serious-discussion

[alpine kindle]

I'm eigenstuff

[brave hollow]

I thought this was standard

[bright hill]

eyyy

it's nyann

[brave hollow]

'ello mate

[alpine kindle]

yo

[bright hill]

ello

[fair mural]

i do not like the standard then but i will deal with it

[brave hollow]

I actually dmed you not so long ago darq

[long matrix]

matrices in infinite dimensional vector space

[bright hill]

I'm just seeing that

[alpine kindle]

OMG ARTIN USING COMM DIAGRAMS

[fair mural]

i am not doing functional analysis, shut

[fair mural]

wow an algebra book using diagrams how surprising

[light needle]

over relying on matrices is not good

[fair mural]

[alpine kindle]

matrices between vspaces of different base fields

[long matrix]

how does one define a linear map here

[alpine kindle]

oh wait

nvm I'm stupid

[inner finch]

math moment

[alpine kindle]

this happens to me all the time

i talk too much

[sleek wing]

me on 500 grams of crack trying to prove the snake lemma
https://cdn.discordapp.com/attachments/397815464954167296/959458568430551080/unknown.png

[alpine kindle]

[sleek wing]

omg I would like the 5 lemma please

hahah the fuckin 16 theorem as well

wait why do I know what these are now

what's happening to me

[fair mural]

from me looking at wikipedia for 2 minutes it seems that these lemmas are defined only for square numbers

explain the 5

[bright hill]

is there any kind of crack which you can survive on 500 g?

[fair mural]

depends on your tolerance

[sleek wing]

god I hope not

[sleek wing]

you want me to actually prove the 5 lemma

that's like

a whole page of diagram chasing lmfao

[frozen merlin]

there's a thing on the 3b1b blog with like puzzle pieces

[light needle]

i mean its a diy type of deal

[frozen merlin]

wait this is snake not 5

[sleek wing]

5 lemma is on the left

kind of

a weaker version of it

[long matrix]

oi wtf, can u link

[frozen merlin]

yeah I don't think this article has 5

https://www.3blue1brown.com/blog/exact-sequence-picturebook

it seems cute but I can't appreciate it without actually learning the stuff first

[fair mural]

that’s not what i meant lol

[modern geyser]

whjat does thsi mean

[fair mural]

oog

[alpine kindle]

is there a study of solutions to multivariate exponential equations (including trig and stuff)

like how alg geom is for polynomials

because the graphs look really cool

like this

and this

i wonder if we can say anything about the structure of these solution curves

also whatever the hell is going on here

there are too many interesting ones

[fair mural]

my entire latex document died because i forgot to close some parentheses

actually cringe

i was freaking out trying to find the error for like 5 minutes

[median zinc]

modularise your document maybeeee

[alpine kindle]

🫂

[alpine kindle]

reiterating question so it doesn't get buried

[rocky shuttle]

I'm not aware of anything except for numerical methods to find them

[frozen merlin]

ping me when you get an answer, I'm interested since the formal power series ring R[[x]] (which is probably what you'd be working with, as opposed to R[x]) seems pretty well-behaved for nice R

[rocky shuttle]

Noetherian?

[frozen merlin]

yeah

[alpine kindle]

wait would these equations work nicely in any noetherian ring

[frozen merlin]

every ideal is finitely generated, so if wikipedia has served me well then you'd be able to write every "variety" as a finite union of irreducible "varieties" (or whatever you call them in a power series ring)

honestly I know 0 alggeo don't take anything from me

[alpine kindle]

yeah

there may be an issue of convergence tho

[frozen merlin]

I wonder if you can make a ring of convergent power series by modding out divergent things

wait no that's not an ideal

nvm

[fervent pebble]

ew

[honest veldt]

fellas for the backwards direction, do i literally just say that {p_n} is a subsequence of {p_n}

[honest veldt]

kinda agree ngl

I just got "proof is left to the reader"'d

[sleek wing]

think that works lol

[honest veldt]

im going with it, thank you wewe

[bright hill]

lmao

[median zinc]

I'm not an analyst but you could try contradiction to be more clear

[honest veldt]

the way I did it is kinda as clear as it gets no? I don't see why it wouldn't be valid

or are you talking about the forward direction

[median zinc]

no the backward

if there exists a single subsequence that does not converge to p

anyway I'm not an analyst

[honest veldt]

that contradiction hypothesis is for the forward direction tho

if i were to use contradiction for the backward, it'd be assuming that {p_n} doesnt converge to p

[median zinc]

no

Forward is
p_{n} converges to p -> every subsequence of p_n converges to p
Backward is
every subsequence of p_n converges to p -> p_{n} converges to p

[honest veldt]

okay, great

so the contradiction hypothesis for the backward would be....?

[median zinc]

assume for contradiction = assume there exists one (or more) subsequence of p_n that does not converge to p

[honest veldt]

i think you're confused about something here, that hypothesis works for the forward direction, not the backward

[median zinc]

[swift sinew]

That’s not contradiction. You just assumed the opposite of the antecedent. This does not affect the implication at all

[sleek wing]

yeah that's proof by contrapositive

[honest veldt]

To prove a statement "If A then B" by contradiction, you say "Suppose A and not B"

[swift sinew]

And still, that’d be for the other direction than he was considering

[median zinc]

Oh yeah

You're right

assume there exists one (or more) subsequence of p_n that does not converge to p and p_n itself converges to p

Right sorry

That should get a contradiction

And prove the backward direction

[honest veldt]

Not quite still

you're still doing the forward one

[median zinc]

[swift sinew]

Pepper, try writing this as p iff q and identifying what p and q are and working with contrapositives and stuff so you know what you’re proving and assuming

[proud quail]

correct contradiction for backwards implication: ||suppose every subsequence of {p_n} converges to p, and for a contradiction suppose {p_n} does not converge to p||

[median zinc]

Oh dam, you're right.
And lmao this is obvious now you mention it

I think this proof works?

[median zinc]

Equivalent to this lol

[honest veldt]

For the forward, I did it directly by saying that
For any $\epsilon > 0$, there exists an N such that $n \geq N$ implies $|p_n - p| < \epsilon$. So, for any subsequence ${p_{n_i}}$, $n_i$ is eventually $> N$ for all $i > j$, for some $j \in \mathbb{N}$. So $|p_{n_i} - p| < \epsilon$ for all $n_i$ with $i > j$

this works?

