enough intuition to think about the things you've learned productively

but that requires doing the grunt work first

[cursive lantern]

oh well

my success is limited by the rate at which i learn new concepts

so i guess learning and health will stay separate until i can get a treadmill desk

[livid silo]

umm

guys

im new

and i need help with math

[true zinc]

!help

[quasi jetty]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[mild mountain]

#linear-algebra

[long matrix]

subaru

[vast wraith]

[vernal token]

Who wrote this?

[vast wraith]

gian-carlo rota

[true zinc]

which book/paper is this from

[vast wraith]

https://www.ams.org/notices/199701/comm-rota.pdf

[proud olive]

That would crush my soul if I figured this out

[gritty crater]

At least you can say that your paper is cited

[vast wraith]

rota’s writing fsr is full of rather too polarizing statements tbh, even if he claims these cited papers were completely irrelevant, i’m skeptical if they really were

[wooden silo]

very quick question: would it be somewhat accurate to say something like "since the utility function returns a continuous value, there is probability of measure zero that two actions have the exact same utility"

like is that how you use the term measure zero

using this for a philosophy essay 🙏

[sage mulch]

i dont think so. "measure zero" has a defined meaning in real analysis.. you could just say "there is zero probability" or "a probability of zero"

[wooden silo]

isn't measure theory like designed for probability

[versed agate]

are we postulating a utility function on something like R?

[wooden silo]

yes but that's not really the part I'm concerned with

I'll explain it more precisely in my essay because that sentence isn't necessarily rigorous atm

[sage mulch]

what i meant to say is, the definition of "measure zero" doesn't really make sense for a probability

[wooden silo]

tbh I think I'll just say probability of zero since that's less stuff I have to explain in the footnotes

[willow hazel]

Anyone have a favorite iPad notetaking app? Especially one that’s good for stem subjects

[hardy iron]

Goodnotes

Goodnotes 5

[willow hazel]

Ok that’s the one I’m considering so far

Or atleast good notes 6 I don’t think they let you download good notes 5🧐

[jagged forge]

measure zero and probability zero are in fact the same thing, since probability is a measure, but yea usually you just say probability zero

[jaunty ibex]

@jagged forge deltoid is doing probability again

Markov inequality mentioned

This is the only thing I comprehended

claps

For example

Wtf is Vysochanskij–Petunin inequality

[jagged forge]

oh yeah this is an important one to know

[jagged forge]

i actually have never heard of this one, seems useful tho

[jaunty ibex]

Seems like the sums has gotten worse

I personally won't be able to apprehend what the fuck deltoid is doing anymore

I'll stay with classic analytic number theory knowledge

I'm good

[jagged forge]

lol

[jaunty ibex]

Brunn–Minkowski theorem

Here's another one

[jagged forge]

bizarre

[jaunty ibex]

real

Also I found something very common

Szemerédi

This guy's name is everywhere

In whatever the fuck deltoid is reading

[jagged forge]

yea i’ve never heard of that either

[jaunty ibex]

Oh

OHHH

I think that makes sense

This guy's name pops up in additive combinatorics

[jagged forge]

i see

[jaunty ibex]

What does it mean when someone says the first moment in probability?

[jagged forge]

uh

no idea

[jaunty ibex]

[jagged forge]

well

do you mean like

“moment in probability”

[jaunty ibex]

yes

[jagged forge]

or just “first moment” in the context of probability

[jaunty ibex]

idk tbh

first moment method

[jagged forge]

idk what that is

but first moment would just be EV yeah

[jaunty ibex]

EV? E[X] ?

Expectation

?

[jagged forge]

yeah

[jaunty ibex]

hmm

[jagged forge]

expected value = EV

[jaunty ibex]

why do u call it first moment

that's weird

[jagged forge]

idk why they’re called moments but i heard it that way from physics

[jaunty ibex]

Second moment then is something variance related?

[jagged forge]

yeah so second central moment is variance

E[(X - EX)^2]

[jaunty ibex]

yea

[jagged forge]

central meaning taken about EX

[jaunty ibex]

If you let I(X) to be the indicator function (1 if the thing is in X and 0 otherwise) then what is E[I(X)]?

[jagged forge]

P(X)!

[jaunty ibex]

why

[jagged forge]

uh

i never thought about the reason it just seemed true to me

[jaunty ibex]

[jagged forge]

i mean if it’s 1 on X and 0 away from X

uh

[jaunty ibex]

well E[x] = sum x P(X=x) right

[jagged forge]

indeed

[jaunty ibex]

$E[X]= \sum x P(X=x)$

[fathom swallow]

vero

[jaunty ibex]

hmm

[jagged forge]

and so P(I_A = 1) is just P(A)

[jaunty ibex]

uhh what if you have several 1's in X

[jagged forge]

uhm

[jaunty ibex]

wait

If you have something like P(X=1) + P(X=1)

Do you just not overcount?

[jagged forge]

well you only count each x once

P(X = x) takes care of all the weighting for you

[jaunty ibex]

right

yeah makes sense

thanks

[jagged forge]

np

[north topaz]

craziest prof page I've ever seen

[peak tide]

"I will prepare for the test better next time" 🤣

[old oak]

They never do

[brittle socket]

Speaking from your experience as a student?

[old oak]

Oh yes

[brittle socket]

[icy locust]

My student!

[ornate canopy]

I can picture myself repeating I love Mathematics and then bursting into tears

[north topaz]

wow this blew up

[neon garnet]

that's adorable

[neat lintel]

A group of Arab mathematicians at The University of Jordan, led by Dr. Mamoun Ahmad Abu Hammad solved the Invariant subspace problem for Hilbert spaces .

#chill message

[tacit otter]

i have fft sound, do you want try ? https://www.desmos.com/calculator/glpcwdybrk

[quaint cipher]

ok just a rant, why are there always toxic people who say "shit read before commenting dumb stuff, shit".you haven't been helpful at all. You didn't even have the patience to read the questions others posted. They already was trying the best to figure out the problem. They didn't ask anything inappropriate or unnecessary.

[old oak]

Heck, same

[jagged forge]

shit read commenting dumb stuff shit
what does this even mean

[quaint cipher]

lol my typo sorry

[jagged forge]

shit read before commenting dumb stuff shit
uh

[old oak]

You've heard of shitposting, now it's time for shitreading

[jagged forge]

im going to assume the two "shit"s are redundant

anyway this is why i never comment anything and then crumple the one time i comment something and it ends up being wrong

[quaint cipher]

idk but they just keep saying this word, start and end their conversations with this word

[old oak]

At least it's not "X E"

[jagged forge]

sounds like it was not a productive conversation

[old oak]

Yeah, jokes aside, sorry to hear you've had such a bad experience :/

[quaint cipher]

I have not encountered such things here, but saw it somewhere else.. Here everyone is so nice and friendly

[jagged forge]

at least we can have some nice things

[old oak]

I'm not! I just don't use profanity very often.

