serious-discussion

[light needle]

i always do the bottom thing

[atomic cypress]

Quick, post your favorite probability textbook and I'll rate your tastes

out of 10

[inner finch]

🧠

what to dooo

im looking for something interesting that's also accessible

but it's pretty hard to find

v cring

[atomic cypress]

Princeton Companion very accessible and interesting?

Or too accessible for you

[inner finch]

Idk isn't that like straight up an encyclopedia

[atomic cypress]

Not really, it reads nice

[inner finch]

tempt me not cringlord

okay one sec

[atomic cypress]

You can read Companion front to back like a bedtime book

[inner finch]

it's sin

[atomic cypress]

No hard math

[inner finch]

hm

[atomic cypress]

They only talk about hard math, they refuse to do any

[inner finch]

🧠

sounds cringe

[atomic cypress]

Excuse me, that's my entire profession

[nimble shuttle]

oh wait the princeton companion has good stuff

[inner finch]

[nimble shuttle]

I hereby revoke my sully

[inner finch]

🤡

[light needle]

so mizra what kind of prereqs are u comfy with

[inner finch]

Not even so sure

[light needle]

like algebra? analysis?

[inner finch]

I know a bare bit of analysis

Some algebra too

[bronze pelican]

[inner finch]

No

[light needle]

wanna read papa rudin

[inner finch]

[bronze pelican]

I remember when I thought Mirza was reading functional analysis textbook

[atomic cypress]

Which one is Papa, R&C or Func?

[inner finch]

rudin society

[light needle]

its umm applied in probability

so applkied math

real and comp

[inner finch]

🧠 🧠

[atomic cypress]

So what is Func? Grandpa Rudin?

[light needle]

yes

[bronze pelican]

No

[inner finch]

Dead rudin

catatonic rudin

[narrow rock]

[bronze pelican]

@inner finch who's the author of the linear Algebra book you were reading

[inner finch]

lax

[bronze pelican]

Yeah

Peter Lax has functional analysis book too

[inner finch]

u thought i was reading the function analysis bone

Yeah i know

[nimble shuttle]

estranged uncle rudin

[bronze pelican]

Yes

[light needle]

fun anal bone

[inner finch]

This is probably the 50th time ive said this on this server

but i really want to learn analysis

[bronze pelican]

[nimble shuttle]

crack addict brother rudin

[scenic narwhal]

Ultra is the most desperate person on the server????

[inner finch]

clearly

[bronze pelican]

Analysis is just epsilon and delta ,what else is there to learn

[inner finch]

Yes

I agree with this

[light needle]

if u wanna do papa rudin hmu, i need someone to read it with (like i have been reading other books, by streaming everyday)

[nimble shuttle]

@neat lintel

[inner finch]

i shud probably do the 1st rudin too for good measure

[light needle]

good measure

[bronze pelican]

John be reading a chapter a day of a random textbook every day

[light needle]

[nimble shuttle]

analoids will have you believe that real analysis teaches anything besides triangle inequality

[inner finch]

Yes

[bronze pelican]

For fkin 9 hours a day

[light needle]

i like diversifying yamin ok

[inner finch]

:yamin: moment

[light needle]

yes and i still wanna do more

[inner finch]

analoid.

[narrow rock]

arnold called analysts "inequality manipulators"

(prejorative)

[bronze pelican]

Bro logic is so cool

[light needle]

how far did u guys get

yall do compactness theorem meme?

[inner finch]

Yeah

[bronze pelican]

We got up to the statement of compactness theorem and an application

[atomic cypress]

People will write one epsilon and think they're an analyst

[light needle]

nice

[nimble shuttle]

yeah you need the delta too

[narrow rock]

are they not

[light needle]

ill try catching up

[inner finch]

analytical society

[light needle]

imagine using epsilons instead of saying "small ball"

[inner finch]

PDE

what is harmonic analysis

ive heard the name b4

[nimble shuttle]

dw it's only partial

so it's easier

[narrow rock]

music of spheres

[inner finch]

🧠

olrite probability it is then

[atomic cypress]

Yeah, harmonic analysis really is just the study of shitty integrals, you can't change my mind.

[light needle]

harm anal and furry anal

[inner finch]

I will need some measure theory though

[light needle]

most prob theory dont need u to know much measure theory

they introduce you to what you need

[nimble shuttle]

bottomos theory

[inner finch]

Isn't there that lurie lecture where he talks about fourier stuff as a consequence of cat theory

🧠

just learn the requisite cat theory bro

[narrow rock]

not a consequence

[inner finch]

idk im not a nerd who watched the vid

[atomic cypress]

Which is a mistake, they should just take real analysis as an assumption for prob theory.

[nimble shuttle]

hsct worried about the wrong kind of "consequence" go to detention

[atomic cypress]

It wastes so much time redoing measure theory except on a space of measure 1.

[narrow rock]

why skip measure theory tho

it is gross

but conceptually interesting

[light needle]

I mean probability theory is kind of a hook to learn measure theory

[atomic cypress]

ur gross but conceptually interesting

measure theory is the best qualifiers topic

abstract algebra? more like 10 definitions, 1 theorem.

[inner finch]

Olrite i got a book

Time for me to do this for a few days and then drop it

:nice:

[last oxide]

not wrong

but thats just a virtue of more abstract areas

you need more sophiscated tools

and that makes for less, more powerful theorems

[light needle]

oh fractal

u were doing galois memes right

[last oxide]

very slowly, at the pace of my class, yes

we just saw cyclic extensions ig

[light needle]

i see, a bunch of us are reading a book together on galois

[last oxide]

I know

coomer theory

[light needle]

oh no thats a different one

[last oxide]

ah

[light needle]

like intro galois

[last oxide]

field class theoryw

oh

I see

[light needle]

yeah, did u get to the fundemental theorem of galois yet?

