serious-discussion

[mortal oasis]

im pretty sure there is evidence that sexuality is for sure mutable i just think its kinda dangerous to study atm

[sick burrow]

Not that I doubt you, it just wasn't something I'd really considered.c

[sharp mulch]

I only took the first one

I don't see why sexuality shouldn't be mutable

[vast surge]

Oh yeah it can definitely be misused to justify like conversion therapy or shit like that

[sick burrow]

Because people will use it to justify conversion therapy?

[mortal oasis]

im pretty sure i have heard that men in prison slowly become attrached to men

ya

[sick burrow]

Oh yeah I was gonna say

[mortal oasis]

or they didnt admit it before

[sharp mulch]

I mean not in a "force people to change their sexuality against their will"

But in a like

[mortal oasis]

no of course not

[sick burrow]

Yeah obviously

[sharp mulch]

People change over time and there's no reason their sexualities shouldn't change with them

[mortal oasis]

its just a dangerous thing to study given today's climate that it could be used for that

[vast surge]

My headcanon is that 90% of "straight people" are somewhere in the pan-to-ace spectrum but are straight passing enough and satisfied enough with straight stuff that they don't question it.

[mortal oasis]

wouldnt everyone be in the pan to ace spectrum

[sharp mulch]

[sick burrow]

See I think people don't understand the difference between "can change over time", "can be changed with effort", and "can be changed at will"

[vast surge]

I guess technically, but I meant like somewhere not 100% heterosexual

[mortal oasis]

ah

[vast surge]

Like, the sheer number of "straight" girls I know who have acted more attracted to girls than "straight" guys I know, for example

As far as my family's concerned I'm straight and just single, but I'm probably very (somewhere between demisexual and graysexual)

[sharp mulch]

I feel like most women I know have some level of sapphic vibes to them

Maybe it's because I only hang out with the queers though

[vast surge]

Yeah I think maybe 75% of my real life friends are lesbians now that I think about it

[mortal oasis]

honestly im pretty positive im 100% straight

like i have given it enough thought

tried it

didnt like it

[vivid halo]

valid

[vast surge]

Yeah, that's valid.

What I mean is, like, bi men who have only been with women and consider themselves straight even though they're also attracted to men but just never act on it or even introspect on it, for example, I think are way more common than actual straight people.

[sick burrow]

Are they?

[vivid halo]

I maybe wouldn't say this is more common than "actual straight people" but yes I agree this is relatively common

[vast surge]

I mean, if we take a brief look at ancient history, say, ancient Athens or Rome, we see 95% of the population is bi.

[mortal oasis]

are they

im pretty sure that is wildy exaggreted

[vivid halo]

oh sure, but those things can change over time

[mortal oasis]

maybe sparta

and also if im not mistaken there was a lot of stigma around it

[sick burrow]

I also wonder if there's something to be said for the fact that society puts more pressure on women to care about their appearance leading to more people being attracted to women overall

[mortal oasis]

still

[static loom]

where is this data coming from

and did you forget to wipe after producing some of it? 🤔

[vivid halo]

there's no reason to expect that sexual proclivities are going to be distributed in the same way across societies and across history

[mortal oasis]

thats a SENTENCE

honesttly true tho

[vast surge]

From Achilles and Patroclus being straight best friends.

[thorn brook]

Tokidoki Lokidoki

[mortal oasis]

I mean i know julius ceasar was a bottom

[static loom]

he took it in the rear 😏

[brave hollow]

now kith

[vast surge]

It's the being a bottom that was stigmatized by the way, not the being attracted to men

[vivid halo]

yea so I mean the actual number is pulled straight out of your ass but the whole phenomenon is very very well documented in that society

[vast surge]

Basically

[vivid halo]

yea that's the other thing too

[thorn brook]

kith

[vivid halo]

they conceptualized this differently than we do, as you say

[mortal oasis]

I think only until you were married

im pretty sure in rome it was okay to be a top with a man until you were married then it was wrong

ill have to double check that

[vast surge]

I thought married men would still keep men (of lower social standing) on the side as adulterous partners fairly frequently without too much stigma, but I could be wrong

[mortal oasis]

def of a lower social

im checking now

[vast surge]

At the risk of being vulgar though, in Roman society, the act of penetrating was deemed as masculine regardless of who you're penetrating, and being penetrated was feminine, whether the person being penetrated was a man or a woman.

[sick burrow]

But yeah I wonder how the sexuality distribution would change if men started actually caring about their looks.

[vast surge]

So men would top for men of lower social standing and bottom for men of higher social standing, because it was one of the most patriarchal cultures in history

[mortal oasis]

most men do care about there looks

i dont think thats true at all

[crystal stream]

ye

[vast surge]

There seems to be a pattern I've noticed of men going out of their way to look like they don't care about their looks

[mortal oasis]

eh i havent noticed that

[vivid halo]

I have noticed this

[mortal oasis]

I think care too much

[static loom]

do they invest as much time into it as women do?

[mortal oasis]

i think too is a very operative word

[vivid halo]

like the whole "I only wear black shirts and jeans" thing

is a trend

[static loom]

I feel like shaving legs, nails, makeup, etc takes a lot of time by comparison

[mortal oasis]

of course not but I dont think that means they dont care

[vast surge]

I was thinking cargo shorts and/or pajamas and also crocs to formal things

[sick burrow]

There just seems to be a lot more things with women's fashion

[mortal oasis]

but fashion is societal so if thats in thats in no

[mortal oasis]

have you actually meant someone who did htat

met

[crystal stream]

Caring about your appearance as a man is more or less just working out, getting a decent haircut and some trendy clothes

[vast surge]

Multiple people, both friends at college and family members and professors and just people out-and-about.

[sick burrow]

Like with men's fashion it's basically just shirt+pants but with women's fashion you also have dresses and skirts

[mortal oasis]

that honestly suprises me

I will say yea loki mens fashion just hasnt changed as much

how long has a good fitting suit been in for

like 100 years?

[vast surge]

How long has a good fittting suit been out for

If you don't have an office job

[mortal oasis]

I mean that has changed through out history the def of "good fitting" but men's fashion i think has been mroe static than womens

[crystal stream]

pre-french revolution apparently clothes were more colourful

[dense belfry]

I've seen a lot of crop tops on men recently

[mortal oasis]

KEK

we are reaching back a bit there

[vast surge]

Like, I'll go through the effort to put on a tie, a nice jacket, match my stuff, do my nails (don't judge, I like it), but that's like 10 times more effort than most men do and less effort than most women do

[dense belfry]

So it's not quite just shirt and pants

[mortal oasis]

if i could do my jails without being judged I would

[crystal stream]

the weird thing here to me is that you haven't bitten off your nails

[sick burrow]

Either way it feels like there's more options with women's fashion

[mortal oasis]

there is

for sure

[vast surge]

Honestly just do it. Maybe it's because all my friends are queer but I've gotten nothing but support when I did my nails at college.