[split roost]

Yo would space (like just empty void, without taking into account radiation and shut) feel warm to a human if we remove thet fact that you would die

Cus like there's nothing to take the heat emitted from your body

[jagged forge]

i misread this as "I use profanity very often" lol

[old oak]

No I fucking don't

[deep mango]

friendly? not to me

:(

[rocky shuttle]

ryc is not friendly, yes

[vocal vessel]

Screw you

[deep mango]

Oh, now you're getting friendly?

[vocal vessel]

lol

[jagged forge]

haven't done linear algebra in too long i swapped the indices when writing out (AA^T)_ij
though i blame my last book for using the opposite convention

[fathom swallow]

suremark

[gritty crater]

I assume not. Because heat is still transferred as radiation so your body is still losing temperature?

And electromagnetic radiation doesn't need a medium

[split roost]

Ohh I thought our heat was only transferred through like our atoms colliding with the air

[flint basin]

I'm friendly to you

[flint basin]

shit read commenting dumb stuff shit X E. X E.

[deep mango]

I can find at least 8 counterexamples

[flint basin]

No you can't. Maybe Ryx was mean to you, but Ryxie was never mean

[rocky shuttle]

ur mean

[proud olive]

You get what you fcng deserve!

[atomic helm]

∣A∪B∣=∣A∣+∣B∣−∣A∩B∣ can anyone prove this and provide ma solution step by step
full question: Suppose that for a finite set S, |S| denotes the number of elements of S,
and let A and B be finite sets. Show that
∣A∪B∣=∣A∣+∣B∣−∣A∩B∣

[jagged forge]

|A U B| = |A - B| + |B - A| + |A \cap B| by disjointness
|A| = |A - B| + |A \cap B| by disjointness
|B| = |B - A| + |A \cap B| similarly

then |A - B| = |A| - |A \cap B|
|B - A| = |B| - |A \cap B|

|A U B| = |A - B| + |B - A| + |A \cap B| = |A| - |A \cap B| + |B| - |A \cap B| + |A \cap B| = |A| + |B| - |A \cap B|

[fresh comet]

uhh, did you mean to post this in #「helpers-lounge」?

ah, you edited

[strong gorge]

love to hear it 🔥

can't wait for more

[fickle holly]

any recommended resources for receiving grad math tutoring online?

[strong gorge]

ah wonderful, mad respect for the process

sounds awesome and good luck with everything 💪

[rich rapids]

hi guys, i wanted to ask something. there is a applet in linux mint for corner bar that usually works like that 'desktop peek' right bottom corner in windows. i was able to modify it there such that when i scroll over that corner bar, it would scroll between the desktops. is there something similar that i can get for windows?

[rich rapids]

nevermind, i managed to write a hotkey script for that!

[foggy finch]

twitter was banned in brazil (where I live) I'm so fucking happy I feel liberated I feel smooth I feel joy

[hard arch]

Any tips for writing an abstract?

[jaunty ibex]

Common Brazilian W

I hope it gets banned in Canada

[shrewd moon]

Yo

[woven rapids]

heaven

[ocean harbor]

I hope this, tiktok, reddit and insta becomes banned too

[old oak]

Just ban all communication over the internet except email and possibly usenet.

[sage mulch]

let me relive the skype days

[maiden steeple]

hello

I come from discussion 1

[static loom]

reported

[maiden steeple]

uhh why

[weary verge]

@quick beacon imagine if they had asked "why you need to compare them under similar terms."

[quick beacon]

lol

[carmine topaz]

Loss of freedom and you are happy?

[vocal vessel]

lol American Alert

https://tenor.com/view/freedoms-internally-freedom-freedoms-eagle-america-gif-23711012

[foggy finch]

YES!!!!!

yeah dude brazil has laws yk freedom in abstraction doesn't mean anything

[deep mango]

Was that last dm too tmi for you then? I can't believe thats what went too far...

[limber thunder]

its a multinational corp blatantly ignoring a countrys laws and expecting no consequences for it lmao, the whole X thing aint about freedom

[slim prairie]

hi

[fresh comet]

hi!

[tropic mica]

hi

[fresh comet]

hi!

[tropic mica]

hi!

[cedar goblet]

Where do you learn math

[foggy finch]

internet

and books

I find on the internet

and videos

I find on the internet

and people

I find on the internet

[foggy finch]

hi

[foggy finch]

hi

[fresh comet]

where's my hi

[tropic mica]

hi

[foggy finch]

hi

[fresh comet]

[brittle socket]

where's my hi

(Free emotional damage)

[rocky shuttle]

https://tenor.com/view/eating-grass-mickey-mouse-funhouse-elds-deer-grazing-disney-junior-gif-25889847

there

[brittle socket]

blocked

very creative zan...

[rocky shuttle]

[brittle socket]

I will zan you to the abyss

[rocky shuttle]

not as creative as your usual puns

[brittle socket]

Yes

I am the king of creativity

[pastel bolt]

Books, uni, and online

[quick bramble]

<@&268886789983436800> help-1

[fresh comet]

oh what the heck

a mod ping

[gusty socket]

hey higher and lunatic3574

[fresh comet]

hi smay, lunatic

how're you all?

[gusty socket]

just took a walk with a friend, there was a frog and a guy playing trumpet and it was a really enjoyable time

[fresh comet]

I went on a walk about a week ago where a woman was playing some flute variant while walking herself

it was really cool

[raven plaza]

I was taking a dump in a mall toilet a few days ago and the bathroom music played Ravel

[deft sorrel]

discussy 2 with no cd

🤭🤭🤭🤭

[raven plaza]

Oops wrong discussy

[tawdry pecan]

no slowmode here lool

[verbal karma]

can we have slow mode here too?

I kinda like it now

[deft sorrel]

no stop

let’s all just move to discussy 2 and have a good night with the boys girls and theys 😌

[ocean harbor]

Why they're adding slowmode now

[deft sorrel]

2 MINUETS

OH NAH

I CANT SO IT

DO IT

[verbal karma]

5 minutes of slow mode. let's gooo

[deft sorrel]

yeah i’m moving here

frick this

crap

[visual breach]

Ok so this place does not have slowmode

@next schooner would you

[raven plaza]

But it's the wrong discussy

[solemn moat]

can I get into graduate school with literally zero research experience or extracurricular math experience

[deft sorrel]

LETS GO

[visual breach]

Ah I see, sorry

[limber thunder]

yes, people have

[deft sorrel]

EVERYONE MOVE TO DISCUSSY 2

LETS GOOO

RAIDDD

[solemn moat]

how rare is it

[limber thunder]

it's not at all weird to finish math undergrad with no publications

[visual breach]

I think you cannot have good publication in undergrad level

Unless like, you are secretly grad level like Tao

[strong gorge]

for most people yes that is true

[fresh comet]

I would be surprised if I had any publication at all by the end of my UG

math or otherwise

[static loom]

If you are a refugee from #discussion

turn back now

[verbal karma]

I mean, if you are pursuing graduate degree to learn how to do research, if you already know how to do a research, that would be weird, no? Sure having one is a plus but like, you are there to learn how to do research anyways

[deft sorrel]

i am indeed

[vivid halo]

Yes you just need good letters of recommendation

[haughty panther]

you can sometimes help the phds/profs if you are good and get mentioned in the paper

[lyric linden]

insanity

rat is a dictator

[visual breach]

Yeah true, but that seems rare as well

Also it depends on country and university, some just understand lack of UG research and take students based on grades.