[last oxide]

I mean
my times are not consistent enough to show up at the right time

ye

we did it a few weeks ago

I mean

[light needle]

well we will read tomorrow at 9 am my time

[last oxide]

the theorem itself is eveyr easy to prove

[light needle]

feel free to join

we just finished doing like, abel-ruffini

[last oxide]

I think the main point is just characterizing extensios very well

[light needle]

(california time for reference)

[last oxide]

abell-ruffini is supposeddly one of the applications we will go through

we went through trace and norm first

[light needle]

the proofs were p neat

oh yeah we havent done that yet

i think

[last oxide]

some cool stuff

they relate closely to the characteristic polynomial too

but its the char polynomial of a linear transformation given by multiplication of an element

[light needle]

yeah auts are all linear maps

[last oxide]

depending on what they fix, ye

theyll always be prime field-linear

[light needle]

ye

[woeful locust]

Why is integral transformation considered linear transformation rather than affine transformation?

[deep mango]

What is affine about it

Integral operators involve multiplying by a kernel and then integrating

[inner finch]

i hav

nugget

khaaamooooshiyaaaaaaaan

lipti huinnnn

khaaamoooshiyaaan

[deep mango]

[inner finch]

Imagine not khamoshiyan posting all day

[cold needle]

oh

what do you mean by multiplying by a kernel

like in laplace the kernel is e^st?

or wait am i thinking inverse

i forgot lmfao

[deep mango]

yes

it's that sort of thing

usually an integral operator looks like $Lf(x) = \int K(x, y)f(y) , dy$ for some two-variable kernel function $K$.

[fathom swallow]

RYC

[inner finch]

Sounds like something klhk would be good for

[atomic cypress]

a kernel is some nice function that's good for integrating next to, it's just a function

there are some distributional generalizations but

[last oxide]

saw the final value theorem a few days ago

a good meme

[cold needle]

we have intermediate value theorem

then final value

when will we unlock initial value theorem

[last oxide]

I had to derive it for something

[cold needle]

but i see teafortwo and ryc

[last oxide]

but it wasnt that trivial to come up with

[devout nacelle]

There's a Final Value Theorem?

[last oxide]

yeah

something about laplace transforms and limits

[deep mango]

So for fourier, it's K(x,y) = e^(ixy). and for laplace it's K(x, y) = char * e^(-xy), where char is the step function that is 1 for y > 0 and 0 elsewhere.

or wait

hang on sorry

[cold needle]

hmmm

[deep mango]

fixed

[cold needle]

ic

[deep mango]

since for laplace, you integrate 0 to infinity right?

[last oxide]

$\lim_{s \to 0^+} s\mathcal L{F}(s) = \lim_{t \infty}f(t)$ if $f$ is integrable I think?

dont recall

[atomic cypress]

If you're a horrible person you might also take K to be the Dirac delta

sorry, I meant physicist

[fathom swallow]

Fractal

[cold needle]

How do you even

[deep mango]

well this is fine right

[cold needle]

with the dirac delta thing

[deep mango]

K can be a distribution

there is a way to make sense of that

this is very important in the study of so-called "singular integrals"

where K might be something like K(x, y) = 1/(x - y)

[forest jackal]

the theory would be a hell of a lot less useful if you did not allow distributional kernels

[deep mango]

now you need to do an improper integral, and usually it will only converge if you do some slimy shit

[forest jackal]

in particular those singular only on the diagonal

[deep mango]

like cauchy principal values

[woeful locust]

F(x) -> G(x)+c

[atomic cypress]

Yeah but only horrible people write the Dirac distribution as a regular integral operator.

[deep mango]

you don't usually call that an integral transform...

[inner finch]

....

cog odot dot dot

[deep mango]

*people who know what they're doing and use easy notation

[forest jackal]

^

[cold needle]

so i have this book called operational mathematics, is this the topic name for this

[inner finch]

sounds like something a horrible person would say

[woeful locust]

uh.....wut?

[cold needle]

it had laplace stuff and this book was where i learned about the inverse laplace transform

[deep mango]

like i got confused about this a lot in harmonic analysis. "wait, we're convolving with a distribution? this looks like a function!"

and then i'd realize and it was fine

and now i get the language and abuse of notation people like to use, and it's much less confusing

[forest jackal]

tbf it takes working through some technical busywork to make sense of distributional convolutions etc but once you do it is very nice

[atomic cypress]

Harmonic analysis is really just about singular integrals and distributions. Everything else is fluff.

[woeful locust]

@deep mango
so, its a abuse of notation?

[last oxide]

harmonic analysis is a big ass field

[deep mango]

what's an abuse of notation

[deep mango]

i wasn't responding to your thing about affine transformations when i said this

[woeful locust]

oh fuck

[deep mango]

i was responding to the dirac delta thing

[inner finch]

Despite being only 35% of the population notation makes up about 70% of domestic violence cases across the globe.

[deep mango]

anyway, yeah that sort of thing is not affine

[woeful locust]

[deep mango]

and this does come up

when you want to, say, take picard iterates i think

[inner finch]

affine more like not fine

grrr

[deep mango]

stuff like that

but no one is claiming that's linear

[woeful locust]

Oh, actually my book said integral transformation is linear, so I asked abt this? I have no knowlegde of Integral transfoormation whatsoever and thought they are talking abt integration

[deep mango]

oh!

i see

they're usually definite integrals

so like

[woeful locust]

I am talking abt indefinite integrals

[last oxide]

$T(af+g)=\int (af+g) = a\int f + \int g$

[fathom swallow]

Fractal

[last oxide]

[deep mango]

well indefinite integration is only linear up to quotienting out by additive constants in the target space

[last oxide]

pretend those are definite

[deep mango]

since like, the integral of 0 doesn't need to be 0

[last oxide]

or improper

[deep mango]

so yeah, you're basically always working with definite integrals

[last oxide]

indefinite is a meme anyway

[deep mango]

if you want an indefinite integral

you're REALLY looking at a transform like this:

[last oxide]

would that kind of transform just be into an eq class of functions?

or rather

well

[deep mango]

$Tf(x) =\int_{-\infty}^x f(y) , dy$

[last oxide]

one about constants

[fathom swallow]

RYC

[last oxide]

not being equal up to m zero

[deep mango]

where f vanishes at -infinity or something

[atomic cypress]

Usually when I see an integral without a range of integration nowadays I assume it's the whole space, the notation for integrals-as-antiderivatives should be switched up.