Then I use nail polish remover whenever I visit family or family visits me.

[mortal oasis]

nah its just not me

its not where i want to fight society

[sick burrow]

Doing nails just seems like a lot of work

[vast surge]

Fair enough

[vast surge]

I actually find it relaxing.

[mortal oasis]

just to much headache nothing but respect for those who do

dont really feel like being judged for it

[vast surge]

That's valid

I don't think I started until I saw a couple other guys I know do it once for a gag.

[mortal oasis]

I’ve seen dudes do it

I have always thought it would be fun

[tall badge]

@neat lintel please don’t offer cash for hw answers

[leaden torrent]

this is clearly a covert way for ryam to offer money for homework completion

banned

[vast surge]

I would be as willing to accept this offer as I would be to give the Nigerian Prince who keeps emailing me my bank details. It's clearly a scam for that amount of money.

[modest rune]

If someone offered me 1mil for homework answers I’d happily get banned from here

[narrow rock]

with or w/o 5k upfront?

[vast surge]

I mean if it was legit and they were able to prove that it was legit I'd take it. It's a lot of money, and I'd do much worse for much less.

[vast surge]

Even 1 mil seems weird

For homework

[limber perch]

@everyone if anyone has 1 million dollars and unfinished homework my dms are open

[velvet dagger]

Actually his DMs are closed, rather mine are open

[odd yew]

Lol? 🙂

[vast surge]

Hi im the clay math foundation ill give you 1 million to do my unfinished homework. please prove a millennium problem please thanks

[odd yew]

If anyone has a solution to a problem worth $1B I will suddenly know LaTex.

[forest jackal]

here you go: https://vixra.org/pdf/2105.0073v1.pdf

how can I collect the $?

[vast surge]

Oh cool @rigid mango this is from your school right

[forest jackal]

this is the proof, for people too lazy to open the link

[vast surge]

Anyway, I'll reach out to you by the email address you provided in the paper

[limber perch]

when the references are longer than the proof

actually this doesn’t seem that unusual

maybe for a math paper yea

[bronze pelican]

What is this?

[vast surge]

A disproof of the riemann hypothesis.

[bronze pelican]

also I'm playing the natural number game on stream

[limber perch]

this “proof” is still more legitimate than that one indian guy who claimed to have proved the riemann hypothesis

[bronze pelican]

Come join if you wanna hear me explain lean :)

[vagrant kestrel]

it's a fun game go watch

[dreamy quartz]

@forest jackal wait

Someone proved Riemann?

What

No someone's trying to sack the whole hypothesis??? That's new

[limber perch]

i thought lean was a programming language

[forest jackal]

nah its just crankery, and crankery is nothing new.

[limber perch]

meanwhile i’m watching an actual game

suns vs bucks

[mortal oasis]

The new dune poster looks so good

God I hope this movie is good

[hoary flax]

hi guys

[rigid mango]

POG

EESTIMAA EESTIMAA

i knew my country would make it

[hollow jackal]

how is the average real analysis/advanced calc class conducted? do they teach you the proofs then test you on those same proofs, or are you meant to intuitively derive proofs on the spot during exams?

im assuming its a mix of both, but i'd like to know for sure

[crystal stone]

It varies on school, professor, and class

Some profs like to throw you things you haven't seen

Others like something you've seen before

[hollow jackal]

kinda figures 😐 hope i get a fun class when i finally take it

[crystal stone]

Also advanced calculus is historically distinct from real analysis

[hollow jackal]

oh? thought it was just a rename

[crystal stone]

You used to have your calc 1,2, 3, linear algebra and differential equations class

Then you had an advanced Calculus course that was a step above Freshman Calculus - you actually do some theory, and maybe some numerical estimation/applied stuff

Then real analysis was what you took in grad school after advanced calc

But somewhere in the 70s-90s advanced calculus classes died out at big name universities

And they just started teaching Real Analysis

Some universities still teach advanced calculus instead of real analysis

Like CSU Fullerton

[hollow jackal]

my school does advanced calc yeah

[crystal stone]

So they aren't quite the same, historically

[hollow jackal]

so when referring to advanced calculus, we're just simply going past what we've covered in calc III and DEs, whereas real analysis would be the "prove calculus" course?

for reference, the advanced calc course at my school is the "prove calculus" type

so it covers limits, differentiation, continuity, series+convergence, Bolzano-Weierstrass, but all done rigorously

[crystal stone]

What text are you using?

[deep mango]

They're usually both prove calculus courses

But real analysis often will have an element of metric space analysis in it

(see chapter 2 of rudin's principles of mathematical analysis)

[hollow jackal]

haven't taken it yet, but the text is P.M. Fitzpatrick, Advanced Calculus, 2nd edition.

from my looking around i've also seen rudin used a bit

in the counterpart class for other schools around mine

[leaden torrent]

fitzpatrick is kind of an analysis text

its not particularly hardcore

but i'd certainly consider it closer to rudin than it is to stewart

[deep mango]

Where would you place fitzpatrick on the stewart - spivak - ross - rudin spectrum?

[alpine oracle]

Wat r the prerequisite classes for combinatorial optimization?

[mortal oasis]

why do authors feel the need to use big words man

like we know you are smart you wrote a textbook

[deep mango]

Sometimes a big word is just the first word that comes to mind

[mortal oasis]

it just makes it harder to read

bad writing imo

[sharp mulch]

Help

How does complex analysis work

For $a,b\in\C$ and $\abs{b}<1$ calculate $\frac1{2\pi i}\int_{\abs{z}=1}\frac{\abs{z-a}^2}{z\abs{z-b}^2}dz$

[fathom swallow]

Unbroken Durindana

[deep mango]

[neat lintel]

[deep mango]

That looks awful

[sharp mulch]

Indeed

[distant vortex]

Then maybe your name is bad, because it's certainly longer than the words you are complaining about

[deep mango]

Maybe partial fractions to get two cauchy integral formula parts

And one which is the z - b bar

In the denominator

But the top function isnt holomorphic

This isn't even a real complex analysis integral

It's a mess

[whole copper]

Can you always split into holomorphic and antiholomorphic parts

[deep mango]

Only if harmonic

[whole copper]

What does harmonic mean? I only remember harmonic real function implies its the real part of a complex holomorphic function or something

[deep mango]

u is harmonic iff laplacian u = 0 iff sum of second partial derivatives in each coordinate is 0

not mixed partials

[whole copper]

Antiholomorphic functions are harmonic as well is the point?

[deep mango]

so you treat it like a two variable function

Yeah

[whole copper]

(so u need harmonicity to split? Oh ok)

[deep mango]

Conjugate commutes with laplacian

[whole copper]

Im guessing this thing ange wrote is not harmonic then? Lol

[deep mango]

I doubt it

[whole copper]

It kinda feel like it should be though? Like you are just writing it in terms of z's and zbars?