[fathom swallow]

gusfringerpro2009

[median zinc]

Seems ok to me

[honest veldt]

Sweet, thank you

[median zinc]

But I'm really bad lol

X_X

[honest veldt]

No worries, it happens lol

[median zinc]

Analysis is my bane

[honest veldt]

isn't it everyone's

[limber thunder]

no, git gud

[ripe wasp]

how is hatcher’s notes on point set topology compared to a standard text like munkres or mendelson?

it seems very short and concise

so i thought i could prob go through it in a few weeks then do analysis from apostol

[limber thunder]

hatcher's notes are the absolute bare minimum point-set anyone (=any mathematician) should know

particularly all you should need to learn alg top from his text

[limber thunder]

if that's your objective then yeah, seems reasonable to not spend a ton of time reading a textbook

[ripe wasp]

my final objective is to work through lee's smooth manifolds atm, so im debating on whether to use hatcher or a combination of lee's topological manifolds and mendelson's intro to topology

because i want a good foundation yk

after i finish linear algebra from ladw, i'm probably gonna be on summer vacation so i'm gonna really grind out some math during that time

hopefully i can make significant progress on apostol during that time

[primal seal]

I think you’re on a different planet

[ripe wasp]

idk how much im gonna get done though

i registered for aops's group theory course

seems like a baby first course in abstract algebra

i flipped through the big ass textbook they sent me and it looks pretty cool

[dire mulch]

Hmm, I am under the impression lee's smooth manifold requires a decent understand of analysis.

[primal seal]

This kid is out of his mind

[ripe wasp]

yeah ik, i'm planning on doing apostol then munkres calc on manifolds for multivariable analysis

[primal seal]

We believe you brother

[ripe wasp]

idk man, i just like planning into the future this is all subject to change, i'm probably gonna take twice as long to do all of this than im planning due to burnout and school tbh

[primal seal]

I think you should regard fairly sophisticated math texts with more respect than the expectation of finishing them in the same time as Harry Potter

[leaden torrent]

#❓how-to-get-help

[fair mural]

when did they ever say they were gonna try to quickly read those books? they’re just planning ahead a bit

[toxic schooner]

not really

this is common here

much to my sadness

[primal seal]

😔

[toxic schooner]

tfw 9th graders want to do diff geo

[primal seal]

They THINK they want to

[toxic schooner]

[neat lintel]

Do it slow

If u do it fast. Chances are that u might understand a concept wrongly

And have to spend more time on it

I did this very mistake

Tried calc 1 in grade 8th

I could do sums. Completed calc 1 in 7 months. Proceeded to calc 2. Integration killed me

[ripe wasp]

i'm not trying to read it like harry potter, i'm just saying i just wanna go through those texts, ofc i will be doing as many exercises i think are necessary and doing most of the proofs left to the reader. sorry if it came off like i was gonna breeze through all of this, that wasn't my intent, i just like to have a solid plan i can follow as i like scheduling and i feel more secure when i know what i'm going to next and in the future. as for my age, i'm not sure why thats relevant, perhaps you think i'm not ready for studying higher level math and thats understandable, but thats what learning is for isn't it? if i'm not ready, i'll probably realize that when i'm actually going through the material and then i can act on that then by reading through some other easier text to fulfill the prerequisites. its better to try and fail compared to not trying at all, as im sure you know.

i'm just genuinely interested in these topics, im not trying to come off as a know it all or something, sorry if it seemed that way

[ripe wasp]

yeah, i'm practicing my integration rn as well, partial fractions are really annoying

[neat lintel]

Substitution is pretty simple. But the parts which follow are terrifying

Luckily I am doing from stewarts

An excellent book

[ripe wasp]

yeah i have stewart as well, i sometimes use it for practice problems and such

[primal seal]

I’m over it bro, and there’s no beef. I’m just letting you know you sound like you’re planning your lunch on the 4th of July today. Fairly unbelievable circumstances I’d say. Best of luck, talk soon 🙏

[toxic schooner]

[ripe wasp]

yup all good, i'll try my hardest to study as thoroughly as possible and ik it seems like a stretch and i agree, i'll probably just do half or less of what i'm gonna say i'm gonna do. Yk when you're really interested in something you just wanna learn everything you see and to me my love of math is what's most important, but i'll 100% make sure to manage my expectations in the future.

[sterile hare]

your love for math? what kind of waffle is this. wasn't you just asking me how to hack your calculator so u can cheat in exams

[primal seal]

And that’s all folks

[ripe wasp]

[toxic schooner]

lmfao what

[primal seal]

I knew it; my spidey senses were going off… through the Internet! At least it’s confirmed

[toxic schooner]

[primal seal]

@velvet dagger case in point above

[bright hill]

good luck sean, I believe in you!

@light needle where are your typed solutions to rudin?

I couldn't find them in your website

also, is this a bug or do you only have 2 posts in your blog?

[feral salmon]

What happened to #help-5

[light needle]

oh did i not add them? oops

yeah i havent updated my website in months rip

i can send em to u if u like tho lol

[dense belfry]

John you have a website?

Lmao

I have never looked at your bio

Well that's not true

But I've never parsed the fact that you have a website there

[light needle]

lol

[bright hill]

that'd be awesome

I like the minimalistic style btw

[light needle]

lol

[dense sorrel]

are you really sophomore tho?

[light needle]

yeah for now

[dense sorrel]

I havent seen any sophomore reading atiyah mcdonald

[light needle]

atiyah mcdonald

[dense sorrel]

wait your even reading hartshorne lol

I admire you

[light needle]

no i went with other sources

hartshorne bad

i learnt AG out of garthmanns notes

[dense sorrel]

https://www.mathematik.uni-kl.de/~gathmann/de/alggeom.php

you mean this?

[light needle]

yeah these are like p well written and honestly p light to read

unlike hartshorne which will make u want death

i didnt finish it btw, only until ch 7 or so

gonna resume the rest in the summer

[dense sorrel]

hmm

aren't class notes concise tho

[light needle]

they are but honestly just give ch1 a read u will see what i mean by light read

[dense sorrel]

i don't have necessary prerequisites but i'll give it a try

[light needle]

oh yeah just blackbox the commutative alg probs

he kinda does that

[dense sorrel]

oh okay

Lang's "algebra". Good reference, I learnt Galois theory out of it and it was pretty nice.

btw how did you even do this

[neat lintel]

HELPERS anyone alive

I NEED HELP

[long matrix]

#❓how-to-get-help

AND the channel descriptions.

[neat lintel]

We all do

[vagrant moss]

So what is tangent, like not what it's used for in triangles, I mean it's actually meaning

I think it's something to do with circles

[long matrix]

googlable

[vagrant moss]

Ok 🤷‍♂️

[neat lintel]

Best approximation by a line

[neat lintel]

This is unhelpful

[long matrix]

neither is your pretty specific definition

that does not seem to apply to the context they need

[neat lintel]

I think otherwise

[long matrix]

I think what I said is plenty helpful

You should try to look up your questions first before asking.