[deep mango]

this

integration for the purpose of integral transforms is basically always a definite integral. i can't imagine a scenario where it isn't.

[last oxide]

just use
\int_M

[woeful locust]

@deep mango
I see, thank you so much for the explanation

[forest jackal]

I don't really see "integrals as antiderivatives" outside of like high school and first year calc courses.

so its not such a big deal

[deep mango]

keep in mind that it still is "linear" in the sense that the correct codomain for the operation of integration does quotient out by constants.

but then you need to be careful about all that nonsense

(by quotient out, i just mean we consider any functions which differ by a constant to be the same)

[last oxide]

isnt that memery used in qm

[deep mango]

(a good way to do this is just to shift every function to be 0 at 0, and have the indefinite integral be the one that makes that happen)

[last oxide]

or

well

[atomic cypress]

what memery

the quotienting?

[woeful locust]

Noted,my lord. Thanks, for explaining to my dum-dum brain

[last oxide]

I think you dont even need to be in qm
only mechanics will already give you contexts in which people call affine things linear

[deep mango]

your brain is not dum-dum

it just sounds like the book isn't super clear

this is a confusing idea, and it's a really good catch on your part.

bro i live for LINEAR equations and LINEAR inequalities.

algebra 1 is so fun

[last oxide]

affine equations and affine inequalities

[deep mango]

yes.

[atomic cypress]

I think affine really comes into play in SR, where you need symmetries under affine transformations. It pops up in QM for calculating the unitary trasnforms from one state to another, but it's not fundamental.

[deep mango]

the word "affine" was so scary to me because the only contexts i heard it used in were "affine variety" and "affine projective blah blah"

[last oxide]

just do the gauss map in your lines

[deep mango]

it was a while before i realized it was just "linear plus shift"

if only i'd learned "affine" in middle school

[atomic cypress]

"linear but I draw the line wherever I want"

[last oxide]

I actually used that in middle school

[woeful locust]

no shit

[last oxide]

but sadly it was used interchangeably with linear

[atomic cypress]

that's the statistics interpretation of affine, which understandably confuses all the stats and ML majors learning PCA for the first time

[last oxide]

"oh yeah, those affine functions? that just means linear"

[atomic cypress]

I'm impressed your middle school teachers knew the word affine at all

[woeful locust]

[cold needle]

same, and then my diffeq professor told me that solutions to inhomogeneous linear differential equations form an affine space and i got less scared

[deep mango]

yeah

that's where i should have learned it

[last oxide]

[cold needle]

[fast ivy]

função afim 😳

I also learned it in middle school too

One funny thing tho

Is that I thought homothety was a more common term, when it actually is not.

I think that the reason why most Brazilian professors call things affine, or a homothety in the first place is because Elon Lages Lima, which is one of the most notorious math textbook writers here, commonly uses these terms in his books.

[atomic cypress]

Maybe I went to a brainlet middle school but "affine" is just too big a word for what I remembered.

I think we were still hung up on arithmetic.

[last oxide]

elon op

[cold needle]

hi

i had to take a day off since i was tired but i looked at the problem 1-8 from spivak com

i looked at what the error was and reproduced it and tried to figure out what the problem was

i think it has to do with adding another condition maybe

perhaps if all of the eigenvalues have the same sign as well as magnitude, then we get angle preserving

and let me try if that works

[rancid meadow]

@cold needle 1-8b has an error

I don't remember specifically what it was, but you need to add an additional assumption to prove that T is angle preserving

oh sorry you know it has an error i cannot read

[cold needle]

yus

[rancid meadow]

apologies for the ping. continue on

[cold needle]

nw

im trying to figure out what the missing assumption is 😌

yeah im fairly sure the eigenvalues have to have the same sign

like

this is what caused the problem with the counterexample given

[forest jackal]

what was your counterexample?

(idk what the problem is, will look in a sec)

[cold needle]

let me get the page up

tterra told me to check out the error on the math exchange post

https://math.stackexchange.com/questions/177005/question-about-angle-preserving-operators

[forest jackal]

right, yeah

[cold needle]

cool cool

😌

[neat lintel]

even jesse knows

[cold needle]

what is that supposed to mean

[neat lintel]

jesse also knew there was an error with 8b

[cold needle]

specifically

lollll

maybe i should continue talking about this in a different channel

lol i keep getting distracted

uh

i do not know where this goes

i finally have to read #❓how-to-get-help

wtf

[rancid meadow]

just keep talking it ab out it here. you have privilege

use it

[cold needle]

i found it

topology and geometry

[rancid meadow]

not for ch 1 of spivak

[devout nacelle]

[rancid meadow]

that goes in #multivariable-calculus or #linear-algebra

[cold needle]

true

[deep mango]

Gomez is immortal.

[forest jackal]

[cold needle]

1 << 9

so like

9 \approx \infty

you know what i mean?

[cold needle]

https://tenor.com/view/stare-cat-confused-confused-look-serious-gif-16884211

[cold needle]

heine borel is kinda cool i think but i think i need to review compact/open/closed and all

[neat lintel]

here is something to consider

closed and bounded doesn't necessarily imply compact in (metric) spaces that aren't R^n

[cold needle]

i dont even know how to show closed and bounded implies compact in R^n

[neat lintel]

spivak will tell you

[cold needle]

but yeah i remember hearing that

oh

ok

[neat lintel]

the idea is that any interval [a, b] is compact in R, and products of those (rectangles, boxes) are compact in R^n

any bounded set can be fit inside a compact rectangle

and any closed subset of a compact set is compact

[cold needle]

and so those sets are compact

yes

[neat lintel]

nice

that's the gist

the only hard part is showing that intervals are compact

[cold needle]

which is what the small bit in spivak showed

the book first does one interval

[a,b]

but idk it's so weird to parse

[tall badge]

do closed+bounded implies sequentially compact which is equivalent to compact in metric spaces