[sharp mulch]

Anyways

Qual preparations are a disaster

[whole copper]

I guess the point is that z zbar isnt wven harmonic? Me confuso

[sharp mulch]

Let f be an entire function with $\abs{f\qty(\frac1n)}=\frac1{n^2}$ and $\abs{f(i)}=2$

[fathom swallow]

Unbroken Durindana

[sharp mulch]

For n in N of course

From the first statement you conclude that $f(z)=az^2$ for $\abs{z}=1$ via the uniqueness theorem or whatever it's called which contradicts the second part...

[fathom swallow]

Unbroken Durindana

[whole copper]

Wait.. What is this uniqueness thm?

Are there no assumptions about existence/not of poles?

[sharp mulch]

If two holomorphic functions agree on a set of points that has a limit point, then they agree everywhere

f is stated to be entire

[whole copper]

Oh ok

Maybe i still dont see whats going on, can you tune the parameter a to match the phases correctly?

[deep mango]

Why would it be

Laplace(uv) is not laplace(u)laplace(v)

The product rule exists

[whole copper]

No idea, i thought ecerything written in terms of z and z bar is nice

[deep mango]

You need to write it as a sum of a function in z and a function in zbar

[whole copper]

It seems like you could choose the phases of f(1/n) so that it doesnt match up with any az^2? Maybe im crazy

[sharp mulch]

But abs(a)=1

[whole copper]

As in, to get your conclusion it seems you need az^2 to match up with f(1/n), how do you get the phases to match?

[sharp mulch]

And $\abs{f(i)}=\abs{ai^2}=\abs{a}=1\neq2$

[fathom swallow]

Unbroken Durindana

[sharp mulch]

I mean they match in modulus

[whole copper]

The magnitudes match clearly ya

That... Doesnt mean that their phases match tho? Lol

[neat lintel]

complex analysis

[crystal stone]

https://www.amazon.com/Million-Random-Digits-Normal-Deviates/product-reviews/0833030477/ref=cm_cr_dp_d_show_all_btm?ie=UTF8&reviewerType=all_reviews

Based reviews

[narrow rock]

$64

the hardcover costs $900 lmao

[sharp mulch]

Anyways

CA is a mess

[hollow ginkgo]

almost 600
628

[forest jackal]

I don't see how you are applying any uniqueness theorem to draw the conclusion you claim, |f| is not holomorphic. For an obvious example to show modulus of an entire function on an accumulating set does not determine it uniquely, look at exp(iz) and 1 along the real line. For a specific example satisfying your hypotheses you could have something like 2^(-iz)z^2.

[sharp mulch]

Oh

[sweet sail]

@rancid echo interesting

[rancid echo]

lol

[dreamy quartz]

I'm going to focus on frege and i think I want to do a what if analysis of his philosophy of mathematics in a sense such as how frege would have reacted if he saw the incompleteness theorems. I mean how his philosophical project would react

I don't want to say anything to my advisor before I have a better skeleton of it

I don't even know if that is good enough for a PhD thesis

It would be modern logicism yes

I thought so

Ugh

I want to do something with Frege but i have no ideas

I feel as if everything has been done

[modest rune]

what department is this for

[dreamy quartz]

Philosophy

[modest rune]

oh ultra did you end up reading any of liam bright's stuff

his stuff on like scientific lying and cheating are really interesting to me

[dreamy quartz]

Hmmm I honestly had an idea that's interesting to me connected to frege and Wittgenstein and that is pretty controversial. Wittgensteinian theory of reference in late Wittgenstein. Most Wittgensteinians disagree with me that late Wittgenstein is still a a linguistic referentialist in his late writings

But that also seems a bit unoriginal

Meh you're the only one here that knows about it except me afaik

Ty ultra

[sharp mulch]

[neat lintel]

[modest rune]

Get into philosophy twitter

I would cut off my hand to get Liam bright to follow me

[dreamy quartz]

I was

[scenic narwhal]

[neat lintel]

[dreamy quartz]

I AM A PHILOSOPHER DAMNIT

I WILL NOT BE BULLIED

Justice for philosophers

[neat lintel]

[dreamy quartz]

I am being overly dramatic intentionally

[sharp mulch]

[rancid meadow]

oh god this yikes emoji is the new worst thing about ange

[sharp mulch]

[bronze pelican]

https://youtu.be/ojjzXyQCzso

LETS GO

[vivid halo]

huh

[limber perch]

those don’t look like integrals

[neat lintel]

quasi projective scheme

hypercohomology

[vivid halo]

yes

nah it's useful

my research has had applications the whole time

at no point have I claimed I am proving useless results

[vagrant kestrel]

it's time to make a math-videos channel

and surprise kontorovich at the end wowee

[vivid halo]

[narrow rock]

[bronze pelican]

I have a video idea

[narrow rock]

what is it

[bronze pelican]

Elliptic Curves are Doughnuts

[narrow rock]

Elliptic Curves are COFFIS CUPS

[bronze pelican]

I think it's a really beautiful story. The Weierstrass p function is the "pillowcase map" from topology

[vivid halo]

ah yes this is a lovely picture

there is a little subtlety about what happens at the corners of the pillow

[solar tundra]

(Sorry if I'm a imprecise in my formulations, I am new to math.)

I recently discovered algebraic structures and they seem quite fundamental, I'm wondering whether Peano arithmetic could be expressed as the set {0,1} with the operation +, if yes this would constitute an algebraic structure.

Is there something I'm missing there ? I think this is incorrect because then 1+1 would be outside the set {0,1}. However if we take the set N (natural numbers) with the operation + then we get Peano's arithmetic but we had to define N first using Peano's arithmetic.

Does this mean that sets and operations are first defined using whatever means (logic, other fields of math, ..) and then those "constituents" are used to define algebraic structures ?

[nimble shuttle]

Zermelo-Frankel set theory is a very common axiomatic system

you can construct the natural numbers using ZFC or peano arithmetic

peano arithmetic itself is a collection of axioms about symbols

it's not a 'set' really

[calm vessel]

Can't you

Frame it as a set of some elements with a relation (function) "++" on itself

No axioms and any set can work

Even empty set and empty relation

Axiom 1

0 is a natural number

And then any set containing 0 works and any relations on that

Etc

[nimble shuttle]

i thought you said no axioms

[calm vessel]

Yeah like without any axioms "Natural Numbers" can refer to anything

[nimble shuttle]

oh i misunderstood your phrasing

[calm vessel]

Srry

[nimble shuttle]

you're saying that you can frame the arithmetic as a set of elements with a relation satisfying certain properties?

[calm vessel]

Yep

[nimble shuttle]

I would agree

[calm vessel]

"Natural Numbers are a set of elements with the relation '++' and satisfy the following 5 axioms"

Rather than symbols

Tho the 5th axiom is weird

[nimble shuttle]

it's just the induction principle

[solar tundra]

what are the children learning at school when they learn to add on their fingers, would it be fair to say they are learning the monoid {N, +} or would it be more proper to say they learn Peano's arithmetic ?