[neat lintel]

What? Lol

[vagrant moss]

I saw an hour long video

And that's a long video

[long matrix]

So explain how one of these lines is 'better' than the other? https://i.imgur.com/RqbykiT.png

it makes no sense.

in the context of euclidean geometry

[vagrant moss]

Yeah but how do I get tan from that

Or cos or sin

[long matrix]

Yeah you should probably look up your question

[vagrant moss]

Well what do I search?

[long matrix]

In the first place you weren't clear which 'tangent'

you were after

It's used to mean different things

[vagrant moss]

Didn't know there were others 🤷‍♂️

[long matrix]

tangent

???

Cmon...

[fiery coral]

Im so black

[neat lintel]

Looking from perspective of which point? They don't even cross on the circle

[vagrant moss]

I'm 15 what do you want from me 😔

[long matrix]

A tangent is the best linear approximation to a curve at a point would be much better

[long matrix]

uh. i think being able to look up answers to questions yourself is a skill a 15 yo should have

if you don't... then time to acquire it

[neat lintel]

If you're so knowledgeable then how about you say that in the first place instead of directing people to google things

[long matrix]

If there's something you don't get from what you look up, then by all means ask

but asking with 0 effort put in isn't the way

[long matrix]

I'm criticizing your answer because it is inaccurate
If you're going to answer, at least get it right.

[vagrant moss]

Just wanted to talk in this server mostly 😔

But whatever

[neat lintel]

It wasn't wrong

And you agreed with me just now by saying it was inaccurate

You just contradicted yourself

[long matrix]

What?

??????

Inaccurate is synonymous with incorrect/wrong

[neat lintel]

No

[long matrix]

sorry?

[vagrant moss]

why is tan(1) positive then tan(2) negative?

Like where is the pattern?

[stark birch]

Look at the definition of tan(x)

In particular, that tan(x) = sin(x)/cos(x)

[long matrix]

indeed, you want the trigonometric tangent it seems

[vagrant moss]

Yes

[stark birch]

Alternatively, interpret it from the unit circle/visual definition (well, one of them):

https://www.desmos.com/calculator/5ws8e9q60w

[frozen merlin]

it might help to look at the graph

it repeats this pattern

[vagrant moss]

Oh ok so then where did the pi/2 come from?

[frozen merlin]

so in particular since 0 < 1 < pi/2 < 2 < pi, you will get tan(1) positive but tan(2) negative

wait are you doing trig in radians or degrees

[long matrix]

I think they have no idea what tan is.........

[vagrant moss]

Either 🤷‍♂️

[long matrix]

Look it up srsly =...=

[fair mural]

there’s a huge difference depending on which you’re doing

[vagrant moss]

Pretty much, I just know how to find x on a triangle 🤷‍♂️

[frozen merlin]

there's an asymptote at pi/2 because tan(x)=sin(x)/cos(x), and cos(pi/2) = 0

[fair mural]

you can’t just say “either”

[long matrix]

now I have no idea what you mean...

[vagrant moss]

Well then what would each do?

[fair mural]

you just have to learn trigonometry

[fervent pebble]

^

[long matrix]

You are asking the wrong questions ngl

[vagrant moss]

Oh ok

[long matrix]

There's no point asking why, what, where

without even first understanding what the thing is!

[vagrant moss]

What's a correct question?

[fervent pebble]

"where can i learn more trig"

the answer is khanacademy

here i'll link

[deep mango]

Gelfand's trigonometry book

[fervent pebble]

https://khanacademy.org

[stark birch]

have a link - https://www.khanacademy.org/math/trigonometry

[vagrant moss]

XD thank you

[fervent pebble]

whenever i see gelfand i think of the chess player 💀

[deep mango]

Israel Gelfand is one of the best mathematicians of all time

Just look at this shit

and somehow even though he's so accomplished and smart, his books for high school math are also really good!

[fervent pebble]

huh

that's actually pretty sick

[light needle]

Gelfand transforms make me coom

[deep mango]

like usually it doesn't work that way

[frozen merlin]

also lasker of the lasker-noether theorem is the same guy who was world chess champion for 27 years

[deep mango]

Wow

That's cool

[fervent pebble]

ooh i knew that much

lasker was dominant

except kindaaaaa disputed?

a little?

his brother has one of the most famous king walk games of all time

[neat lintel]

Very well hidden lol 😂

[long matrix]

@ mniip, rename it to locked to stop these fools from complaining

[cold needle]

i think its funny that its hidden but not really hidden at all

[modern geyser]

it is indeed not hidden

because everyone can see it

[ripe wasp]

i always wondered

why r those channels hidden

is it bc it would clutter up the available math help channel too much if they were all there

[limber thunder]

yeah you don't want 42 help channels at all times

[ripe wasp]

yeah good point

[rich grove]

the current system is shockingly well designed

I'm used to much more inefficiency in big servers

[charred mortar]

yeah it's pretty efficient here

occasionally you have the weirdos who somehow don't see the clearly visible help channels and ask their questions here, but for the most part it's good

[fervent pebble]

occasionally?

[limber thunder]

occasionally

I wish

weirdos, more like pampered children who just want people to answer their HW or w/e

[charred mortar]

yeah fair

[silk flower]

Chemistry has math right?

so can I send help here for our chemistry assignment?

[ripe wasp]

i mean just because one part of chemistry has math doesn't imply ur chem hw is gonna have math

but if it is the math part you need help with, sure

just use #❓how-to-get-help

[long matrix]

We should try this

then i dont have to see anything here

[flint canyon]

Physical/General chemistry does involve mathematical approach and calculations

So yea

[cyan goblet]

can someone explain an eigenstate to me as if i were five

the definitions online just arent clicking

as if i were five with understanding of basic quantum mechanics*

[static loom]

do you know what an eigenvalue and eigenvector are?

[rocky shuttle]

A typical 5 years old person does not, ig

[static loom]

I agree but I'm not gonna waste time reexplaining something they already know for the sake of a fantasy

trying to gauge what this person really knows first lol

[cyan goblet]

ye

i get that eigenvectors are referred to as eigenstates in quantum mechanics, i just can't draw the connection

[static loom]

eigenvalues are the results you can get from doing an experiment and those correspond to your distinct observable states, those are your eigenstates

generically speaking your state is a superposition of these which is basically your probability distribution for how to get the outcome of doing your experiment

[cyan goblet]

oh i see

[static loom]

it probably helps to focus on the double slit experiment

remember, these operators are hermitian so they have all real eigenvalues and distinct eigenvalues correspond to orthogonal eigenvectors (well, eigenspaces)

[cyan goblet]

mhm

[static loom]

when you make a measurement, you're doing a projection, that's the "collapse of the wavefunction"

[cyan goblet]

i dont think ive learned about wavefunction yet but continue

[static loom]

no

[cyan goblet]

i know the collapse part

oh

[static loom]

like I'd rather not just ramble

but I'll have dialogue with you

[cyan goblet]

mkay

so ik that observing an observable collapses it into a state right?

like measuring spin up/down on z axis of a particle will collapse the particle into either spin up or spin down

[static loom]

sure

[cyan goblet]

is eigenstate then just a measured state of a particle?

like if we measured spin up, then that is its eigenstate?