[haughty panther]

i did that, though the paper didn't get accepted
trying again in grad i guess

[visual breach]

Damnn, the feeling..

[hardy iron]

Apparently there’s no slowmode here

[verbal karma]

we should have one here

[fresh comet]

@next schooner if you put it at 10s, then it hasn't taken effect yet

at least not for me

[next schooner]

slowmode is weird sometimes

[fresh comet]

hmm

I think I actually have to wait out the 30min

[next schooner]

no

[haughty panther]

just a rat

[next schooner]

i am answerable to the server owner

[ocean harbor]

It says 6h for me

Well 5 now

[next schooner]

wait seriously

[verbal karma]

if you just happened to message when the timer is large, then you will be timed out for that time

[haughty panther]

i think slowmode counts the delay that was there when the message was posted, not the current one

[verbal karma]

there is no refund in terms of the delay

[visual breach]

Are you becoming the server owner?

[fresh comet]

this is what I see on my alt

[next schooner]

interesting

[fresh comet]

alt has no img perms

[next schooner]

lemme fix this

[next schooner]

no

[fresh comet]

oh, this account is back to normal

let me check my alt

[next schooner]

server owner is @compact tartan and if you have complaints about my actions (or anyone on the senior mod staff) you can contact them directly

[neat lintel]

@next schooner I am trapped in discussy, I have 6 hours to send my next message, please help me

[deft sorrel]

I’m going to speak to your manager

[visual breach]

I see, I believe mniip will trust you and your actions

[neat lintel]

you banning philosophy was not nice, but I wouldn't complain about it

but please explain to me based on what rule you told me to stop talking about philosophy and muted me so it not get repeated

I always talk about philosophy there

[next schooner]

i instructed users in the channel to stop discussing the topic that was being discussed

you did not do this

philosophy is not "banned" in discussion, but sometimes individual discussions get out of hand or heated or any manner of unpleasantness and need to be terminated

[neat lintel]

I was the only one muted because of it, and I still don't understand why did you instruct them in the first place

I am not trying to argue or anything. I am good, I just want to understand.

[next schooner]

i made the judgement that that particular discussion had run its course, so terminated it

[next schooner]

you were not the only one muted because of it

[fresh comet]

I do believe more than one person was muted

oh, can I go back to posting a few art images now?

or is the chat still too fast for that?

[visual breach]

Maybe you can contact modmail for this instead?

[neat lintel]

Did you see that our discussion of the meaning of science and absolute truths would get out of hand or heated or any manner of unpleasantness and need to be terminated?

[neat lintel]

I don't want to make it official or make a complaint, I just want to understand what happened

[next schooner]

i saw that it had run its course, was going around in circles, and occupying the entire channel for a disproportionate amount of time

[visual breach]

Ah, sorry

[neat lintel]

oh I am sorry, I got the impression that I am the only one muted because I saw some of my partners in the discussion participating in the chat

[next schooner]

i only started muting people who continued after I had given the instruction to stop the discussion

you and some other users did, and were timed out

[neat lintel]

and how does break the server rules or the channel rules? meaningless talk I think doesn't break either of the rules

[wooden falcon]

rat is super based

[lyric linden]

it's just 6 hours lmao

[next schooner]

#info message and the subsequent comment

[neat lintel]

yea I respect that, I didn't see the instructions but that was an error in my end.

I am just wondering about the basis of stopping he discussion, not muting; I respect it, if someone broke a rule after a warning then what you did is justified and it is not the matter of concern of my question

I hope you understand that.

[next schooner]

i have the permissions and the mandate to make moderation decisions as and when they arise

if other moderators disagree with me, we discuss it and resolve it

if other individual users disagree with me, their can either message #〖modmail〗 or DM the server owner directly

[neat lintel]

even if these moderation decisions isn't strictly stated in the server rules or the channel rules?

Again, I am not trying to question your authority

[next schooner]

yes

any such decisions are subject to scrutiny by my colleagues and by the server owner

[lyric linden]

being a moderator must be hard lol

[next schooner]

i do not do hands-on moderation all too much these days

[neat lintel]

ok then, thanks for explaining and being patient with me

[lyric linden]

imagine having to explain your decisions when you can watch skibidi toilet 💔 /j

[next schooner]

i mostly work behind the scenes on the bot and other server stuff

[neat lintel]

about the bot, can I discuss a recommendation with you about the bot because I tried to dm modmail and got no reply?

[next schooner]

sometimes modmail gets very busy and individual messages from users get lost

what is your recommendation

[ocean harbor]

I lowkey hated this

cringe

[neat lintel]

it is a concept of idea that I am trying to do to replace #book-recommendations in its messy nature

and also have the good format of resources present in the physics server

it is a database built by community recommendation of books/papers/lectures/websites and any source for education

and the idea that I made it goes a little further than being just a library of organized resources, it recommends the best resource(s) for each subject based on community rating and based on individual preferences

and it can also makes self-studying plans because I can see that a lot of people here are struggling with self studying (I am one of them) and it makes roadmaps and subjects to study based on an importance system I made

I can show you a prototype of the bot I made in dms if you want

[next schooner]

The place to raise this is #1162503966056272023

[neat lintel]

yes this is what I was asking about in the mod mail, when will I be able to do a meta suggestions?

like I didn't test the bot as much and I don't have a large database yet. I just have bunch of code organized by ChatGPT

[lyric linden]

haters will hate 🗣️

[ocean harbor]

[weary verge]

@plain island can you check #help-24

[plain island]

sorted out (but just ping the Moderators role next time)

[weary verge]

Sure

[old oak]

Philosophy

[quaint cipher]

what's this notation

[raven plaza]

Probably |an - L| < ε

[quaint cipher]

if {xn} converges, then {f(xn)} converges?

[old oak]

If f is continuous then yes, in general not necessarily.

[quaint cipher]

why only if continuous?