[neat lintel]

interesting theorem: a normed vector space is finite dimensional iff its closed unit ball (a closed and bounded set) is compact

so if you want closed and bounded sets that aren't compact, just take any infinite dimensional normed vector space's closed unit ball

[cold needle]

h m m m m

[neat lintel]

the -> direction is easy

other is trickier

here's an example

let X = C([0, 1]) with the norm |f| = sup f. (this exists by the extreme value theorem.) let B be the closed unit ball of X, i.e., the set of all continuous functions on [0, 1] which are bounded in absolute value by 1. it's not compact since the sequence {x^n} has no convergent subsequence with respect to the given norm. (see rokabe's message)

C([0, 1]) = real vector space of all continuous real-valued functions on [0, 1]

convergence in this space is the exact same thing as uniform convergence

[devout nacelle]

[neat lintel]

and {x^n} (or any of its subsequences) doesn't converge uniformly on [0, 1]

[cold needle]

h m m

ic

[devout nacelle]

Wait so

Compact means sets in which convergence coincides with uniform convergence?

At least for R^n

Oh nvm

I got confused with continuous and uniformly continuous

[neat lintel]

[tall badge]

[cold needle]

its 4 am i need to

[devout nacelle]

[cold needle]

brain sleepo

[devout nacelle]

Sleep

[pale orchid]

compact tteppa

fits in the pocket

[devout nacelle]

compactteppa

[pale orchid]

comppactttteppa

[cold needle]

there are like

1000 pages in d&f

and all the text is small

[neat lintel]

[cold needle]

this is gonna be a good read

[neat lintel]

d&f is incredibly boring

[cold needle]

Totally

[pale orchid]

dungeons and fragons

[cold needle]

i tried reading the preface

i could not

please

pain

how in the world did poros get through this?

[torn willow]

Do it quickly. I usually just skimmed through the text and spend most of the time doing exercises

I usually didn't read the explanations and derived all the proof for theorems on my own,reading the explanations only if I don't get it

[cold needle]

alright

is two semesters timely for chapters 1-13?

assuming i have other classes to think about too ofc

[torn willow]

I think so

[cold needle]

alright

[torn willow]

The first few chapters are super easy

[cold needle]

ah ok that's good

[torn willow]

You might struggle with the end sections of ch4 and ch5

But that's about it for the group theory part

(Also,you probably don't need ch6 assuming you don't want to get into finite group theory)

[cold needle]

o ic

[bold ferry]

which book?

dandf?

[toxic schooner]

yes

[neat lintel]

dummit and foote?

[toxic schooner]

yes

[neat lintel]

well why not Gallian?

[toxic schooner]

coz gallian is a book for kids, they say

idk i havent read either of them

im doing artin

lol

[bold ferry]

gallian book is also good

[neat lintel]

for kids?

[toxic schooner]

yes

[neat lintel]

I haven't seen kids doing AA

[toxic schooner]

exactly lol

[light needle]

good artin is good

[toxic schooner]

ayeee john u got honorable!

[light needle]

yep

[toxic schooner]

see the message i tagged in #discussion

[neat lintel]

I read that

Isn't it a good thing?

[toxic schooner]

Idk

i dont mind if my book looks colored

as long as it is good

[bold ferry]

read for urself

[toxic schooner]

yeaa, i will read it later on

[bold ferry]

it doesnot matter what other says

[toxic schooner]

true

[toxic schooner]

interesting john, ur birthday is exactly 5 months before mine

[storm agate]

am i dumb or is proof by induction saying "prove n by assuming n is true"?

[neat lintel]

it's saying "prove n + 1 assuming n is true," so that if you know it's true for n = 1, then it's also true for n = 2, and then n = 3, and so on

i guess at some point you do have to assume that n is true when you're trying to show n holds

it is sort of strange like that

[stone valve]

Using the assumption to prove the assumption

[bold ferry]

ur using induction property of natural number

something along this line
i forgot the exact word

[storm agate]

thats sketchy man

is induction an axiom?

[storm agate]

what is monkey s

[errant kiln]

[torn willow]

I guess it's equivalent to the existence of N or sth

[storm agate]

yoyoyo is time the 4th dimension

[neat lintel]

induction is the same as well ordering

this is all i know

[errant kiln]

[neat lintel]

no mathematician outside of set theory or logic (or inside) cares

[compact tartan]

induction is about well founded trees

[neat lintel]

*planted

[torn willow]

I mean even if a set is well ordered, how do you know you "P(n)=>P(n+1)" implies P is true for everything in set

[compact tartan]

because you want proofs to be well founded trees

[storm agate]

yes

[torn willow]

Don't you need the set to be bijective to N

[compact tartan]

consider the set of counterexamples

well orderedness gives you the smallest one

[storm agate]

0 is divisible by an integer n right?

[torn willow]

Yrs

0=0(n)

[storm agate]

hmm

is 0 apart of the set of all positive integers?

[bold ferry]

0 is not positive

[leaden torrent]

unless youre french

man, "apart" vs "a part" totally changes that sentence

wtf

we need to stop using english

[bold ferry]

i want to integrate a function over a torus. where do i start?

[neat lintel]

start with a volume form

[toxic schooner]

i am ready to teach yall hindi

[neat lintel]

integrating a function on a torus requires a choice of volume form and thus a choice of riemannian metric

and there are at least two natural choices you could go with

[leaden torrent]

no heres the plan

we switch to japanesse with 0 notice

and then if anyone seems vaguely competent at it

[neat lintel]

iie

[leaden torrent]

we ban them

for excessive weebism

[neat lintel]

[toxic schooner]

nami thats a good idea

im safe from being banned

[bold ferry]

One piece is great

[toxic schooner]

coz i dont see anime

lol

[leaden torrent]

"i don't see anime" sounds like a very underwhelming superpower

like if a TV happens to be displaying anime, you have x-ray vision of the TV only

until they change the program

would such a superpower apply to anime-style chinese/korean works as well?

or just "genuine" japanese anime

[dim flame]

oh this will be good

[toxic schooner]

Lol no

I suck at hindi

ironically my best score in 10th boards was in hindi

still

[neat lintel]

anyone have a cool differential geometry fact

[leaden torrent]

ℝ⁴

you know exactly what fact is gonna follow from here

[neat lintel]

i do

[leaden torrent]

it is objectively the coolest math fact

unfortunately nothing else in diff geo is cool

[neat lintel]

my hair is falling out

Your hair is a topologic space

with the discrete topology

[willow pulsar]

what is it

guys how do i solve limits easily

why cant i solve limits 😭

[leaden torrent]

that is a concerning mixture of messages to reply to

[neat lintel]

R^4 admits uncountably many distinct smooth structures.