[static loom]

think of eigen-anything as being relative to a specific operator

[cyan goblet]

mkay

[static loom]

so like if you're measuring up/down you have its corresponding eigenstates because the operator simply scales by the eigenvalue

[cyan goblet]

mhm

[static loom]

but up is a superposition of left and right, which are not eigenstates of that operator

but they are eigenstates of their own corresponding operator

it's really just linear algebra, eigenstate is just an eigenvector of a linear operator

[cyan goblet]

so like up would be the eigenstate of an operator on up/down?

[static loom]

yeah

[cyan goblet]

ohhhh okay

tyvm

[static loom]

then it's a kind of important thing to look for, what operators can be simultaneously diagonalized in a basis

[cyan goblet]

i just got to simultaneous diag/triangulization in h+k lol

idk if spelled that right

[static loom]

like when you're looking at certain properties you will find that certain states in one basis are a superposition of multiple states in another basis

like how up is a linear combination of left and right or position is a fourier transform of momentum stuff like this, you can't ever cleanly measure both exactly because one is literally made up of multiples of the other

[cyan goblet]

ohh i see

[static loom]

so for two things like this, that trickles through in looking at their standard deviations as being bounded below by the expectation of a multiple of the expectation value of their commutator

that's your heisenberg uncertainty principle

[cyan goblet]

aha

learned about the uncertainty principle but never drew that connection ig

makes sense now

[static loom]

well it makes (a little) more sense when you derive it yourself directly from the representation

[timid spindle]

there is is thing called critical state

after which a material fails

it turns out critical state surface is a tensor

it's looks kinda cool

if you plot

it

[bright hill]

bertrand russel is cool

[dense sorrel]

actually his book on philosophy is good too

https://www.amazon.com/History-Western-Philosophy-Bertrand-Russell/dp/0671201581

[bright hill]

what do you guys think of proofs such as these?

I feel like I don't learn much other than proof reading

they look elegant and simple

and they do make sense

but the arguments seem like they were knit out of thin air

[primal seal]

🙄

That’s Rudin

How are you at all surprised

[dire mulch]

I feel you on this. But it's rudin.

I guess you should ask question. why does he use the conjugate of b_j instead of using b_j. When do we have lhs is equal to rhs.

[bright hill]

that's a good idea

[dire mulch]

But you can just move on.

[bright hill]

do you think attempting to prove the theorem beforehand is helpful?

and should I spend too much time on that?

"only"

[dire mulch]

Some people will say yes. But for me sometime I do, sometimes I don't.

[bright hill]

[primal seal]

@bright hill what is your background and experience?

What are your goals through reading the book?

[bright hill]

for the memes?

obviously

[dire mulch]

Doing rudin because I like analysis. Also the way he does stuff makes it fun. I am not a side character when reading rudin.

[bright hill]

but seriously tho, I wanted to know what rudin was like and see what everyone is talking about

[dire mulch]

Pencil and paper, writing stuff down. Trying to figure out what he is saying. Using other resources.

That is fun for me.

[brave hollow]

random question plegasus, irrelevant to this conversation but

[primal seal]

@dire mulch certainly; the way it was intended to be done

[brave hollow]

are you into masochism by any chance?

[dire mulch]

lol I don't think so.

[brave hollow]

well I am :)

[bright hill]

well, I certainly am

[brave hollow]

you can use this info however you like

[primal seal]

Whats your background? It’s not exactly a self contained book, so that may be a problem

[bright hill]

took that out of my mouth smh

[primal seal]

At least in terms of “maturity” requirements

[dire mulch]

Also I did a few chapters of abbot understanding analysis before starting. So I already have the so called maturity.

[bright hill]

not much

a few chapters of hubberd

I'm just starting to seriously learn maths

[primal seal]

Ah ok; it might help to try a different analysis book- they’ll have the same info but others can be better at explaining things

[charred mortar]

I’d probably end up using another analysis book for exposition and coming back to Rudin for some of the exercises tbh

[primal seal]

And having friendlier exercises

Lol

Confirmed

[brave hollow]

if you are not starting analysis with papa rudin are you even doing analysis?

[bright hill]

[dire mulch]

lol.

[bright hill]

that seems like good advice

[primal seal]

But if you want an answer to your question

[dire mulch]

papa rudin .

[primal seal]

If you get stuck on a proof usually 2-3 days of thinking about it is decent

[bright hill]

you mean diy style or just reading the proof?

[primal seal]

Read the theorem and try the proof without looking

[dire mulch]

DarQ try using other references if you want to stick with rudin.

[primal seal]

Give yourself 2-3 days before asking for help

Then get s hint

2-3 more days

Etc..

[bright hill]

he was 28 tho

[brave hollow]

maybe you can say he duked it out during his thesis defense

[bright hill]

I think I'll do that

[dire mulch]

https://www.math.ucdavis.edu/~hunter/intro_analysis_pdf/intro_analysis.pdf

My favorite one I use.

[bright hill]

but I'm just doing rudin on a whim so I'll go back to calc 3 after finishing like,

point set

[dire mulch]

lol I haven't done calc 3 yet.

Still stuck doing analysis and linear algebra.

[bright hill]

cool

hubberd is really good if you want to do calc 3 and lin alg at the same time

that's what I'm doing

[dire mulch]

Probably going to calc on manifold by spivak.

[dire mulch]

That's a big book.

[bright hill]

it covers a lot

more than 3 courses, someone told me

[primal seal]

These guys are just talking

[brave hollow]

lucy is your pfp a popular math/physics youtuber?

idk she reminded me of some1 on youtube

[bright hill]

I thought it was you

[toxic schooner]

who?

[bright hill]

lmaoooo

[toxic schooner]

[brave hollow]

it would be weird if some1 had a gif file of themselves saved as their pfp

[toxic schooner]

chrew

[brave hollow]

physics girl

I think

[dire mulch]

The content looks nice.

[bright hill]

have you met the guys around here?

[brave hollow]

yeah there's only a few people with their own mug as their pfp let alone gif :/

[bright hill]

wut

hubberd has 800 pages lmfao

[bright hill]

that's not what I meant lol

[toxic schooner]

[toxic schooner]

[bright hill]

nah, the first chapter is pretty easy tbh

[dire mulch]

Yep.