[surreal sapphire]

its essentially the definition of continuous

[old oak]

Left f(x) be the integer part of x, and let x_n = 1+(-1)^n/n. The x_n converge to 1, but f(x_n) alternate between 0 and 1, so they don't converge.

[quaint cipher]

f(x_n) is 1+(-1)^x/x?

[old oak]

No, it's the integer part of 1+(-1)^n/n

I'm defining $x_n = 1+\frac{(-1)^n}{n}$. $f(x)$ is the integer part of $x$, so $f(x_n)$ is the integer part of $1+\frac{(-1)^n}{n}$, so if we want to write it entirely in symbols, we could write $f(x_n) = \left\lfloor 1+\frac{(-1)^n}{n}\right\rfloor$

[fathom swallow]

Outsider

[quaint cipher]

ooh sorry i misread

[storm sage]

You can write a thread there as soon as you have read #『meta-info-old』

[neat lintel]

thank you, I will

[gritty crater]

If your brain overheats, does it freeze? 😔

[neat lintel]

https://youtu.be/NyxjfIdKpwo?si=7Rm3w-GHanBcX9IE ipssee

[ocean harbor]

she dances like her mom

[neat lintel]

yesh sure she does 💀

[ocean harbor]

lmao

[neat lintel]

lol heheh

[sonic sentinel]

the idea that there are very general heuristics which being told improves your problem-solving is so weird

that's just like free mental ability?

why didn't we evolve that?

(im not talking about heuristics specific to math problem-solving btw

im talking about ideas like "think in reverse" or "sunk cost" have a wide range of applications and can be understood basically for free)

[sonic sentinel]

you don't even need to have these ideas explicitly programmed into your brain. being predisposed to quickly accept the heuristics sounds sufficient, you just need someone in your community to come up with the heuristic then you're set basically forever

[leaden skiff]

Well the sunk cost fallacy is itself a decent heuristic

I've heard of people who dropped out of college in their last year that regretted it

[sonic sentinel]

?

[leaden skiff]

The idea that if you've already invested effort in something, it's "worth more" because you're closer to the payoff

[sonic sentinel]

this is an invalid example of sunk-cost?

[leaden skiff]

Wdym

Like there are people for whom dropping out in their final year is the right decision and not doing so would have been sunk cost fallacy

But it's hard to be an objective judge

[sonic sentinel]

at least as long as people are making their decision to stay in college because there's a short cost to graduate (i.e. time in college until graduation), and not because they already spent some years in college

[sonic sentinel]

making a decision based on sunk cost is a fallacy because it uses incorrect reasoning. you can come to a correct conclusion, yes, but so can you with any other fallacy.

[leaden skiff]

Well it doesn't matter if it's incorrect reasoning if it's right more often than it's not.
Like I can't imagine it's easy to biologically program in reasoning like this

[sonic sentinel]

the sunk-cost fallacy is always wrong?

heuristics might have too specific of a word, maybe "widely useful ideas"?

[sonic sentinel]

i think you're misunderstanding the sunk-cost fallacy.
the dropouts you mentioned should only have cared about whether taking the rest of college is worth the graduation.
someone in this situation who goes "i only need to spend a year in college to graduate but i also don't care about how many years i've already spent" (doesn't use the sunk-cost fallacy!) is probably going to make the decision not to drop out.

[leaden skiff]

I mean some people think "it doesn't matter if it's only one more year, I can't handle it" and then later regret it and think that they could have pushed through

In a sense the reasoning is correct, it's just that their assumptions were wrong

[sonic sentinel]

semi-related but i wouldn't trust that kind of hindsight :P

[vale plover]

https://x.com/PublishersWkly/status/1831357570365497379

Publishers Weekly (@PublishersWkly) on X

BREAKING: The Internet Archive has lost its appeal in Hachette v. Internet Archive, the long-running, closely watched copyright case over the scanning and lending of print library books. Full story to follow.

Twitter · Sep 4, 2024, 3:44 PM

[sonic sentinel]

:(

that's so stupid

[vast wraith]

In later life, she belonged to the circle of the Tolstoyan pacifist publisher, C. W. Daniel; she chose the name The Crank for his magazine because, she said, 'a crank was a little thing that made revolutions

from the wikipedia page on Mary Everest Boole

[old oak]

So basically if we don't stop being mean to the people who have proven Collatz or argue that 0.999.... != 1, we'll be the first against the wall?

[vast wraith]

[prime thistle]

the thing is that

The sunk cost fallacy can be very easily misguided

With time based things it's easy to call it a fallacy when it's not

[vast wraith]

also damn how big is this server again? and how old? yet it seems she's never been mentioned here before, after a quick search

[old oak]

Another sad commentary on the struggle of female academics to be remembered.

(This is more black humor than snark, because I see that as a genuine problem)

Sort of made me think of this:

[vast wraith]

i finally realized why i have bad dreams

from Mary Boole's "Philosophy & Fun of Algebra"

[old oak]

You believe such fables?

[vast wraith]

yes

i see grandmother Cunning-Greed behind every other corner

eating kernels all by herself

on talking about "Boole's method" presumably, some sort of propositional logic by means of manipulating formal expressions,

The Boole method is a conveyance which will take you safely to wherever the Great Unknown directs you to go. Some people mistake it for the carpet in the Arabian Nights, which took whoever stepped on it wherever he or she wished to go–which is a quite different thing. The true Boole method depends essentially on making a right use of imaginary hypotheses. The magic carpet depends for its efficacy on making a wrong use of imaginary hypotheses.

most amusing language, though i'm a bit confused who this is written for

every now and then it also turns rather dramatically religious

like...

[burnt ledge]

WTF

ITS OVER

[solid snow]

What the hell lol

Was this written during a psychotic break

[old oak]

It was written in the early 20th century, so yeah, pretty much

[vale plover]

https://x.com/DiscordPreviews/status/1831066626411880866

Discord Previews (@DiscordPreviews) on X

Discord is lowering the free upload limit back to 10MB, citing operational and financial concerns. The previous free upload limit was 25MB.

Twitter · Sep 3, 2024, 8:27 PM

there goes my ability to post 10+ mb fumo pics...

[burnt ledge]

Billions are dying

[old oak]

Truly the end times are upon us

[neat lintel]

what the hell

why does he have an ear

[candid compass]

Okay, I have completed the geometric transformations unit. Now I just have to relearn how to do systems of equations word problems and I would have mastered all of Khan Academy's PreK-8 course.

[vale plover]

special soyjak variant

[plain kayak]

what book?

[empty mirage]

Basic money grubbery

[old oak]

Yes, but apparently successful

[safe stag]

德国如果。

[forest vale]

?