[willow pulsar]

lmao

ok

[leaden torrent]

if they dont know limits im not sure thatll be that approachable

ultra/tterra

hate to say it

[neat lintel]

they asked

[neat lintel]

[leaden torrent]

Wikipedia disagrees

[willow pulsar]

wow lmao

[willow pulsar]

xd

i was talking about limits in general

i cant solve them

[leaden torrent]

#❓how-to-get-help

you might wanna be more specific when you ask, though

like give some examples of problems that give you difficulty

[willow pulsar]

neverminf

i ll practice more

ok

[neat lintel]

[crystal stone]

My family is visiting for the holiday weekend

Which includes today July 5th

Woke up to an email that there's teaching and I gotta do some work

Email back saying "As per university calendar there are no classes and campus is closed"

go back to sleep

[modest rune]

lmfao proud of u

[crystal stone]

I was getting work emails on July 4th

[nimble shuttle]

based

[crystal stone]

IS THIS DUE TODAY

No. Read your freakin' syllabus

Also the GRE is optional for a second year in a row

Praise be

[narrow rock]

[crystal stone]

I don't have time to study for it

[narrow rock]

I don't want to study for it.

[crystal stone]

That too

[bronze pelican]

PRAISE

[bronze pelican]

Source?

It depends from school to school no?

Do the schools already say GRE is optional for the next admission cycle?

[crystal stone]

Well you need to go to the school website

[bronze pelican]

Which school?

Like are you stating a general fact that most schools will have GRE optional or are you referring to a specific school that has GRE optional?

@crystal stone

[crystal stone]

The schools I'm applying to don't require it

[bronze pelican]

Ah ok

Yeah cause I imagine it (still) varies from school to school

[vast surge]

If you apply to a GRE optional school, is there anything else expected to make up for that, or is the application all done on the basis of grades/letters of recommendation/maybe an interview?

[mortal oasis]

Bro fuck the GRE

[cinder zephyr]

I am only a sophomore

praying GRE goes away by the time I have to look at grad school

[cold needle]

same

[velvet dagger]

Just manifest it

[vestal river]

Bumping this

[crystal stream]

The hecc is a gre

Oh sorry ultra, had that message for some reason.

[leaden torrent]

typically no, just the standard stuff

the GRE isnt really weighted highly in the admissions process regardless, its more like a "filter"

[vast surge]

So it's basically all letters, grades and REUs?

[leaden torrent]

like if you get below the minimum GRE for a school your application is thrown out, but an 80 gre vs a 90 isnt a big deal

yes, but remember that quals are a thing as well

also your statement of purpose and stuff

[vast surge]

Yeah but quals are for after you get in, right?

[leaden torrent]

yes

[vast surge]

And statement of purpose should be done in LaTeX, right?

[cold needle]

i don't think that's necessary lol

[vast surge]

Is there an interview process as well?

I don't even know why I'm asking all these just yet I'm only going into my junior year of undergrad

[atomic hornet]

Just do cs and no mgre!

Regular gre is pretty easy

[cinder zephyr]

idk what i like more lol

pure math or theoretical CS

we'll see

[vast surge]

Hey so not quite a math question but how do I get my goddamn housemates to do their fucking dirty dishes instead of just leaving them in the goddamn sink and letting flies gather around?

[inner finch]

have to solve a certain ode

[vast surge]

Great

I'll solve it

What's the ODE?

(Do numerical methods work or do I need to find an analytic solution?)

[inner finch]

analytic solution

To find the ODE you have to first accurately model your housemate's behavior as a system of ODEs

[vast surge]

Okay and what kind of ODEs am I looking for here. Constant coefficients? Something harder?

[inner finch]

The ones that you can solve to get your goddamn housemates to do their fucking dirty dishes instead of just leaving them in the goddamn sink and letting flies gather around

[atomic cypress]

Having housemates is lame

[deep mango]

You should ask ange.

He's experienced in coping with dirty roommates

[mortal oasis]

Have you told them

Like I know that might sound obvious but

[vast surge]

I do not have their contact information.

[mortal oasis]

Don’t y’all live together

[vast surge]

I barely see them. They might as well be ghosts that produce dirty dishes

I contacted resed to try to get their contact info and got nothing back

[mortal oasis]

I mean you’ll here them come home right

[vast surge]

I haven't yet

I wouldn't be surprised if they made a massive mess two weeks ago and then just fucked off

[mortal oasis]

Jesus

Idk I’d do em for now and tell them next time

And be like hey I did they this time but like come on that shit is nasty

Like I know that sucks but I think that’s the best way of getting it to change

[rancid meadow]

i have had that same experience Quintic

I just seethed about it because I did not want to have a bunch of drama with strangers I live in the same house with

i often just moved their shit somewhere else

[ornate thistle]

hello i just want to ask something to the upper level/uni students here

is it important to know how everything is defined for math? like the specific definitions of integers or rational numbers. or should you just have a solid intuition on it?

cause for me at least, i wasn't really taught the definitions and stuff when i learnt integers or rational numbers in like middle school

[sharp mulch]

I heard about dirty roommates

One thing you can do is sigh disappointedly at them

Another thing that works is a chore rotation

[pure sun]

it depends, sometimes you need to know the precise definition so you can go back and use it to prove something, but i would say in many cases knowing properties of an object or how it behaves is more important

[ornate thistle]

ok thanks!