[bright hill]

haven't seen the exercises yet tho

[dire mulch]

I was more excited to get to chapter 2, so I only did half of the exercises in chapter 1.

[fair mural]

doing half the exercises of a chapter is good though

[grand axle]

What should I learn first: advanced calculus or advanced chemistry, or should i learn both at the same time

[dire mulch]

Lol is that a typo.

advanced chemistry?

[grand axle]

What part of it do you think is a typo

[dire mulch]

nvm.

[grand axle]

But I guess advanced is the wrong word, I'm just thinking stuff like electrochem and thermochem to get ahead

[dire mulch]

I meant it more like I thought it was typo comparing those two subjects.

[grand axle]

Ahhh

What you are saying is that they are different in terms of difficulty?

[dire mulch]

No, nvm. I was mistaken.

[grand axle]

Ah, no worries

[dire mulch]

If you can manage both do both. But I would will pick advanced calculus.

Since I don’t like chemistry.

[grand axle]

Makes sense

[toxic schooner]

based

[grand axle]

I've already started taking notes on advanced calc

[fair mural]

nah just correct

[toxic schooner]

even more based

[dire mulch]

Leave us alone.

[primal seal]

You can do both I’d say, but how are you defining ‘advanced chemistry?’

[grand axle]

That is a good question, and to be honest I'm not entirely sure

[primal seal]

Yeah then if you’re just building up start learning both

[grand axle]

I'm not even sure how I am defining advanced calculus

[dire mulch]

Advanced calculus all I think about is spivak calculus.

[fair mural]

do you just mean analysis

[grand axle]

I probably better start with basic calculus

[primal seal]

Some calc shows up early on in things like higher-order rate laws; but you don’t really need to understand it formally, just computationally

Yeah basic calc and basic Chem work well together

[grand axle]

I don't know a lot of calculus, and my knowledge is spread throughout.

[dire mulch]

That is normal if you haven’t study/taken calculus yet.

[primal seal]

It’s mostly differential calculus early on

Reaction Kinetics/rate laws

[grand axle]

Yeah I don't know why I said advanced calculus 😂

[random bronze]

What

[primal seal]

Some diff Eq maybe for radioactive decay and such

[grand axle]

Yeah I did notice that zero-order, first-order, and second-order uses derivatives

[random bronze]

what is advanced calculus

[dire mulch]

Usually intro analysis.

Something like spivak calculus.

[grand axle]

[A] = -kt + [A]o -> ln[A] = -kt + ln[A]o -> 1/[A] = kt + 1/[A]o

[primal seal]

Looks right

About to get in the car though so can’t confirm

[grand axle]

No problem

I looked it up

[primal seal]

Advanced calc is usually the in-between class that marks the point at which you can’t just fall asleep in class anymore and expect to understand things

Cool ok

[random bronze]

Interesting

[grand axle]

latural nog

[fathom swallow]

The current time for DarQ is 09:06 PM (CEST) on Fri, 08/04/2022.

[vocal jewel]

,ti

[fathom swallow]

You haven't set your timezone! Set it using the interactive timezone picker with ,ti --set.

[vocal jewel]

,ti --set

[fathom swallow]

Your timezone has been set to Europe/Paris!
Your current time is 09:15 PM (CEST) on Fri, 08/04/2022.

[vocal jewel]

,ti

[fathom swallow]

The current time for ................................ is 09:15 PM (CEST) on Fri, 08/04/2022.

[random bronze]

,ti

[fathom swallow]

You haven't set your timezone! Set it using the interactive timezone picker with ,ti --set.

[random bronze]

,ti --set

[fathom swallow]

Your timezone has been set to America/Detroit!
Your current time is 05:05 PM (EDT) on Fri, 08/04/2022.

[random bronze]

,ti

[fathom swallow]

The current time for Clive is 05:06 PM (EDT) on Fri, 08/04/2022.

[swift sinew]

@vocal jewel @random bronze
In the future, this stuff is better suited for #bots or #latex-testing

[mild echo]

hey guys, not sure if the news was broken here (I did a few searches but nothing came up) but I'll put it up anyways.

Michael David Spivak was born May 25, 1940, in Queens, New York.
He died October 1, 2020, in Houston, Texas.
He suffered a broken hip earlier in the fall, and had been confined to an extended care facility following that mishap.
—Obituary in TUGboat Vol 42 by Barbara Beeton (https://www.tug.org/TUGboat/tb42-3/tb132beeton-spivak.pdf)
(emphasis added by me)

Information about his death was very slow to reach most of his colleagues and collaborators (afaik, the news only broke around October 2021, a year after his death), so I just wanted to put it out there. There were previously rumours of his demise and so on, but this is just to give some closure to anyone who may have been concerned.

since there is a lot of discussion about his books etc, I thought it may have been appropriate to just let people know.

Most of his books are available via the Hindustan Publishing Corporation, although many other texts by the Publish-or-Perish Press aren't at the moment.

ah, I just found a discussion talking about the first edit on Wikipedia; it was unfortunately correct, but now there is a proper source in his obituary linked above.

[fervent pebble]

yeah, i actually learned he was dead yesterday :(

tragedy

well

he'll live on forever in his writing

[limber thunder]

is he really

I've seen it come up in searches but nothing confirms nor denies the claim

[fervent pebble]

yeah, spivak's dead

it's on his wiki

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

[fair mural]

i’m sorry but

[tender tulip]

Let’s say you have a complex Laurent series with a radius of convergence R, could you determine it’s behavior on the boundary by substituting z for Re^it

[vivid halo]

perhaps, but note that the behavior on the boundary can be pretty bad

for instance you can have power series with radius of convergence 1 that converge nowhere on the boundary, or converge at exactly 1 point on the boundary

[tender tulip]

I know

[vivid halo]

yeah just saying that you probably need more than just doing a basic variable substitution to check the behavior

like you can do this substitution, then what?

how can you use this to see e.g. that every convergence set has to be F_\sigma\delta

[tender tulip]

This came out of random thinking about summing over (x^n - x^-n)/n

for n natural

[vocal jewel]

Alright thanks

[mint patio]

Are moments "linear"? Idk if that's the right word

I think it is

Say you have a random variable X = A + B + C + ...

Then the pdf of X will be the sum of pdfs of A, B, C, ...