[neat lintel]

This server has done nothing but bring me down as a person. everyday i come in here and all you do is tear me down insult me hurt me with your words and do nothing but harm me emotionally physically mentally and I just can’t take it any longer this server is so abusive and toxic it’s crazy. no one even realizes how disgusting all of your behaviors are. every single time I talk or type or even do anything or interact with anyone in the server everybody just goes against me and gangs up on me like a pack of wolves and just attacks me and i didn’t do anything to deserve these attacks and these hurtful words. i literally just try to be nice to everybody but nobody ever wants to be in my shoes and nobody ever tries to sympathize with me and see where I’m coming from all of you just see me as the enemy and as the bad guy that’s trying to ruin the server or something when really I’m just trying to spread positivity. you guys act like I’m some kind of virus or disease, constantly casting me out so much, making me feel so left out and so alone in this server. it’s fucking driving me insane I feel mental and I feel like a weirdo just being around all of you because of how you treat me. at this point in time, I’ve given up on ever trying again and ever becoming any of your friends because I just know your feelings towards me clearly. i know all of you hate me and never want to be around me again or never have anything to do with me. it’s clear that you all think I’m a joke and that I’m stupid, idiotic and boring. it’s so mean because I literally don’t do anything to you guys but you guys always act like you hate me and it makes me feel so confused because I don’t know what I did to deserve it. I feel like I should just leave because clearly nobody wants to be around me and everyone would be happier if i left anyways so i’ll just go and i hope all of you find happiness in life and i’m sorry for all the troubles i’ve ever put any of you through. i give up. goodbye.

[hardy iron]

Nice copypasta

[neat lintel]

🤥

[tulip hull]

Holy camole

[vivid halo]

lol

[old oak]

I mean, that is all true.

[vast wraith]

i aint reading all that

[latent edge]

I think he is talking ahout motivic cohomology right?

nice

[old oak]

To be honest, this copypasta isn't that far off what we're genuinely seeing from cranks now and again

[neat lintel]

man... im glad im dead

[woeful trout]

You're formally invited to the dead gang

[ocean harbor]

This server isn't bad at all

We do

[tropic mica]

Sir this is a Starbucks

[lapis torrent]

By any chance, is there someone who knows domain and range that can identify which is the function based on a given scenario? I’m gonna use it for review because I got that question wrong 🙂

[ocean harbor]

#❓how-to-get-help

[dry fractal]

hi guys i'm new

[old oak]

Hi new, I'm Outsider

[dry fractal]

hi

nice to meet you

[neat lintel]

Hello Outsider and new

[rocky shuttle]

new Outsider for Bequi

[ember bay]

hi!! y'all wanna see something i made?

on desmos

https://www.desmos.com/calculator/2hgvikwrh3?lang=it

[strong gorge]

that is nice

[ember bay]

https://www.desmos.com/calculator/h3dydkhygx?lang=it fixed some things!!

[spice knot]

womp womp

[neat lintel]

com com

[calm lantern]

What if we make the radii to be in a geometric series?

[latent edge]

At least don't be mean to the guy who proves it eventually whether it is in your lifetime or afterwards

[unborn meteor]

yoo deltoid's back

[old oak]

I promise not to be mean to anyone who proves it after my lifetime

[vast wraith]

but will you hold to that promise? 🤨 only time can tell

[vast wraith]

i spent eight hours at uni today... in that time i managed to write down only a single line of (very easy) mathematics

[latent edge]

I spent a lot of time today at uni writing logs

[neat lintel]

i have best notes of simple mthematics

I have a disproof of collatz, I found a counterexample, unfortunately it is over 50 petabytes long so I can't upload it online

[vast wraith]

ok bro

[vast wraith]

Abel sent a paper on the unsolvability of the quintic equation to Carl Friedrich Gauss, who proceeded to discard without a glance what he believed to be the worthless work of a crank.

average Gauss moment

[old oak]

Come back georgecane, all is forgiven

[rocky shuttle]

https://github.com/Georgecane/cardano

[old oak]

Yeah, I know he's still in this server, albeit under a different username and not very active.

With the prime generation and RH solved, presumably he's quietly working on some other Millennium Prize Problem

[jagged forge]

oh dear

[true zinc]

Who? And what did they do

[old oak]

#math-discussion message

This is when he announced he had the best prime-number-generating function, a few days later he came back with a proof of RH

As evidenced, he deleted the georgecane account, he's still active on a different one which I won't divulge

He doesn't post much anyway

[true zinc]

What thr hell this is frankly hilarious

[old oak]

I agree! That's why it stuck in my memory

We get cranks fairly often, but not all of them are equally memorable

[noble pond]

Lmao

[foggy finch]

omg he has read 15 books a day he's so good omg

[sinful shell]

hello

should i study calc rn
Or codin?
Or prepare for uni

[karmic dock]

condin

[sinful shell]

what should i do afterthat

[sinful shell]

calc or prepare for uni 🤔

[karmic dock]

calc

[sinful shell]

i js plan stuff and never execute 🤧

[karmic dock]

ok

then play some video games

[sinful shell]

im too broke to buy a game

[karmic dock]

cs2

do you have steam?

[sinful shell]

thats why i was tryna make game to learn code

and get a job

[karmic dock]

you shouldnt make game

make game is too hard

[sinful shell]

so i could buy a game

thats the only way i could learn

[karmic dock]

ok

do you have steam?

[sinful shell]

i js reverse engineer old shit

[sinful shell]

its not available on mac

🤧

[karmic dock]

why do you have mac?

[sinful shell]

ofc

[sinful shell]

cuz its unix base os

[karmic dock]

wat

[sinful shell]

when there is a shell there is a way

[karmic dock]

ok

im in 9th grade

alg 2

I use mac

it sucks

I like to play cs2

not minecraft

[sinful shell]

bro there were soo many windows laptop to choose
but on mac theres like buy which one u could afford

so i bought a mac book

[karmic dock]

yes

[sinful shell]

now i cant game

[karmic dock]

that is bad

becasue game is helpful

[sinful shell]

i have an old computer tho i could try and play cs init

[karmic dock]

how old

[sinful shell]

but my gpu is dead

[karmic dock]

then how is it going to work?

[sinful shell]

that doest matter much now since my gpu is dead

[sinful shell]

i js put a cheap display card init

[karmic dock]

what version of macbook do yo have?

[sinful shell]

it also need a new ssd

[sinful shell]

monterey

[karmic dock]

no

version

like the m3

m2

the processor

[sinful shell]

oh

yeah no its old mac book

i bought it from a friend

to cod

[karmic dock]

ok

[sinful shell]

he kinda scammed me tho

[sinful shell]

why was u asking btw

[karmic dock]

I dont know

[sinful shell]

even if i had those i could still not game

[karmic dock]

you can

minecraft runs well

[sinful shell]

btw arm keeps winning on battery

[sinful shell]

i dont have money to buy minecraft 🤧

[karmic dock]

its only 30 dollar

you can just do like

[sinful shell]

:(_ _

[karmic dock]

the thingy

stock

[sinful shell]

what thingy 🤨

[karmic dock]

and in like 15 days

you will have enough

not even like serius

[sinful shell]

im not gonna do illegal stuff

[karmic dock]

how the hell is it illegal?