[nimble shuttle]

I'm not familiar with elementary school math education

sry

[calm vessel]

Yeah but it doesn't conform cleanly to the set theory I based stuff on.

[nimble shuttle]

true

well

the regular statement of the induction principle does

[calm vessel]

Everything else was a statement about the set itself or the relation itself

[nimble shuttle]

I think

[calm vessel]

Peano arithmetic is more proper I think

[solar tundra]

I was thinking of Peano's arithmetic as the formal definition of N, how would you define N if that's not it ?

[calm vessel]

Yeah with the 5th axiom it leans into logic and things not in the same space as set theory. And that can be weird.

[nimble shuttle]

I disagree

[solar tundra]

I guess my question boils down to is Peano's arithmetic an algebraic structure ?

[nimble shuttle]

it's still very much set theory

peano's arithmetic is a collection of axioms it's not really a structure

I would say N is the algebraic structure

[calm vessel]

Yeah ^

Algebraic structure is all about behaviour

Not the elements themselves

For example a clock has the same structure as N I think

[nimble shuttle]

are you saying it feels like logic? because it can be expressed in the language as set theory

[calm vessel]

Both

[calm vessel]

Children seem to learn the algebraic structure and not the peano thing. Kind of whack now that you point it out

[chilly smelt]

This seems dumb

[solar tundra]

according to wikipedia an algebraic structure is a set with operations, so in my understanding {N, +} would be an algebraic structure, but first you have to define N and +

[nimble shuttle]

the axiom is equivalent to "forall sets S, if 0\in S and n\in S implies s(n)\in S, then S = N"

[chilly smelt]

Kids are just learning random number concepts. You can put your big words on it and pretend that they represent the sort of mathematics they’re doing but it’s just pictures in a kids head

[nimble shuttle]

i'm using the term algebraic structure loosely

[chilly smelt]

Words 🥱

[nimble shuttle]

this is strictly in peano arithmetic

[calm vessel]

I'm kind of a noob so I don't get the notation

Was that supposed to be latex?

[nimble shuttle]

no

[calm vessel]

Oh okay I get it

The definition I had for axiom 5 is. A bit different

Yours is talking about 0 and if n then also n++

And strictly only about belonging

[nimble shuttle]

yeah i was wrong it isn't equivalent to the "regular" induction principle

but same structure

[calm vessel]

But axiom 5 is sort of infinitely many of those

[chilly smelt]

And apparently you can’t even show axiom 5 gives you N is one of them

It just says some exist, you can’t pinpoint N as being one of the ones given by it

[calm vessel]

I don't get what you mean

[chilly smelt]

Prove N is a set

[calm vessel]

Wasn't this sufficient to create N???

And it is an application of the axiom 5 I had in mind

[chilly smelt]

Which application

[solar tundra]

the reason I'm confused is because there seem to be some kind of conceptual overlap between Peano's arithmetic and an algebraic structure such as {N, +} but I can't really wrap my mind around that

[calm vessel]

Consider a statement that uses the variable x.
if the statement is true for X=0 and also whenever the statement is true for X=n then the statement is true for X=n++. Then the statement is true for any natural number as X.

[calm vessel]

You can define and talk about the same thing from many different foundational viewpoints and it depends on what you're trying to achieve. Usually what happens afterwards is that the definitions are linked.

[chilly smelt]

What’s your definition of N?

[nimble shuttle]

@calm vessel

[calm vessel]

If this is axiom 5 the statement can be just about belonging

[modest rune]

the existence of the algebraic structure {N,+} comes from PA

[calm vessel]

The one Jon presented

[modest rune]

i don't see the issue

[chilly smelt]

Can you @ his definition

I didn’t see it

[modest rune]

Or rather from whatever axiom system you are working in

[calm vessel]

(the way I prefer rn, is to call N a set with a relation ++ on it that satisfies the 5 peano axioms)

[solar tundra]

not sure who you ask to @chilly smelt I would define N with the Peano's axioms

[nimble shuttle]

max I think they were trying to reconcile the existence of two identical mathematical objects in different axiomatic systems

[chilly smelt]

But lots of things satisfy those axioms

[solar tundra]

I was wondering whether {N, +} was equivalent to {0,1,+} but I don't think it is the case because 1+1 would be outside the set

[chilly smelt]

There isn’t a unique thing which satisfies those axioms so how can you define N as the thing which satisfies them

[modest rune]

huh

[calm vessel]

Can you give me an example

[chilly smelt]

Of what?

[calm vessel]

Different things that satisfy the peano

[nimble shuttle]

this isn't how peano arithmetic works

[chilly smelt]

Although the usual natural numbers satisfy the axioms of PA, there are other models as well (called "non-standard models"); the compactness theorem implies that the existence of nonstandard elements cannot be excluded in first-order logic.[16] The upward Löwenheim–Skolem theorem shows that there are nonstandard models of PA of all infinite cardinalities. This is not the case for the original (second-order) Peano axioms, which have only one model, up to isomorphism.[17] This illustrates one way the first-order system PA is weaker than the second-order Peano axioms.

[modest rune]

the right way to think about N is as the natural numbers

you know what numbers are

[solar tundra]

well I think {N, +} is somewhat equivalent to Peano's arithmetic, although the Peano's arithmetic is more logically explicit

[calm vessel]

Dang

It's all Cantors fault?

[chilly smelt]

No it’s zumbino and frankies fault

[solar tundra]

by PA you mean Peano Arithmetic, right ? could you elaborate on your statement, why does {N,+} structure come from PA ?

[modest rune]

You cannot talk about the set N or its addition operation unless you can build it from your axioms

[solar tundra]

right !

that's my point since the start

i was seeking validation

[modest rune]

this isn't like

special of N

this is true for any set

[solar tundra]

basically you build N with PA and then you can use this "constituent" in the algebra structure theory to build an algebraic structure such as {N, +}

[modest rune]

algebraic objects are just sets and functions (which are sets)

[solar tundra]

alright, then i still have a question

[nimble shuttle]

algebraic objects are just glorified sets.

[modest rune]

lol

[solar tundra]

PA already has the "addition" + right ? it's the successor s()

[modest rune]

additions is induced by iterated succession in N

[solar tundra]

so what's really the difference between the algebraic structure {N, +} and PA

are those two concept equivalent but expressed "differently" ?

[modest rune]

addition*

I think there is some misunderstanding

one is a set of axioms

the other is just a set paired with a function

[solar tundra]

but isn't it a set of axioms (PA) that describe the same conceptual reality as the set paired with a function ({N, +}) ?