[sturdy bluff]

anything linear is basically proportional

[mint patio]

And E[X^n] = int x^n * f_X(x), where f_X(x) is the pdf for X

[sturdy bluff]

x go up y go up

etc

[mint patio]

Then just decompose f_X(x) as f_A(x) + f_B(x) + f_C(x) ... and distribute the x^n and then split the integrals up (linearity) and convert those into expected values

[lone carbon]

God I love fractals
https://www.desmos.com/calculator/g7bz6azse2

just wanted to share that

[mint patio]

I AM IDIOT THIS IS NOT TRUE

[fervent pebble]

lmfao

[limber thunder]

I see, the claim wasn't confirmed until nov last year according to https://en.wikipedia.org/wiki/Talk:Michael_Spivak#Dead?_(2020)

[static loom]

fun question for you, what's the height of the maximum points on the graph?

obviously you can't use the standard calculus trick of f'(x)=0 and solve for x because it's not differentiable

solution: ||https://www.desmos.com/calculator/5gb3dev0e7||

[lone carbon]

ooh that is a good one. I can see visually it's 4/3 but it's not clear why

just playing around in Desmos it seems the trick is to add terms two at a time instead of one at a time to get those flat intervals where it's at the maximum

and then you get 1 + 1/4 +1/16 + etc

the solution you gave is obv a lot cleaner 😅

[wind abyss]

ooh mero that’s beautiful

[dense ledge]

do you guys know a software for digital writing? I'll use my drawing tab to do math scratches. Any suggestions?

With smoothing feature please

[stark birch]

OneNote is common enough.

Could also literally just use MS Paint, that's more my vibe. I also used Microsoft Whiteboard a few semesters back for teaching a class (I forget why, I think MS Paint wasn't playing nice with my art tablet?)

[dense ledge]

I tried onenote but I'm not getting use to it. Ms paint sucks, you can see the squigliness.

I want it with a photoshop smoothing brush effect

[stark birch]

Oh I missed the bit about smoothing. My bad.

[dense ledge]

I have a very hideous handwriting so I need that

[toxic schooner]

i like Xournal++

[toxic schooner]

[bronze pelican]

Mspaint is for when I need to make quick notes

That don't need to be saved

OneNote is for more formal online presentations, things i need to prepare in advance

[toxic schooner]

i hate ms products

they never work nicely for me

[dense ledge]

it doesn't have smoothing option, right?

[toxic schooner]

it has some extent of it ig?

it smooths out lines and stuff

not sure about handwriting

[dense ledge]

yea it has a bit. It's actually better than MS. I'll still look for better. Thanks for the reco.

[frozen merlin]

could you also get the height straight up by solving h = 1 + h/4 ?

[devout nacelle]

Xournal++ is the one I use as well

I'm not sure about smoothing features but it's good enough for my usage

[delicate knoll]

Guys, how would you write good morning using math expressions where mathy people would understand?

Silly,but I drink to much coffee to by the way

[vast surge]

$\mathfrak{good}\text{ }\mathfrak{morning}$

[fathom swallow]

Zorn's Lemon

[delicate knoll]

I think the nable gradient would a start

[delicate knoll]

I am with the concepts

It strange explaim this

Analogous

I would use gradient for first step
$\nabla$

[fathom swallow]

THCampbell

[delicate knoll]

Humm

[delicate knoll]

With maths notation comrade

[ripe wasp]

$\mathbb{G} \mathbb{O} \mathbb{O} \mathbb{D} \ \mathbb{M} \mathbb{O} \mathbb{R} \mathbb{N} \mathbb{I} \mathbb{N} \mathbb{G}$

[fathom swallow]

sean

[vast surge]

@delicate knoll

[delicate knoll]

i would like some king of equation that would describe the phenomena

i working that out by using nabla

i know it silly, but c´mon let man dream a bit with possibility

and to impress a girl

[vast surge]

Let $S={\text{mornings}}$. Theorem: For all $x\in S$, $x$ is good.

[fathom swallow]

Zorn's Lemon

[ripe wasp]

u could use like quantifiers to make it look more math-y ig

[vast surge]

Also just use this: https://www.desmos.com/calculator/ke8mqdod5e

[delicate knoll]

she really like maths, but i cannot step that futher yet if you know what i mean

[vast surge]

I do not.

[toxic schooner]

zorn here only knows maths

feelings and "knowing what i mean" are things beyond them

[vast surge]

And I'm not even good at maths!

[cyan goblet]

i one up you

,w ContourPlot3D[(x^2 + 9/4 y^2 + z^2 - 1)^3 - x^2 z^3 - 9/(200) y^2 z^3 == 0, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}]

[fathom swallow]

Results provided by WolframAlpha

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

Requested by anamono#1010

[cyan goblet]

[vast surge]

Okay someone in #discussion suggested "UwU let's do math together". You could try that?

[cyan goblet]

LMFAOO

[vast surge]

Or, if you guys have done complex anal, you could ask her to leave a residue around your pole.

(sorry, I was being gross there)

[cyan goblet]

i gotta write these down

[ripe wasp]

oh my god

[hushed turret]

that's a pretty good one

[ripe wasp]

thats actually a good one

[toxic schooner]

explain

i dont get it

😭

[vast surge]

I'm not explaining the part of it that's dirty to you, but it was a pun on Cauchy's residue theorem

[toxic schooner]

explain the dirty part

😭

[vast surge]

butt sex

[ripe wasp]

you could also say something about the hairy ball theorem 😏

[toxic schooner]

how is residue theorem related to butt sex thonk

[mild echo]

the source used in the wikipedia article is the one i've linked. his obituary in tugboat (the TeX Users Group journal, since he was active with the developement of AMS-TeX) is at the moment the only easily available source.

it's not helped by the fact there have been rumours of his death for years now.

so sadly no more parts to the Physics for Mathematicians series.

[vast surge]

I'll explain when you're older.

[toxic schooner]

im 18 what are u saying

[vast surge]

I'll explain it to you when you're older

[toxic schooner]

fine whatever

[vast surge]

After you've taken complex analysis

[toxic schooner]

goddamn it

that will be like

at least a year from now

not fair 😭

[delicate knoll]

"pin heart"

[delicate knoll]

pardon, what?

[vast surge]

Hey, it might work. You could also try my complex analysis suggestion.

[vast surge]

To impress the girl, I should have clarified.

[delicate knoll]

oh you mean, me and her doing maths togerther?

[delicate knoll]

she does not understand complex analysis.

[vast surge]

I mean, honestly, yeah. It's less tacky, you guys both like math, and it'll give you time to get to know her better to see if you actually like her as a person or if you're just infatuated. If you get to a point where you're comfortable, also feel free to just point-blank ask her out. No cheesy lines or anything; just actually ask her.

Unless I'm misunderstanding you; you did only say that you want to impress her, not that your interest was romantic.

[supple totem]

Hi. I am planning to move to Canada. If there are people here who are also interested, please write to me. I am looking for people who are planning to immigrate to Canada)

[vast surge]

I'm in parts of upstate New York which are illegally occupied by Canada, as is evident by the presence of Tim Hortons. Is that close enough?