[sinful shell]

OHHH

[karmic dock]

stocks

[sinful shell]

what should i invest in

[karmic dock]

i dont know

[old oak]

Basically you brew a few gallons of stock every day and sell it

[karmic dock]

anyone that is really low

just buy it one time

then wait for it to rise then buy minecraft

thats what I did

[sinful shell]

no i thought u was asking me to get it from a third party store for free they guy who reverse engineered the thing yk

[karmic dock]

ohh

thats actually a good idea

[sinful shell]

damn we got an outsider 🤨

[karmic dock]

you can't vene do that bro

[sinful shell]

but its bad yk

[karmic dock]

because you open miencraft through mineccraft launcher

so you cant like open it

[sinful shell]

we need mojang to make more money dont we?

[karmic dock]

its not like windows

[sinful shell]

there r ways 😈

ways ppl dont know

but ever since i started making games i realised

how much effort it takes

[karmic dock]

can you let me test your game

[sinful shell]

to make em

my game?

[karmic dock]

yes

[sinful shell]

its not on web bro

[karmic dock]

no

[sinful shell]

..

[karmic dock]

is it unity?

[sinful shell]

like u want the executable?

[karmic dock]

obviously

post the game files on itch.io

[sinful shell]

i mean i kinda made my own 2d thingooo

did some vector stuff

[karmic dock]

wat do you mean?

[sinful shell]

everything basically from kinda scratch

[karmic dock]

what the hell is vector

[sinful shell]

just used a lib for blittting?

[sinful shell]

like i didnt use any game engine

like unity or gotod

to make it

[karmic dock]

I only know translation vector 💀

[sinful shell]

u dont know vector?

[karmic dock]

im 9th grade Algerba 2

[sinful shell]

https://www.britannica.com/science/vector-physics

why is this not embedding

[karmic dock]

im not reading all that

I will wait a few years

[sinful shell]

so like in a 2d world

ok

[karmic dock]

look

I did

19.5

[sinful shell]

what?

[karmic dock]

out of 20

on my first test

on year

[sinful shell]

in physices?

[karmic dock]

so I might be able to get

a all year

no

algebra 2

[sinful shell]

do u know co ordinates

x and y axis

[karmic dock]

geometry coordinates?

[sinful shell]

yeeah?

[karmic dock]

yes

[sinful shell]

so can u imagine ur computer screen having x and y axis

[karmic dock]

yes

[sinful shell]

so imagine u have a blank white screen and u draw a dot lets say
(x = 50, y = 89)

[karmic dock]

ok

[sinful shell]

and u want to move that dot by a pixel

[karmic dock]

ok

[sinful shell]

from x axis how would u do that

[karmic dock]

translate?

id

idk

[sinful shell]

i mean x = 50 right?

so u wanna move that dot from 50 to 51??

[karmic dock]

YEs

[sinful shell]

so what would u do to vector (x = 50, y = 89)

to move that dot by one pixel

[karmic dock]

vector is 1,0?

[sinful shell]

on the x acis

[karmic dock]

with like the vector sign?

component form

[sinful shell]

ig? idk what u mean by that vector is 1,0? tho?

[karmic dock]

LOOK

MAN

[sinful shell]

yes

im looking

[karmic dock]

THE SIGN

bro

[sinful shell]

what sign

[karmic dock]

you cant post pictures

its like

<

[sinful shell]

:(_ _

[karmic dock]

<1,0>

vector in component form

translation vector?

idk

I just finished geometry bro

[sinful shell]

i mean basically what u would wanna do is delete the vector (50, 89)
and draw the vector (51, 89)
on the screen to move it :)_ _

[karmic dock]

ok

I need to do enlgish

english

[sinful shell]

😭

[karmic dock]

lmk

when

you are done with game

[sinful shell]

💀

[karmic dock]

I need to play it

[sinful shell]

i dont think i could ever finish making a game 😔

[karmic dock]

what

bro please finish

[sinful shell]

like i dont really have an end goal yk whenever i see anything cool out there i wanna add it

[karmic dock]

I need to play it

[sinful shell]

i could like try to push an mvp out there

[sinful shell]

u play 2d stuff? 🤨

[karmic dock]

I play

games

idk 2d or 3d

[sinful shell]

i see 🙉

i hated school

:(_ _

[sinful shell]

higher

_ _

-#

-# |./

[prime thistle]

so high

[sinful shell]

bro i cant do the same thing in #discussion

sadly

😔

ppl keep texting

there

[karmic dock]

BRO

WHAT HTE FUCK

I GOT A 1.5/20 ON MY TEST

[sinful shell]

nice

[prime thistle]

nice

[sinful shell]

oh

i mean

damn

[prime thistle]

new pb?

[sinful shell]

well now everyones sayin it

so why not

[karmic dock]

yes

I got 1.5 th place on my test

[sinful shell]

is there a 0.1th place too?

[karmic dock]

probably

some people got 20th place so yeah

[sinful shell]

can many ppl have same sth place aswell?

[karmic dock]

yes

[wooden gazelle]

seeking advice:

should i accept an interview offer for a research position at a lab in my uni even if im not 100% interested in the subject? there's no guarantee ill get in of course, the induction process is very selective, but lots of very cool people work there, including people who do work in fields im actually really interested in, just not in that particular lab. if i do get in, itll obviously be a lot easier to network.

for some context im an undergraduate and id be working with mostly other undergrads and some masters/phd people under a particular prof. there arnt too many other labs like this here in my uni that accept undergrads without any research experience, and i might not get this opportunity again next year or next sem.

[karmic dock]

just play soem video games

[noble pond]

An opportunity is an opportunity, if you don't have any better options lined for this time period take it

[timid bronze]

girll…

[brittle socket]

Consider asking in #advanced-lounge instead. There may be a greater number of responses, which are likely to be helpful.

[neat lintel]

https://youtu.be/NyxjfIdKpwo?si=SQFDCbPJ-Ngv9ihj ool

[grave rapids]

okay, id like to borrow someone tomorrow, lets say from 11am AEST, to 6pm AEST, i have an exam on Tuesday, and the only way i can memorize the things i need to pass is to teach someone else, if you either have slight interest in surds, trig, and probability, or would like to learn about it, i probably need you, idk if this is how this place works but all my friends are busy and this is my last option, and im hoping it will work, sorry that this is all one sentence im not very god with grammar. and im also very sorry if the time i say changes idk what my parental guardian is planning for tomorrow, i just said a decently available time for me usually.