[dense belfry]

Nope

[chilly smelt]

No set theory sucks

Another victim to its lies

[solar tundra]

in my mind those two concept seem to point to the same "thing" but I may be wrong

by thing I mean the natural numbers on which we can perfom addition

[chilly smelt]

The group theory axioms don’t point to a single group

These axioms don’t point to a single “N”

It’s just some random cousins of N that have some of its properties

[solar tundra]

@chilly smelt according to wikipedia algebraic structures are broader than just group theory, algebraic structures can be : Group-like, Ring-like, Lattice-like, Module-like, Algebra-like (https://en.wikipedia.org/wiki/Algebraic_structure)

[chilly smelt]

Why are you telling me this

[solar tundra]

what's part of the confusion is if you scroll down in the "examples" section they even put arithmetics there

[chilly smelt]

Right

[solar tundra]

i tell you this because you speak of group theory

[modest rune]

(just to point out N is not a group)

[chilly smelt]

It’s because it’s a familiar example to compare this with

When you have a collection of axioms there are many things that satisfy those axioms

You have some axioms that you think describe N but they sadly describe more than just N

The group axioms don’t isolate individual groups.
The arithmetic axioms don’t isolate N

[solar tundra]

let's say N would be at least included in the set described by PA

[chilly smelt]

I couldn’t prove it

I think it’s all a lie

[dense belfry]

Lol honestly it is good that PA doesn't uniquely describe N

If it did computability theory wouldn't exist

[solar tundra]

could you elaborate why you said no by the way ?

(about PA and {N,+} pointing to the same conceptual reality)

[chilly smelt]

You’d hope so but can you prove it

Does it have 1?

[dense belfry]

Lol sorry I was confusing PA with a different axiom set for a second

Well a good reason is because there are nonstandard models of PA

[chilly smelt]

How do you know N is a set tho, surely to say it’s a model it has to at least be a set

[solar tundra]

@chilly smelt check the video of 3blue1brown about the monster group, at one point in the video he mentions groups with infinite set vs groups with finite sets

[dense belfry]

Also saying it describes the same conceptual reality is too vague for my taste

[chilly smelt]

The short answer is it doesn’t, they’re playing make believe

[solar tundra]

@dense belfry fair enough, it's certainly vague I guess that's how I'm experiencing those concepts in my mind haha

[chilly smelt]

I don’t know what you want me to learn from his video

[vivid halo]

okay I'm too fucked to read the whole thread above what are you confused about

[solar tundra]

well why N wouldn't be a set ?

[vivid halo]

how do you know N is a set
you actually need to enforce this by axiom

[chilly smelt]

No idea, do the axioms allow you to prove it is?

Which axiom proves it’s a set

[vivid halo]

in ZFC set theory there is a "natural numbers set" axiom

[solar tundra]

I'm confused about the seeming conceptual overlap between Peano's arithmetic and the algebraic structure (N, +)

[chilly smelt]

Which axiom is that

[vivid halo]

that essentially describes what N is, you need an axiom to ensure the set exists

otherwise like

[dense belfry]

Not really, there is an infinite set set axiom

[vivid halo]

you can have models of ZFC minus the natural numbers axiom that only include finite sets

okay sure

[chilly smelt]

It doesn’t describe N

[vivid halo]

depending on how you formulate the axioms

[chilly smelt]

The axiom says that an inductive set exists

Then you can show that a smallest inductive set exists

Now it’s up to you to show that it must be the N you know and love

[vivid halo]

ehhh that might be a weird way to define it

[dense belfry]

But it isn't necessarily the N you know and love

[vivid halo]

^

[chilly smelt]

Checkmate set theory, waste of my time

[vivid halo]

well

so the "standard model of the natural numbers" is minimal among these models

so this is fine

there are nonstandard models of the natural numbers that are weirder, and indeed these are all models of PA

it's just there's a minimal model that is the one we know and love

[solar tundra]

it's an interesting angle of attack you have there, my mind is satisfied with calling the PA inductive set N

[chilly smelt]

How do you know N is a model of PA

[vivid halo]

uhhh

literally by definition

[nimble shuttle]

if it looks like a duck

[chilly smelt]

Bad definition

[vivid halo]

by this I mean

you write out the definition of your model of standard natural numbers

you then verify that this model satisfies the PA axioms

which is essentially by definition, since in the model you're imposing like

[chilly smelt]

What’s are you referring to when you say “N”

[vivid halo]

the minimal possible thing you need for these axioms to hold

[ancient flame]

PeAno axioms

[vivid halo]

when I say N I mean standard N

there are other nonstandard models N' of PA that are weird

[chilly smelt]

The minimal possible thing might not be the thing I mean when I say N

[vivid halo]

but standard N is minimal

oh hmm

okay well then you're talking about something possibly different

[brazen bough]

Peanal axioms

The type of axioms u need

[vivid halo]

which is fine, there are interesting things you can study that involve nonstandard N

but "standard N" is an unambiguous statement

[chilly smelt]

When I think of the standard N I think of finite applications of the successor on 0 and then putting them all in a bag. I want to know exactly what you have to do in order to prove it’s a set. Otherwise the minimal thing might be weird

[solar tundra]

@vivid halo would you say it is fair to say that Peano's arithmetic points to the same conceptual reality as the algebraic structure (N, +) ? By conceptual reality I mean natural numbers that we can add ?

[vivid halo]

yes and no

yes in the sense that like

you're specifying these axioms and from this you can obtain a minimal model that does what we intuitively expect these axioms to be capturing

no in the sense that without this minimality assumption you can't pin down one model, so PA is really about a richer class of structures (of which the familiar standard N is the simplest)

[chilly smelt]

I’m claiming you need some secret sauce to actually prove the minimal thing is N

[vivid halo]

you don't

[chilly smelt]

You can call the minimal thing N all you like, defining it as such is cheating because I already have a definition of N

[vivid halo]

that doesn't make sense though

[chilly smelt]

Call the minimal thing M. Show N=M

[solar tundra]

great this discussion settled me a bit thanks to all :)

[vivid halo]

okay but you're simply redefining what N is now

which is fine, but like

then we're simply talking about other things

[chilly smelt]

No, I had the definition first

[vivid halo]

lol

I mean this is similar to like

[blazing pawn]

Truly based

[vivid halo]

if you look at ZFC set theory

there is also a minimal model, and this is sort of the one that people have intuition for, namely Godel's constructible universe L

there are of course other models of ZFC!

now in this case there is something more subtle going on, there's some arguments you can make that the minimal model is not the one that you want to use

in some sense this subtlety still exists in PA, as you are arguing for a nonstandard N to be the preferred one

however the main argument against this perspective is one of intuition: we have an intuition for what natural numbers "should" be in some platonic or philosophical sense, and the minimal model is precisely this

whereas we don't have enough intuition about sets to cleanly distinguish which models do "what we expect" and which don't

this is why, for instance, the axiom of choice is largely uncontroversial among set theorists, since we have some idea of what sets should be in our head and they obviously satisfy this axiom

what's not clear is, for example, do sets satisfy CH

so this is where the ambiguity begins and we have to think harder

but for natural numbers things are more or less fine philosophically speaking

[chilly smelt]