[supple totem]

._.

[delicate knoll]

well i wanna impress her and step further into romantic thing.
i send to her poem about math equation...Actually was transforming mathematical physical equation into a poem, because, well we can see the formulas is analogous a poem about the workings of our universe .

[delicate knoll]

well i gonna try ask her to do math. i just need to right moment

[delicate knoll]

thanks for advice

you are nice Guy

[delicate knoll]

ah and she likes the poem

[odd narwhal]

I just took it to mean secretions

I won't elaborate further

[fair mural]

that joke is actually disgusting

[sleek wing]

LOL

[vast surge]

I mean yeah it's really quite gross.

[cold needle]

no more pls

[limber thunder]

yeah I was reading this just the other day, seemed interesting

[stray kite]

apparently this year at some point there is suppoesd to be smth in AMS notices confirming it

some guy in the wiki talk page said so lol [i know very good source][

[sick burrow]

Where can I find the ceo of geometry

I just wanna talk

[odd narwhal]

Which one

[rocky shuttle]

Euclidean geometry?

[sick burrow]

Euclidean geometry especially

[rocky shuttle]

He died

[sick burrow]

But really the ceo of all forms of geometry

Actually algebraic geometry seems kinda cool though I don't know any

Diffgeo can go to hell though

[fervent pebble]

im the ceo

wdyw

[sick burrow]

🗡️

[fervent pebble]

hmmmm

you want a knife?

nah

ryc typing 👀

[rocky shuttle]

Someone's picking a fight with geometers

[deep mango]

Unfortunately your arch nemesis also has a sword: 🐧🗡️

[fervent pebble]

ryc is a penguin?

[deep mango]

No

Brofibration

[sick burrow]

You're holding the knife wrong

🐧 🔪

[deep mango]

Oh yeah they should be switched

[sick burrow]

Is what you want

[deep mango]

Thanks

I'm not holding the sword though

Also I don't like geometry

Well I do but I have geometry hw to do rn which I don't want to do

[sick burrow]

Holy shit based ryc

[deep mango]

I have to compute the coefficients of the riemann curvature tensor in arbitrary coordinates

[rocky shuttle]

Urgh

Why not do it coordinate-free

[sick burrow]

I despite any computations involving trig functions

[deep mango]

The problem is literally just to compute them, we did everything coordinate free in lecture

It's fine

[rocky shuttle]

Phew, that's good

[deep mango]

I much prefer how we learned it to how I learned it in undergrad

Which was "here's the definition in coordinates, somehow by some magic it corresponds to holonomy of parallel transport"

[rocky shuttle]

Yeah, I also hated Christoffel symbols before doing it coordinate-free

[delicate knoll]

"Pin heart2"

[narrow sedge]

hi guys im new but i hope we will all get along ❤️

[deep mango]

Welcome!

[tender tulip]

Can I simply define the symmetric group as (set) automorphisms

because I’m proving it the order of S_n is n! through the stabilizer of every element having cardinality (n-1), and proceeding with flat out saying that the cardinality of the orbit is the cardinality of S_(n-1) by def, of which the orbit is “set isomorphic” to S_n/stab(x), so you can use Lagrange’s theorem

[deep mango]

Yes

But careful to specify set

[tender tulip]

Let x_n be an arbitrary element, S_0 = {}, S_(n+1) = S_n union {x_(n+1)}

Just use a different variable for the group

[torn willow]

I think I have a new perspective on induction.(or maybe this is really really obvious)
So you start with a base set satisfying property X. The induction step involves adding more elements to the set using the fact that elements of the base set have X.

You can say X holds for all elements in some set A,if there exists a non empty base set with X and given any element a in A,you can eventually get it in X in a finite number of steps

Well,This is a bit more nuanced than that

And is not limited to natural numbers

According to this perspective strong and weak induction are clearly the same thing

[sick burrow]

Wait what is the regular perspective on induction that isn't that?

[torn willow]

I have no idea

Maybe this is the regular perspective?

[sick burrow]

The chad perspective on induction is deriving a contradiction from a minimal element not satisfying the property

Because then you can induct on the ordinals

[torn willow]

That is generalisable to more than just N right?

I am looking for a definition of induction that's as "general" as possible

[sick burrow]

Yeah that's how you do transfinite induction

[swift sinew]

https://proofwiki.org/wiki/Principle_of_Mathematical_Induction/Peano_Structure

This might suit your fancy

[sick burrow]

I feel like transfinite induction is better/more general

[torn willow]

Doesn't Peano Structure always reduce to something bijective to N

[swift sinew]

After glancing at it, I think you’re right. But that’s too out of my wheelhouse for me to contribute valuable input

[sick burrow]

Peano structure is unique

isn't this just... trivially false?

by Lowenheim-Skolem

https://proofwiki.org/wiki/Peano_Structure_is_Unique

seriously though what the fuck is this

I'm trying to read their "proof" to find the issue but the notation is so bad it's difficult

[acoustic surge]

0'

[sick burrow]

that's not even that bad

certainly isn't the worst part

so it seems they just casually assume that P is N?

[swift sinew]

Maybe the induction principle regarding wffs is what he’s looking for

[sick burrow]

wffs?

[swift sinew]

Well-formed formulas

https://proofwiki.org/wiki/Principle_of_Structural_Induction

[sick burrow]

wait so how is that related to the "uniqueness" of Peano structures?

[swift sinew]

I wasn’t intending for it to be. I was referring to Bye’s inquiry into the most general form of induction

[sick burrow]

I'm not sure how much I trust proofwiki now given that they stated and "proved" a "theorem" that's verifiably false

[fervent pebble]

proofwiki is dumb as fuck

gods some of the things there are idiotic

[sick burrow]

what else do they say

[swift sinew]

I’m still a bit confused on your claim that this is false

[sick burrow]

are you familiar with the Lowenhim-Skolem theorem?

[swift sinew]

Admittedly, no

[sick burrow]

it states that if a first order theory in a countable language has an infinite model then it has a model of all infinite cardinalities

so in particular, Peano Arithmetic has an uncountable model

how do you find a bijection between that and N

[fervent pebble]

with big brain

[sick burrow]

I mean it's a trick question because uncountable sets don't exist and all of modern mathematics is a lie

https://cdn.discordapp.com/attachments/596513400922701825/951597752570236998/20220310_164934.jpg

[devout nacelle]

Do Peano Axioms actually constitute a first order theory?

[sick burrow]

I think so

[devout nacelle]

Wikipedia says induction is second order

[devout nacelle]

So I guess this holds

[fervent pebble]

this meme would be better with \aleph than \omega

[devout nacelle]

I vaguely remembered Tao mentioning something along these lines in Analysis 1

[fervent pebble]

manan did u go to ucla

also were u a cali resident?