[solid yarrow]

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

[grave rapids]

very good idea i might, but the main reason i need a person is that i get side tracked easily (ADD( attention deficit disorder)) and a person at least will react so that ofcourse talking to someone would keep me on track for some reason

[open basin]

are you nsw

[grave rapids]

qld

[open basin]

y11?

[grave rapids]

10. math methods

[open basin]

lmao both guesses wrong

[grave rapids]

its okay

[grave rapids]

will you allow me to teach you? i need to go to bed in a bit

if so just dm me, i gtg now

[still yacht]

https://www.youtube.com/shorts/tJ6glE90U3U

[neat lintel]

i've transitioned to discussion 2

[vast wraith]

hi

[loud oxide]

Hey, I have a math theory set for average of distances from point to shape 3d with either planar straight line polygons or lines, what should I do with it? I have a website and would like to publish but like my site literally gets like 20 visitors a month. X E.

It could help with computer vision and graphics maybe. X E.

[tough island]

Anyway to get a grasp on calculus fairly quickly?

[limber thunder]

do a lot of exercises to get the derivation and integration "rules" and usual tricks down -- alongside that I think it's good to keep a visualization of each concept in mind, try 3b1b's Essence of Calculus series for that

[tough island]

Okay awesome appreciate the help and not just saying “you can’t”

[tough island]

Where do I go about “learning” it like should i watch YouTube videos or is there a quick book?

[solid snow]

remove the notion of “quick” from this

you’ll learn as fast as you’re able to if you do exercises and study the material consistently

[tough island]

I meant a short book, something that isn’t 3000 pages long but understood

[dawn zenith]

Hey guys I’m starting year 10 and I’m scared about gcse I have scored very good my whole life with getting 98% in year 9 but I have tried past papers and know it gets way harder

[verbal karma]

frankly speaking, most of calculus books are not 3000 pages long

[tough island]

sigh sarcasm

[verbal karma]

but like, in all seriousness, you don't read entire 1000 pages book to learn calculus either

the whole content is like... 400 pages? and the rest are exercises and some examples

[tough island]

I didn’t say you do 👍, gotta do exercises books are just nice to learn from in my case

[verbal karma]

might be even less

[tough island]

Yep

[verbal karma]

my point is, even the book seems thick, it does not necessary means it is that bad. It is meant for the semester long class after all

[tough island]

Okay

[verbal karma]

some even for the entire year or 2. so just put it on your pace

it is a bit hard to read short note for something you have not fully learned yet but https://tutorial.math.lamar.edu/ is a good starting point if you think your math is strong

[tough island]

Oh I love his notes

Used for algebra

[verbal karma]

Calculus note here is... good but you need to spend a bit of time trying to digest it

[marble river]

Could anyone help me with this please?

[lyric ivy]

Why is algebra so hard

[ocean harbor]

which algebra?

abstract algebra? sotrue

[fresh comet]

how's everyone doing today?

[vast wraith]

currently taking a break from my trying to sleep

[supple bridge]

Basic algebra is not hard once you learn the rules

[ocean harbor]

https://tenor.com/view/baby-scared-power-cute-stare-gif-16980488

[karmic dock]

https://tenor.com/view/stfu-gif-16877154335684082486

[ocean harbor]

no image perms laugh at this user

[bright hill]

Real

Doing the same rn

Hopefully you're asleep LMFAO

[shadow reef]

First thing that popped out my mouth is a picture of a guy who has a dog and is wearing a hat and hat and I am not sure how to feel but I am not a fan of his hat or his shirt so he looks so cool and he is very cool but he’s very cute so I’m just not sure if I can see the hat but it would look nice and if he was wearing that would look nice I don’t think that he is a bad man to have a picture

[shrewd moon]

To be a fully fledged mathematician, you can't have any thing distracting you, correct? Your attention must always centered on becoming a mathematical geek, not a geek per se, central to the stereotype, but instead your chance of living is determined by your understanding in language of mathematics.

[shadow flax]

New copy pasta?

[shrewd moon]

Well, up to you to decide that.

[light horizon]

Maybe don't spam things in multiple channels

[vivid halo]

this is extremely stupidly incorrect

[coarse bridge]

yes and in fact you do need to become a geek stereotypically as well

https://tenor.com/view/um-actually-nerd-nodding-um-actually-gif-18328531869583136293

if you dont look like this consider yourself cooked

[neat lintel]

i look like this

[next socket]

hey folks, quick survey: If you were searching for a math solver, which name would you click on when you see it? 1.MathOS
2.Mathmate
3.MathPlus
4.MathDog
5.MathSOS
6.Math911
7.Mathos

[rocky shuttle]

MathSolver

[neat lintel]

https://youtu.be/NyxjfIdKpwo?si=eo88hYoR8Uanbx4m sueush

[neat lintel]

something awesome with alpha in the name like all the best sites

[ionic star]

4 > 7

the rest sound useless

[safe stag]

ege

[neat lintel]

hey guys

i am a highschooler

[burnt ledge]

2 or 3 only

[neat lintel]

i wanna know

if equation of a space exists ?

i mean an equation that would represent an entire space

[old oak]

0=0, I suppose

[neat lintel]

yes

thats what i just learned

when learning equations of planes

[neat lintel]

nothing better ?

[old oak]

"Better" is subjective; especially if by "equation that would represent an entire space" you mean our 3D sd space

[dusky jasper]

any equation works so long as its true for every value of x,y (z, w, etc depending on how many dimensions you're working with), in other words your equation is a tautology
0 = 0 is trivially true, that's just the reflexive property
if you wanted it to involve the variables that span each axis you could write something like x + y + z = x + y + z but its very obvious how that will simplify to 0 = 0 (and really, any equation you try to write as an 'equation that represents an entire space' will simplify to 0 = 0)

i mean if you really wanted to argue it you could say that 0=0 is actually the best way to represent an entire space because its the simplest way of writing it lol

though i will say that the equation doesn't really describe anything about how many dimensions are in the space, if you thought that was important then you could add some stipulation of it being in like ℝ^2 or so

[neat lintel]

wdym by R^2

[dusky jasper]

thats just the notation that gets used when we are referring to something that exists in two dimensions
it would look like R^3 if it were in three dimensions, R^1 in one dimension, etc

[neat lintel]

hmm

thanks for your explaination

[vivid halo]

the best solution here is the "empty equation"

in general if you have a set of equations {F_1,...,F_n} then the set of simultaneous solutions to this set of equations is by definition the set of all x such that the equation F_i(x) is true for all i=1,...,n

but there is no reason you can't just take this set of equations to be empty

what does it mean to take the set of simultaneous solutions to this empty set of equations?