I have a very clear picture of what I expect the minimal model of N to be. It’s the thing I learnt when I was 6 and it’s the thing I’ve been using for my whole life since that point. Then set theory comes along and defines N as the minimal model, it’s now up to it to demonstrate in a convincing fashion that it is the thing I expect of it. ZFC isn’t much of a foundation if it isn’t even describing the thing 99% of mathematicians consider N to actually be in a platonic sense

[vivid halo]

well so the thing missing from this is like

you can literally construct "standard N" in the way you expect, you can construct this "minimal N" and then you can prove within ZFC that these are the same

[chilly smelt]

How do you do that, that’s the thing I’m missing

[vivid halo]

ah okay great

there's a nice explanation of this here: https://math.stackexchange.com/questions/2257984/are-the-standard-natural-numbers-an-outstanding-model-of-pa

[chilly smelt]

Just so I am clear, what do you mean when you say standard model

[vivid halo]

to me "standard N" means "minimal N" in the model theoretic sense explained here

there are philosophical arguments you can make that "standard N" should be taken to be a different, non-minimal model of PA but I don't think these are particularly convincing

[chilly smelt]

I want to make my position clear

[vivid halo]

by analogy a lot of people take "standard ZFC" to mean "minimal ZFC," that is Godel's constructible universe. There are philosophical arguments that "standard ZFC" should be taken to be something different, and now the difference is that these arguments are somewhat convincing

[chilly smelt]

What im calling N is a platonic definition. It’s not defined as a minimal anything, i can define it outside of set theory as the bag containing 0,1,2,… where you know what I mean by …

[vivid halo]

okay sure

[chilly smelt]

How do you know THIS THING, whatever it is exactly, is the minimal thing

[vivid halo]

So of course it depends on how you define N "platonically," however you are doing this

[chilly smelt]

You know what it is

[vivid halo]

but I think most sensible "platonic" definitions will give you something that matches "minimal N"

[chilly smelt]

Just as much as I do

[solar tundra]

(that's what i call conceptual reality btw)

[chilly smelt]

It better match the minimal thing, that’s what I want

[vivid halo]

right so if we're saying "we take N to be what everyone knows N to be, it behaves in the way we expect"

like in the way that we all kinda know without getting argumentative about it, you know what I mean

then this definition agrees with "minimal N"

[chilly smelt]

Not behaves the way we expect, because many things behave like it

[vivid halo]

sure

but yes most sensible platonic definitions give you the minimal model

again by analogy there is a similar issue in set theory where we have a platonic idea of what a set should be

a "bag of elements"

the ZFC axioms are all derived from this platonic idea

the big issue is there are other axioms like CH where our platonic idea of what sets should be isn't clear or unambiguous enough to decide whether this should be an axiom or not

so this requires a deeper exploration into how these models are related and what happens much much later down the road as consequences of these axioms

e.g. you might have an axiom that seems compatible with this platonic idea but maybe you can derive a consequence that is clearly contradictory of this idea, or deeply undesirable in some sense

people joke about the axiom of choice in this way, since the actual statement is very intuitive and "obviously true" but a consequence like the well ordering theorem is really weird in some ways

[chilly smelt]

I guess what you do with that conflict tells you a lot about what type of mathematician you are. If the axioms cause weird things to happen, is it the ideas themselves which are broken or just the particular system you’ve used to express those ideas

I’m on the side of my platonic view. If the axioms can’t pin point N in a way I’m satisfied with (not claiming they can’t) then I blame the implementation of the foundation, not my idea

I don’t change my actual concept of the natural numbers because the foundation would prefer I think of it that way. I see the foundation as a map and the natural numbers as an object that is being drawn by the map

[vivid halo]

Well right so it is very rare the axioms can indeed pin down infinite objects like this

So you’re left with one of two choices

One is to be satisfied with the minimal model and argue that it is ontologically satisfying because it has the least baggage

[chilly smelt]

CTMU pins down GOD

[vivid halo]

That or you need to keep putting more and more axioms into your model to filter down the models

[chilly smelt]

If one man can do it with GOD then a whole team of nerds should be able to do it for N

[vivid halo]

It’s also worth pointing out that even though we don’t have a specified model of ZFC The basic axioms are still enough to do the vast vast majority of mathematical arguments

So in some sense the fact that we can’t pin down a model isn’t as philosophically worrying as you might think

[chilly smelt]

I wonder why they can’t just define the actual N to be a set, they’ve left themselves wiggle room on purpose for some reason

[vivid halo]

You can though

One version of ZFC Literally does this for the axiom of infinity

In either case you can write down an unambiguous set which agrees with this minimal model

[neat lintel]

Do you support that a linear algebra book talks about rings without teaching them, knowing that the first time you study linear algebra you haven't studied yet anything about abstract algebra?

[vivid halo]

This can be a useful perspective yes

[neat lintel]

I mean

[vivid halo]

It’s certainly good to talk about fields in abstract

[neat lintel]

Without defining anything

They just say

[vivid halo]

Oh hmmm

You’re a logician you don’t count

[neat lintel]

Theorem:

$(\mathfrak{M}_n(\mathbb{K}),+,\cdot)$ is a non-conmutative ring if $n > 1$

And nowhere in the book a "ring" is defined

[fathom swallow]

Reduced row echelon form

[neat lintel]

I mean that situation which is basically what I'm referring to

You may want to know which book has that

It's "Álgebra lineal con métodos elementales"

[calm vessel]

What is this??

[chilly smelt]

Art

[calm vessel]

Also how can you ever connect a "platonic" concept with mathematical theory??

[chilly smelt]

It just has to satisfy me, this doesn’t just yet

[calm vessel]

At best you can construct math theory that looks similar enough to what you would recognize

Also It seems the non standard models involve introducing elements that satisfy the axioms but arent there usually

What's CTMU??

[chilly smelt]

It’s not even about non-standard. I can’t tell that the standard one is the one I am thinking about. I need a clearer picture to see why it is the one I know already

[solar tundra]

I searched what it was, the IQ thing is certainly off putting, sounds like a scam, but the few review on his book and votes on his videos are good so idk

Keith Ranierith also liked to advertised heroic IQ

[modest rune]

Maybe I should try that

I could be a fantastic grifter

[solar tundra]

hah

I was going to say you don't have to take the IQ route with your gender

[modest rune]

My name is not actually Karen

[chilly smelt]

Sure Karen

[gloomy marten]

Is grifting the thing with the branches

Like in jojolion

They grifted the branch or smth to a tree

Speaking of frauds

You guys know that guy on YouTube who invented new calculus

He claims several things

[chilly smelt]

Wildburger?

[gloomy marten]

Not sure

He says that pr/qr ≠ p/q which is like saying that there exists an intrinsic meaning to the fraction other than the ratio

[rancid meadow]

That's grafting. You're welcome 🙂

[mortal oasis]

R = 0

[mortal oasis]

I want to hear more about this

[limber perch]

probably some drunk guy

[summer egret]

john gabriel?