[devout nacelle]

No and no

[fervent pebble]

wat

was tao not always at ucla or smthn?

[devout nacelle]

Oh I was referring to his book, Analysis 1

Not any class with him haha

[fervent pebble]

ohhhhh

[light needle]

no manan signed up for his masterclass

[devout nacelle]

10/10 you can't call yourself a real mathematician if you don't pay for his masterclass

[toxic schooner]

so true..............

[vast surge]

Is his masterclass worth getting?

[delicate knoll]

counter argument where you start to counting between 0 and 1?

[delicate knoll]

oh if you dont have degree

consider a open interval

what is next?

[primal seal]

Yeah Tao is here

Has one of the funniest faculty webpages that exist I think

Basically tells everyone who’s trying to see/meet/email him to F off

😂

It’s great

[toxic schooner]

?

where

[hushed turret]

he's not quite so abrasive about it

[charred mortar]

We’ll never know who’s really tao here

[torn willow]

It's clearly Terrence Tao

[rocky shuttle]

@ tao

[toxic schooner]

i am tao

[neat frost]

Yesh

[shadow glacier]

What to do with a method which produces all the correct results for a certain example, but doesn't work when generalized.
Is the method correct?

[toxic schooner]

😌

[neat frost]

If the method is correct, then the method is correct

Extreme example: Algorithms for addition work for addition but don’t work generally for all operations

Doesn’t mean the algorithm isn’t correct

It’s just meant for a specific case (addition)

[shadow glacier]

An algorithm that works for all cases that you care about, but not all?

[neat frost]

Again

It depends

Sometimes there won’t be a general algorithm

Obviously if there does exist a general algorithm, then in most cases it is preferable to one that works only under specific conditions

[shadow glacier]

The one that works only under specific conditions doesn't feel like the "true" or "correct" algorithm.

[neat frost]

It depends on what you’re trying to do

[shadow glacier]

Hmm

[lunar spear]

Everyone who isn't from finland is missing out smh, we have ville to help us with math

[swift sinew]

I do miss how gamy the burgers were in Finland

[loud iris]

Villi

[lunar spear]

ville

[neat lintel]

did you know jesus is a lir

he called it the last supper

he knew it was going to be his last

he planned it from the start

[swift sinew]

Haven't you already been muted once or twice? Why ping me with this stupid shit

[fervent pebble]

pogggg my parents are finally getting me tested for adhd

[limber thunder]

pog I guess

[fair mural]

[fervent pebble]

shush

im gonna get adderall 😎

[signal glacier]

I started on adderall a few days ago

[wind abyss]

is it nice?

[neat lintel]

hey guys

are there any periodic functions aside of trigonometric ones?

[surreal sapphire]

constant functions

[hushed turret]

f(x) = x mod n

[static loom]

pick an interval [a,b]

now define any function on it

[swift sinew]

Differentiability wouldn’t affect the infinitude of this set

[static loom]

now repeat this left and right, done

another fun periodic function is f(x) = 1 if x is rational, 0 if x is irrational

[hushed turret]

o wait im dumb

[fleet raptor]

Series for integral x^-x what you think?

[inner finch]

beautiful

[sleek wing]

maths truly is beautiful

[neat frost]

[fleet raptor]

Yes

[frozen merlin]

cos(0x)

[neat frost]

Wew when are you gonna change your name to "Penis Wall"?

[sleek wing]

shaking my head

[neat frost]

shaking my smh

[brave hollow]

nice pfp wew

where'd you get it

[sleek wing]

internet

[brave hollow]

I thought it was a selfie

[fleet raptor]

When evaluated from 0 to 1 the integral equals the descrte sum from 1 to inftnty

Just beautiful

[sleek wing]

yeah hahahahhahah

[neat frost]

It is

Someone doxxed him, uploaded a selfie to the internet, wew found it and made it his pfp

[fleet raptor]

Mans built like a tomato

[neat lintel]

So the non-zero-ity of rational numbers, and only rational numbers make a periodic?

How stunning.

[inner finch]

among us

[neat lintel]

nah

its a fact about f(x)=f(x+p) for all x there is a fixed p and we know that this doesnt hold for all irrational numbers

i put it badly and wrongly

but more like irrationals and rationals stay what they are upon rational addition

The fact that the function changes from 1 to 0 in no time is just wow

[neat lintel]

lol

it isnt continuous so yeah

So it can't be differentiable?

[static loom]

not a chance, for a limit to converge all its subsequences must converge to the same thing, so you can pick your values to be purely rational or irrational to make the limit of the difference quotient to go two separate things

[neat lintel]

This begs the question

Are there more irrationals than rationals?

[fair mural]

yes

[long matrix]

'more'

the rationals are countable, the irrationals are not

[fair mural]

bigger infinites shuri

[long matrix]

if thats some indication

[fervent pebble]

gods imagine believing in bigger infinities

[neat lintel]

How come?

They don't go in one direction

Or anything

[fervent pebble]

look up cantor's diagonalization argument

[neat lintel]

ok

[fervent pebble]

and also a proof of density in r of q

[cyan goblet]

ok i feel like i cannot wrap my head around what spin is

like ive watched youtube videos and stuff and i get that an electron isnt literally spinning

and spin is the "intrinsic angular momentum" but i have no clue how to interpret that

ive also read some sources that compare spin to magnetic moment?

so like would this be spin up on z axis?

shitty drawing courtesy of ms paint and my mouse

[ancient flame]

what the fuck am I looking at

[cyan goblet]

my attempt at an electron

[ancient flame]

that looks obscene

[cyan goblet]

yeah...

[ancient flame]

you committed a war crime

but yeah maybe ask on the physics discord lol idk

[cyan goblet]

blo once said that we have better physics majors than the physics server

[ancient flame]

oh damn

[steep mountain]

no.

[leaden torrent]

mathematical contrivance

are you learning this from a book or from wikipedia articles

if youre learning it from a book, just look at the worked examples

or the exercises or w/e

[cyan goblet]

im reading McIntyre

[leaden torrent]

then yeah, stop trying to intuit it and just view it as a mathematical quality

[cyan goblet]

shit

man that sucks

ive been trying to visualize it

[ancient flame]

mathematical contraband

[sonic ether]

even andrew doesnt know what spin is

intuitively

[cyan goblet]

like that one physics youtuber?

[neat lintel]

https://tenor.com/view/cat-funny-cat-cat-playing-cat-gif-black-cat-gif-19037766

[neat lintel]

lol

u drew hairy balls

[neat lintel]

lol who the fuck andrew