Well again it's just the set of all x such that F(x) is true for every equation F in the set

but the set is empty, so this is vacuously true

so the set of simultaneous solutions is just all x, the full space you're asking for

just as the empty set of equations works for this, so does any set of vacuously true equations like 0=0

but why make choices by adding equations like 0=0 if you can just take the minimal (empty) choice

by the way quantification over the empty set is a good think to contemplate in general, it's something that comes up surprisingly often and it's easy to stumble over if you haven't thought about "trivial" cases like this

for example, what is the determinant of a 0x0 matrix?

[neat lintel]

0 ?

[vivid halo]

:^)

it's 1 actually

good to think about why, it's very related to empty quantifications

[neat lintel]

but what would a 0x0 matrix mean

[vivid halo]

well, an nxn matrix represents a linear map from an n-dimensional vector space to an n-dimensional vector space

if n=0 this would be a linear map from the 0-dimensional vector space {0} to the 0-dimensional vector space {0}

there is only one such linear map, namely the identity map

the identity map always has determinant 1

an nicer way to say this is the determinant is the product of eigenvalues, but an empty product is always equal to 1 (can you see why?)

so again this is a funny case of empty quantification, in this case you're taking a product over an empty set

[neat lintel]

i understand the determinant being the product of eigenvalues

[neat lintel]

so you mean product over an empty set does not give me an empty set?

[vivid halo]

it does not!

(if you don't know words from category theory what I'm about to say will be annoying) it depends on what category you're working in, in general an empty product is the terminal object of the category, and an empty coproduct is the initial object of the category (assuming al these things exist)

so for sets an empty product is the 1-element set *, and the empty coproduct (disjoint union) is the empty set

[neat lintel]

no i am not familiar with category theory

[vivid halo]

right I included the example of sets for something concrete

I think my favorite reason for why empty products have to be 1 (or a terminal object more generally) is that products ought to behave nicely with respect to disjoint unions of the indexing sets

if you have a product indexed by a set I, and if you decompose the set I as a disjoint union I=I_1 (disjoint union) I_2, then you should always have like

$\prod_{i\in I}x_i=\Big(\prod_{i_1\in I_1}x_{i_1}\Big)\Big(\prod_{i_2\in I_2}x_{i_2}\Big)$

[fathom swallow]

nGroupoid

[vivid halo]

in other words you can always break up products as a product of (smaller) products

because like, of course you can

[neat lintel]

yes

that is true

[vivid halo]

now take either I_1 or I_2 to be the empty set

this implies the empty product has to be 1

[neat lintel]

yes

wonderful

[vivid halo]

by identical reasoning an empty sum is always 0, and so on

any "for all" quantification over an empty set is vacuously true, any "there exists" quantification over an empty set is vacuously false, etc etc

[neat lintel]

hmm

do you learn this in category theory ?

@vivid halo

[vivid halo]

yes this is very much covered in category theory

particularly when you learn about universal constructions like limits and colimits (of which products and coproducts are special cases)

[old oak]

Although you also learn this in set theory

[vivid halo]

yes this too, you just learn it a bit more generally later as well

but yeah as I mentioned category theory people have names for empty products and empty coproducts, these are terminal objects and initial objects respectively

these sorts of universal constructions are EVERYWHERE and one of the main benefits of learning some basic category theory is that you can think of these as instances of the same universal construction in different categories, instead of being like "woww I have learned the definition of product for the fifth time in abstract algebra for a different class of algebraic gadgets, but the definitions always look the same, how queer"

[neat lintel]

lmao

[raven plaza]

Categorical arguments are almost always nicer

[bright hill]

how queer (derogatory) or how queer (literary)?

[vivid halo]

oh definitely the latter lol

this isn't a thinly veiled quip about gender demographics in category theory

[bright hill]

@wooden falcon

[north topaz]

I hope your day goes by gaily today

[raven plaza]

Les Groupes de Barsotti-Tate

[bright hill]

https://tenor.com/view/annoyed-andrew-tate-confuse-puzzled-cobra-tate-gif-26870852

[brittle socket]

Hi 暗

[raven plaza]

黑暗

[lyric river]

Hii evreyone! I sent a suggestion message to ModMail asking for an Advanced Math channel for "Machine-Learning" or "Deep Learning" channel. I think it would be great to discuss such topics since they are based on heavy mathematical background as much as combinatorics, optimization, and modelling.

If you agree with me, it would be nice that more people request it to make it actually happen ❤️

[river moon]

most of the content in ML or DL isn't math oriented though

and the one that uses some math already has a dedicated channel, #optimization , #probability-statistics , #linear-algebra , #multivariable-calculus , #advanced-stats

[lyric river]

I mean... those are literally 6 different channels you mentioned for 1 single branch of mathematics and none of them covers Machine Learning or Deep Learning totally 😄 It is math-oriented as much as #optimization or #combinatorial-structures are math oriented, and I am not talking about a channel for applications of ML. I am talking about the mathematical structures behind the ML, DL, or NN because their content are mostly integrated to advanced math, not just computer science. Even CS people having a rough time because its seemingly so "out-of-context" advanced math content compared to CS.

[river moon]

I mean... those are literally 6 different channels you mentioned for 1 single branch of mathematics
no, it's a single topic whose math requirements are completely covered by 6 existing channels, so why create another one if it's a combination of existing 6

you effectively apply the results from these fields in a ML context and that's it

while the actual questions of ML are of the form "what's a good heuristic to process this kind of data" or "how do I tell if my model is good"

which aren't that mathematical in nature

[neon garnet]

i like ur pfp!!

[lyric river]

I don't believe that is a fair direction to discuss the point since many math topics, including some of those in "advanced math" here, are also made-up of different topics in math. Also it is not a discussion of "if ML is a distinct mathematical topics or not". I'm suggesting a channel to talk about a hot topic in Math in a single text channel with people studying and research on ML & DL.

[lyric river]

That is one interpretation you have I believe so, but there are other mathematical ways to investigate too. For example, there distinction of interpretations for other topics, like, mathematical nature in combinatorics is "to count things with different ways" while, in application, many people interested in only faster counting techniques.

So yeah many people interested its relation with data but the mathematical structures, Transformer architecture, Neural Networks, Gradient Methods, and Statistical Learning (in general) do have interesting mathematical features for people like me

By the way, if you believe that it is not necessary it's fine of course.

I just wanted to let people know that I made a suggestion and they can support me if they think as I think ❤️

Maybe the name "Statistical Learning" could be more appropriate since it is the actual mathematical topic that combine the usual ML ideas and Functional Analysis to make "Learning" heppen actually.

which one seems more appropriate to you is fine to me in case it is accepted 😄

[astral flicker]

Can somebody suggest a decent book on functions? Please 🙏🏻

[neat lintel]

kind of a broad request