[inner finch]

@cold needle this is what i was talking about

[sick burrow]

In Cauchy’s and Sylow’s arguments, the group G was taken to be a subgroup of a symmetric group on some [n]. The first proof of Sylow’s theorems without this assumption is due to Frobenius

[gloomy marten]

For r ≠0

[gloomy marten]

Yoooo I think that's it

https://www.reddit.com/r/mathematics/comments/gyx5e8/is_there_any_validity_to_john_gabriels_new/?utm_medium=android_app&utm_source=share

[neat lintel]

He is the only mathematician since archimedes to understand math

[reef carbon]

jgtgmsa

[neat lintel]

🕯️

[bold ferry]

guys can someone explain how a sequentially closed set is different from a closed set?

[compact tartan]

sequential properties can only examine sets in a countable number of points at once

this might be insufficient in topologies with sufficiently rich open sets

a closed set is always sequentially closed

but the sequential closure of a set can fail to be sequentially closed

let alone closed

[bold ferry]

in a closed set, every convergent sequence in this set converges to a point in this set right

[compact tartan]

are you asking for a definition?

[bold ferry]

i dont understand this defintion
let me post it

oops i cant post a pic here?

[compact tartan]

sure

that's the definition of a sequentially closed set

[bold ferry]

ah my internet was bugging

so if A sequence in this set converges to a point in this set, it is sequentially closed?

[compact tartan]

iff

yeah

[bold ferry]

we dont need every convergent sequence to converge in this set?

[compact tartan]

all convergent sequences need to converge to elements in the set

[bold ferry]

wouldnt that make it a closed set?

[compact tartan]

no

[bold ferry]

but a set is closed iff every convergent sequence in this set converges to a point in this set right

[compact tartan]

no

that would be a sequentially closed set

[compact tartan]

that's for metric spaces

in metric spaces closed and sequentially closed is equivalent

[bold ferry]

oo right

ty

[whole copper]

(e.g. https://math.stackexchange.com/questions/3663565/sequentially-closed-but-no-closed-subset)

the difference between closed and sequentially closed seems like the difference between using nets, and sequences?

[compact tartan]

yeah the only example I had at hand was omega_1+1 in order topology and I hesitated to bring that up

[whole copper]

if you use nets, you're all good?

[compact tartan]

yeah nets can be "long"

[whole copper]

yeah for all small enough spaces its probably fine to forget the distinction lol

[compact tartan]

I've always wondered but never cared to check

can the kind of limit that you take in the riemann integral be expressed as a net limit

[neat lintel]

I have "one" question

When did mathematicians start analysis research?

[bold ferry]

btw that is a nice cat gif in ur profile thing mniip

[compact tartan]

like, you would need to construct a filtered category out of partitions of an interval

filtered category ~~ directed set

except it can be thick

but in this case I think it makes sense to be thin

that looks degenerate though

if tau_1 and tau_2 are partitions with choices of points on each segment and l(tau) is the longest segment,

we connect tau_1 -> tau_2 whenever l(tau_1) >= l(tau_2)

this is a thin filtered category

yeah I guess this is it

it looks really odd though

wait how do you take a limit

is it "for any neighborhood there exists a final set?"

yeah I'm just used to filtered categories looking more like lattices/DAGs

this is more like flow in a pipe

morphisms go from left to right

[last oxide]

everything is first countable

[toxic schooner]

[bronze pelican]

[sharp mulch]

Just have mathematica open instead

[static loom]

middle schoolers doing algebra with polynomials looking down on graduate students doing algebra with polynomials

[inner finch]

wolframalpha and all of its consequences have been a travesty for the human race

[bronze pelican]

I use it to factor polynomials

[neat lintel]

some people don't???

[inner finch]

synthetic long division

[blazing pawn]

This is what category-brain does to you

[neat lintel]

wolframalpha is a liar

true

[deep mango]

Finally, a reasonable post

This is why I thought algebra was so awful

[odd narwhal]

True, let's go back to doing exhaustive calculations on paper

[inner finch]

😋

Sounds good to me

[deep mango]

Analysis is not calculus. Complex analysis is calculus. There is algebra that is not HS algebra, but the ring theory in a groups rings fields course is ha algebra.

[odd narwhal]

Wanna numerically evaluate an integeal but don't know how to program hold on bro lemme just draw a bunch of rectangles

[inner finch]

imagine being a greek mathematician whose lifes work is literally just that you drew a bunch of rectangles and added their areas

[odd narwhal]

Imagine your most notable achievement being fucking killing someone for implying not everything is a ratio of 2 whole numbers

[inner finch]

Greek mathematicians were the original "omg math is so beautifal fibonnacci in flower!!" people

[deep mango]

So many ancient greek mathematicians were complete hacks.

[odd narwhal]

We need to bring back maths cults

Wait we already have category theorists

Nvm

[odd narwhal]

Fr tho

[deep mango]

Archie Meaties, Pythagorean, and Euler. All hacks.

[bronze pelican]

Platonic solids? More like elementary particles

[sharp mulch]

The best way to evaluate a definite integral is by weighing pieces of paper

[deep mango]

Ah yes. Play doh.

[inner finch]

We call aristotle arastool in urdu because we realize how shit he is

[odd narwhal]

Oh and can't forget finitists

And ababou

[deep mango]

How to tell someone is practicing for complex analysis quals

[sharp mulch]

I'm still so angry that that one integral was 0

[deep mango]

Oh dear.

[inner finch]

[narrow rock]

all integrals are 0

[deep mango]

Ange angy.

[crystal stream]

for large values of 0

hmm

this got me thinking

if you consider the set C([0,1])

what is the measure of the set of all functions whose integral is 0

[deep mango]

0

Surely

It's like

A dimension less

[sharp mulch]

What is the measure on this set

[deep mango]

What measure?

Yeah I mean

Putting measures on infinite dimensional spaces is always gonna be bad

[sharp mulch]

Obviously if you use the counting measure the measure will not be 0

[deep mango]

Since you can't inherit some fubini thing from [0, 1]

[odd narwhal]

Define the measure such that that set is 0

[sharp mulch]

Ok use the 0 measure

[crystal stream]

just googled

[odd narwhal]

Nah, the trick is to make it just nontrivial enough such that it looks interesting at first glance but it's actually extremely boring and formulaic

[crystal stream]

C([0,1]) doesn't have a natural measure

so yeah my question doesn't make much sense

[sharp mulch]

Why would it

It has way too much stuff

And not enough structure

[crystal stream]

I imagined it didn't

[latent forge]

You are reminding me about something when it comes to structures and stuff in algebra.
Since most of the concrete things people work with early in math are numbers it feels uncomfortable when taking a first algebra course because a lot of the objects are talked about abstractly straying away from concrete examples. Im not sure if its just me, but it looks like a lot of higher math just talks about properties of these abstract constructions rather than examples. Is it just more or do most things in higher math have concrete motivating examples?