[past zinc]

so why can something be true without a proof

[pure sun]

what does that even mean

[past zinc]

the difference between proof of A and A

[pure sun]

i have no idea what you mean

[rancid meadow]

[pure sun]

the way you establish the truth of a statement is via a proof

[past zinc]

so proof of A implies A right? but A is true shouldnt imply a proof of A

[rancid meadow]

maybe means true on some syntactic level?

[pure sun]

are you saying that "there is a proof of A" implies that "A is true" but "A is true" does not imply "there is a proof of A"?

I mean, sure -- if "ZFC is consistent" is true, you won't be able to prove it in ZFC

[mortal oasis]

Honestly @vast surge the thing I did one time was asked them nicely to move it and when they refused I put the dirty shit in there room or on there bed

[pure sun]

there is a difference between truth and provability, but I think most of the time in math (when you're sufficiently far away from logic and foundations) people use them interchangeably

[past zinc]

so why is ZFC cant complete not a proof of it being consistent

[rancid meadow]

[pure sun]

what?

maybe you weren't ready for that example yet

the way we know that something is true is by proving it

[rancid meadow]

I believe he is asking why Con(ZFC) being true is not the same as a proof of it existing

[pure sun]

that is a very subtle question

at least for someone who isn't used to thinking about stuff like this

[neat lintel]

[pure sun]

are you asking about godel's incompleteness theorem?

[rancid meadow]

no buncho

maybe buncho

[pure sun]

I mean, that's sort of the prototypical example of "true but not provable"

or like, that's the context in which most people first encounter the idea that truth and provability are different

at least in my experience

[mortal oasis]

If you prove something it’s true right

[pure sun]

that's soundness

or something like that

[rancid meadow]

yes its soundness

[mortal oasis]

Ah ok I feel like this is getting into logic

And foundations?

What’s the difference

[rancid meadow]

$\Gamma \vdash \varphi \Rightarrow \Gamma \vDash \varphi$

[fathom swallow]

jesse

[rancid meadow]

"if you can prove it then it is true"

[past zinc]

well apperently its proven if a proof of a proof of that implies that

[mortal oasis]

Do you mind me asking how important is this really out side of like a niche field

Of math

I don’t mean that glibly either

[rancid meadow]

soundness? very

If you prove something in FOL then of course you want to know that it's actually true

[mortal oasis]

Ah I think we are too advanced for me atm

[rancid meadow]

sorry, FOL: first order logic

[rancid meadow]

[past zinc]

so what exactly happens if we add the notion that A is only true if proof of A

[rancid meadow]

this is Lobs theorem right

[past zinc]

yes

[rancid meadow]

A is only true if proof of A
what do you mean

this language is not clear to me

[broken delta]

Probably the converse of the image they posted

[rancid meadow]

oh okay

so we have $PA \vdash (Prov(P) \to P)$ iff $PA \vdash P$?

[fathom swallow]

jesse

[past zinc]

lol i guess

[neat lintel]

that is a nice font

[past zinc]

since all that shit implies proof of A

or P or w.e

anyways what exactly happens when we only let A be true if proven proof of A

[rancid meadow]

"proven proof of A"?

[past zinc]

proof for proof of it

box A

anyways is parallel prostulate even true in strictly eculdiean

[rancid meadow]

Okay sorry the language is confusing me. Are you asking what happens if "If there is a proof of A, then it is true" is the only way that things can be true?

[past zinc]

i guess. i mean why would it be true

[rancid meadow]

sorry, your language is making this very hard to answer lmfao

or maybe i am stupid, but can you clarify exactly what you want to know

[past zinc]

parallel prostulate is true in ecludean?

[rancid meadow]

If your geometry at work is Euclidean geometry then the parallel postulate is an axiom, no?

Or, it will be equivalent to one of your axioms

there are geometries where they remove the postulate, or they modify it

[past zinc]

if they made it axiom perhaps its becaues they couldnt prove it or something

[rancid meadow]

The postulate is independent of the other Euclidean axioms

i think

i need to qualify all my statements with "I think".

yeah this shit is irrelevant anyways, go study a real field like applied math

[past zinc]

its relevant to computer science and language

or so they say

[rancid meadow]

""they"" is the deepstate trying to convince you to be interested in fruitless pursuits

[past zinc]

afaik they initially tried to prove the postulate

but without it could imply non eculdiean geometry

redundant?

[rancid meadow]

ultra. why is the converse of lobs theorem false

or is it

huh. wonder why they didnt make it a biconditional

it looks obviously true but u never know

[past zinc]

i guess it reduces it to something like quantification logic if A is just a proof of A

which is proababy it needs that disnction

to what does it apply to then

k4 doesnt have quantification?

anways what does it apply to with it being unidirectional

[rancid meadow]

[chilly swift]

@celest pasture

imagine being in a math server

yikes

what a weirdo

[nimble shuttle]

e-couple raid

[chilly swift]

OMG NO

[steel mantle]

matching pfps

https://i.imgur.com/kjEwA4m.png

[chilly swift]

PLEASE I LOVE HIM 😭

NOO

[velvet dagger]

And that's the problem

[chilly swift]

[pure sun]

oof

[velvet dagger]

begone

[pure sun]

friendzoned

in the math server

[chilly swift]

LMAO

STOP

[sacred geyser]

we don't have friends here

[nimble shuttle]

[chilly swift]

ITS A JOKE

[sacred geyser]

we hate everyone

[chilly swift]

im being bullied

[pure sun]

stephie in shambles

[velvet dagger]

Math is fueled by anger

[sacred geyser]

and coffee

[past zinc]

kringe imo btw giys fyi

[compact tartan]

what

[chilly swift]

nah bro stephie isnt in shambles

he friendzoned ME

because I didnt know how to calculate limits 😩

[steel mantle]

oh fuck i'm gonna cyberbully

[nimble shuttle]

there was ping spam but it seems to have...disappeared

[chilly swift]

no

[pure sun]

[compact tartan]

shall we do a little trolling

[past zinc]

this is so pog right now??

[sacred geyser]

a mild amount of tomfoolery?

[chilly swift]

no that was

ur imagination

[steel mantle]

minuscule amount of trickery

[compact tartan]

a tidbit of subversion

[sacred geyser]

[nimble shuttle]

i have never heard that one

ultra is even more terminally online than I am

[sacred geyser]

thats a good one ultra

[chilly swift]

nice try

[sick burrow]

What is going on here

[sacred geyser]

imagine when ur crush sees you getting roasted in #serious-discussion

not sure tbh

[nimble shuttle]

i need the version of this where it says "no mom you can't pause an online game"

i can't find it

[fierce cloak]

What's this?

[past zinc]

so if A is true only if there is a proof of A means modal collapse, when do we exactly need modal proof

nvm

[neat lintel]

@chilly swift @nimble shuttle @pure sun
have a great day guys!!!
we apreciate what you guys are doing, and want to encourage you for doing what you do

[chilly swift]

thanks :)

[neat lintel]

this is something very obvious but only something i consciously realized about half a year ago

similarity in notation doesn't mean that an identity/theorem is more obvious

like say the MCT

i used to be like wth, all you have to do is swap the limit and integral, obviously u can do that

but like that was because i was only focusing on the notation and not like what things were actually saying

idk if anyone else ever thought this

or rn i'm learning fourier analysis and sometimes there's so many symbols but like u gotta try and understand what's rly going on

i guess my point is that sometimes notation is too good lol

[deep mango]

I kind of get your point.

Like, sometimes I feel like notation is so slick that it leads me to do things I can't actually do

like sometimes I'll have something which is a distribution and I'll try to evaluate it, because we kind of write distributions like functions under an integral.

But it makes no sense to evaluate it

so even if this is the morally correct way to view distributions, the notation leads me to do some incorrect things without thinking

[leaden torrent]

i think viewing definitions as notational statements can be useful though

like the proper definition of continuity in various contexts is yucky

but typically its usually equivalent to "commutes with limits"

not always ofc but often

[thin valley]

what do you guys think about the collatz conjecture? Do you really think our mathematics isn't ready for that yet?

[bold carbon]

i think this server isnt ready for you spamming every channel with that question yet

[edgy atlas]

Unironically what do you guys think of the unique games conjecture (if youve ever heard of it)

My prof for a class next semester conjectured it

and maybe if you guys have any intelligent thoughts on it i can relay them to that professor and he will have mercy on me

[modest rune]

maybe state the conjecture

[inner finch]

Guys what do you think about the conjecture i thought of right now (if youve ever heard of it)

[neat lintel]

how can we know what you thought of right now

[limber perch]

tbh it could use some work

but it seems promising

[inner finch]

Thanks

[distant vortex]

What about mine? There are no powers of 2 with more than half of its digits (in standard decimal notation) equal to 0.

[devout nacelle]

[distant vortex]

Why did my conjecture get thonked?

Sullied too

The bullying culture here is unreal!

[devout nacelle]

Yes.

[neat lintel]

proof

ok actually idk and idc im going to sleep

good night Ledog

[distant vortex]

When one of 3 people on the server who has blocked you tries to solve your conjecture. You are not qualified, Ledog, but good night.

[neat lintel]

good night godel

GODEL???

all my life. i thought it was le dog

[sleek wing]

le dog is his online name

[whole sand]

Newton’s third law is wrong, I discovered a new Gravitation theory which breaks the wall of Planck scale! What does everyone think?

[limber perch]

that’s cool and all but who asked

[whole sand]

Example: the interaction between a black whole and a planet, or a star:
“The gravitational force exerted by the black hole on the planet is much higher
than the gravitational force exerted by the planet on the black hole. Because the
energy of the gravitons emitted by the black hole is much higher than the energy
of the gravitons emitted by the planet”
Because the reaction is not simultaneously, because the gravitons which mediate
the gravitational force, have a finite speed, not an infinite speed.
This is another proof that my Gravitation theory is right.
Only my Gravitation theory explains that Newton’s third law is wrong!

[inner finch]

[pure sun]

Why dont you go tell the physics discord server instead of the math one

This sounds like something they might be interested in

[whole sand]

Link?

[pure sun]

Check #old-network

[whole sand]

Thank you, may they listen that Einstein Gravitation theory is wrong

[cold needle]

uhh

[pure sun]

Good luck

Metal, just let it happen

[cold needle]

ok

[pure sun]

:)

[cold needle]

:3

[whole sand]

They do not accept my chinese phone, error message is obtained after trying to register. Clear case of unfair conspiracy.

[cold needle]

what

how did you get here then

[pure sun]

Sorry to hear that. We arent experts in physics so we cant really help you

[broken delta]

It says you're in the physics server for me?

[cold needle]

maybe the physics server has some kind of special join thing u have to do

like sth to read and then u can get in

[pure sun]

Maybe they just didnt take the time to read the “react with this emote to get server access” message lol

[whole sand]

Yes but I cannot speak because first the phone number is &invalid phone number&

[cold needle]

?

oh

is the server only for those with a valid phone number associated with their account

strange

[dire sandal]

Bro I'm trying do logarithms here not gravity

[unreal skiff]

yeah that's cool and all but aren't gravitons theoretical and as of now have no properties to speak of which makes your statements false?

[whole sand]

I have calculations with gravitons. Consider this:

[pure sun]

Oh no

[whole sand]

For example, we can find their momentum. Because the graviton has the rest mass equal to zero and the speed is equal to the speed of
light: E = p × c
E = a × f from here p × c = a × f, and because c / f = λ, we have:
Graviton momentum:
p = a / λ
That is why the gravitons are too small to be detected by today’s technology.

If experimentalists can catch a graviton they should try to measure my momentum theory.

If you need details on how to obtain a I have it written: Here I calculated ratio of electromagnetic force to gravy force strength: "The strength s, of the electromagnetic force relative to gravity force: s = F_e/F_k = k_e q_e^2 / G m_e^2 = (8.99 x 10^9) (1.60 x 10^-19)^2 / (6.67 x 10^-11) ( 9.10 x 10^-31)^2 = 4.166 × 10^ 42." I use this "s" in my theory to calculate a using equation s=h/a, h = 6.62606957×10−34 J·s is Plank's constant to get a = 1.590511178×10-76 J·s. The momentum of a photon is p = h / λ, so the momentum of a graviton must be p = a / λ. If experimentalists can catch a graviton they should try to measure my momentum theory.

[rose dock]

Your graviton theory sounds fascinating, but have you heard of embi's DNA ordinal theory?

[whole sand]

Not quite, who's embi?

[rose dock]

Oh, he's a googlogist who I'm sure would love to hear your graviton theory

[whole sand]

You speak of googol but I googoled his theory and all I got was this "salad of numbers", where's the real stuff? https://googology.wikia.org/wiki/User_blog:Nayuta_Ito/DNA_Ordinal

[rose dock]

You'd have to ask embi

[vagrant kestrel]

Don't be so dismissive of DNA Ordinals

[deep mango]

what does the A stand for?

ok. who wants to join the Deez Nuts Alliance.

[unreal skiff]

“Graviton has rest mass equal to zero” you have no proof of that, like I said they are only theoretical

[hallow wasp]

oh yes the secret to eternal life in the murim

dna ordinals
AK

[bronze pelican]

I should probably start grinding qualifying exam problems

[limber perch]

3 hour logic exam

[blazing pawn]

Sadge

yet another day of battle against introductory algebraic geometry

literal enemy of the people

[bronze pelican]

Yes Moth has surpassed me

I'm still reading Riemann surfaces chapter

[limber thunder]

good luck with that

[rancid meadow]

Can anyone here help me to analyze my DNA ordinal?
It's (0,0,0)(1,1,1)(2,2,2)(3,3,3)(3,3,0)(4,4,1)(5,5,2)(6,6,2)(7,7,0)(8,8,1)(9,9,2)(10,9,2)(11,9,0)(12,10,1)(13,11,2)(13,11,2)(13,11,1)(14,12,2)(14,11,1)(15,12,2)(15,11,1)(16,12,0)(17,13,1)(18,14,2)(18,14,2)(18,14,1)(19,15,2)(19,14,1)(20,15,2)(20,14,1)(21,15,0)(22,16,1)(23,17,2)(23,17,2)(23,17,1)(24,18,2)(24,17,1)(25,18,2)(25,17,0)(26,18,1)(27,19,2)(27,19,2)(27,19,1)(28,20,2)(28,19,1)(29,20,2)(29,19,0)(30,20,1)(31,21,2)(31,21,2)(31,21,1)(32,22,2)(32,21,1)(33,22,2)(33,21,0)(34,22,1)(35,23,2)(35,23,2)(35,23,1)(36,24,2)(36,23,1)(37,24,2)(37,23,0)(38,24,1)(39,25,2)(40,25,2)(40,25,1)(41,26,2)(41,22,1)(42,23,2)(42,23,2)(42,23,1)(43,24,2)(43,23,1)(44,24,2)(44,23,0)(45,24,1)(46,25,2)(47,25,2)(47,25,1)(48,26,1)(49,27,0)(50,28,1)(51,29,2)(52,29,2)(52,29,1)(53,30,0)(54,31,1)(55,32,2)(56,32,2)(56,32,0)(57,33,1)(58,34,2)(59,34,2)(59,34,0)(60,35,1)(61,36,2)(62,36,2)(62,36,0)(63,37,1)(64,38,2)(65,38,2)(65,38,0)(66,39,1)(67,40,2)(68,40,2)(68,40,0)(69,41,1)(70,42,2)(71,42,2)(71,42,0)(72,43,1)(73,44,0)(74,45,1)(75,44,0)(76,45,1)(77,46,0)(78,47,0)(79,44,0)(80,45,1)... ... ... ... in a notation known as Bashicu Matrix System

stay mad metal

[cold needle]

i nearly almost had a knee jerk reaction

don't do that 😭

[rancid meadow]

just admit u cant analyze my DNA ordinal

[cold needle]

i can't it's too divine

sorry

Stay mad metal.

[deep mango]

Stay mad metal.

[neat lintel]

Stay mad metal.

[narrow rock]

Stay mad metal.

deez nuts role

[shell roost]

stay mad metal

[inner finch]

13th one is wrong.

[vast surge]

What's googolology?

I just clicked on the link. The study of big numbers. What? Like, numerology mixed with "haha recursion go brr"?

And making silly words

[deep mango]

it's stupid

[vast surge]

A bit of clicking around, and a guy called Jonathan Bowers appears a lot on that website.

And has his own personal website

He looks like an interesting cank.

[broken delta]

Googology isn't math (at least, not in the traditional sense), but it doesn't claim to be. I don't think googologists are cranks

[sacred geyser]

ur just jelly you can't come up with numbers as big as the ones on that site

[rose dock]

Would googlology not be a branch of set theory or smth?

[errant rock]

my dna ordinal is 0.

[vast surge]

Everything on that website just looks like recursion.

So, just keep doing more recursion, I guess?

[sacred geyser]

wouldn't you want to be awarded with discovering the largest number

only for someone to take it away by adding 1

[lean mountain]

@bronze pelican that looks terrible

[atomic cypress]

The biggest number is probably 6 or something

[deep mango]

@inner finch did u get to the thing yet

[inner finch]

yeah i did

the gall of that building

mmm yes let me just shoot this out of the sky haha

i bet it thinks its so quirky

[deep mango]

i bet u didnt go in the building lol

[inner finch]

I did

i got the booger cubes

[deep mango]

🤨

[inner finch]

am going to set up another mission there :nice:

[deep mango]

Exciting

[inner finch]

tho now that the event is over idk where it is once i returned home to make a beacon

mirza memory moment

[deep mango]

You can reactivate past location markers in the pda i think

I dont remember if that works for the sunbeam

It's probably on the audio logs page? Maybe not

[inner finch]

hm