[bronze pelican]

Angy ange.

[sharp mulch]

Just do applied math and not abstract algebra

Then your concrete motivating example is reality

[odd narwhal]

Numbers are a methamtician's worst enemy

[crystal stream]

I get the feeling that in general the deeper down the rabbit hole the more things are generalized

[bronze pelican]

There are layers of abstraction.

Abstraction of an abstraction of an abstraction

[crystal stream]

I find it useful to try to find intuition in the more concrete case while first learning the generalization

though that doesn't always work

[latent forge]

Does it ever become concrete is there a motivation,

Is it really just abstraction for abstraction sake?

[bronze pelican]

Depends on the particular thing you're studying

Usually there is some particular reason for considering an abstract definition

[crystal stream]

the good thing about generalizing is that it covers the more concrete case by definition

if you want to study some property of R^3 but you know all about R^n just set n = 3

[odd narwhal]

Honestly a lot of times generalisations can help understand some deeper structure behind the object you were originally studying

When you.pull back the curtain so to say

[deep mango]

I would argue that there are a lot of concrete examples to pretty much any any widely used math object that you'll ever encounter. The reality is, not all math things admit concrete realizations (a lot of times, this is when you have some super abstract tool for understanding something that is rather concrete)

The problem here is that "concrete" is in the eye of the beholder. To some people, it may not be very concrete to say "this math fact manifests itself really clearly through collections of matrices, or through examples in quantum mechanics"
But to someone working in the field of , that's a very nice concrete way of thinking.

Note the use of "almost every widely used you'll ever encounter". There are people who spend their time on crank shit like arithmetic geometers or Ultraproduct and you'll just never have any clue what they're going on about.

[vivid halo]

[deep mango]

Sully farming while telling not a single lie.

[vivid halo]

Lol

arithmetic geometry is crank shit

This is literally one of the most popular areas of math lol

[deep mango]

My point is, sometimes you have to look hard for the concrete realization, and sometimes it's a waste of time to do so, but usually something exists.

[vivid halo]

Sure

[deep mango]

Yes, popmath is what we should all aspire to model our careers toward

[vivid halo]

[deep mango]

Sullies for preposition at end of sentence?

Sorry!!!

*Yes, popmath is that toward which we should all aspire to model our careers

[vivid halo]

Dang the way you are pretending to be a moron is extremely likable and endearing, keep it up

[deep mango]

Hey nG, I didn't even at you.

I atted this dude.

Are you gonna die on this hill?

[vivid halo]

Yes

[deep mango]

🤨

[vivid halo]

Honestly every area of math has nice concrete examples that clarify things, except for the exact fields that ultra studies for some reason

[deep mango]

"physicist"

[sharp mulch]

[bronze pelican]

What does ultra study

[vivid halo]

Foundations

[bronze pelican]

"Everything"

[deep mango]

Also ultra at least cares about and those are plenty concrete

See?

Just present the pauli spin matrix example

[vivid halo]

Yea that stuff is fine

[deep mango]

That's how you explain to a high schooler what that field is like

[sharp mulch]

Foundations of QFT have no applications

[leaden torrent]

just spam the emote without explanation

[deep mango]

Physics is an application

[sharp mulch]

Do physicists care about foundations of qft

[thorn brook]

When Rin Hoshizora as an emote

Instead of nozomi

[sharp mulch]

The impression I got was no, they don't care

[leaden torrent]

do physicists care about physics

[deep mango]

Ultraproduct does, they are a physicist.

I suppose you also need to be clear about what level of specificity you want when trying to find concrete examples for things

[bronze pelican]

Yes

[latent forge]

Yea you answered me perfect, I was thinking of concrete realizations just being tools that could find a wide use in math and not something super duper specific to a certain field.

[deep mango]

Like, if you just want to get a good idea for why people care about homology, it's not so hard to explain. But if you want a good idea for why people care about sheaf cohomology, it won't be as easy.

[bronze pelican]

There are levels of abstraction

[latent forge]

Like seperatricies

[deep mango]

Yeah

[latent forge]

https://en.wikipedia.org/wiki/Separatrix_(mathematics)

But even then this is concrete enough to have wide use in diffeq

[bronze pelican]

People care about sheaf cohomology to understand when local solutions can be glued to gather to get global solutions

[deep mango]

Sure

My point is that unpacking the definitions toward something concrete is going to take a little more time than if the person is just happy to hear something about triangulating surfaces.

[latent forge]

Is a little an understatement?

[deep mango]

I haven't been sully farming for a while by the way

[deep mango]

I'm being political to try to find common ground.

[latent forge]

👍

[velvet dagger]

It's harder to explain because people haven't caught up to it

Hard to explain to a child why anything is interesting

[neat lintel]

Physics is cool

[deep mango]

😌

[odd narwhal]

Wrong

[neat lintel]

I respect your opinion, but also disagree

[last oxide]

not sure about that
I think my grandma didnt exactly grasp the nuances in poincaré-hopf when I explained it to her

[fallen delta]

is the icon of this server related to the rotating donut?

[last oxide]

I guess it seems to be a rotating donut

[cold needle]

Coffis cup.

[odd narwhal]

Aka the 1-donut

[last oxide]

so the n-donut is (S^1)^(n+1) now

[errant kiln]

Weird thought, but is posting copyrighted pictures here in Discord actually allowed?
I can't see how it's different from putting a copyrighted image onto one's blog, which isn't.

[bronze pelican]

Can I put copyrighted images in my youtube video

[errant kiln]

Of course not.

Well, I guess it could differ depending on the country you're currently living in.

[vivid halo]

strictly speaking no but there's absolutely zero way for this to be enforced, so nobody cares

e.g. people stream movies through the discord screen sharing feature all the time

[vivid halo]

lol

[blazing pawn]

Lmfaoooo

[vivid halo]

based

honestly more people should be told this

yea honestly that's a good answer

yes, in public

[blazing pawn]

oh nGroupoid and ultra you guys should listen to this https://www.youtube.com/watch?v=Jzmuq2Vu-U8

I am going to try and find avant garde nagauta and hayashi-kata ensembles

[vivid halo]

idk it annoys me when people ask questions that could have immediately been answered by a simple google search

[bronze pelican]

People are looking for perspectives not definitions

[vivid halo]

" Basically, I would like to know what the definition of the elements of the shape group is."

like idk

I care less when people do this on discord since it's like, something that would be okay to do in a casual mathematical conversation

[blazing pawn]

Wait this reminds me theres something i wanted to ask on MSE

[vivid halo]

even if the question were changed to like

here's the definition I looked up, what is the reason for defining it this way? How did people come up with this definition in the first place?

[bronze pelican]

That's a good question

[vivid halo]

that's immediately like 100% better

yea!

[rancid meadow]

holy shit before it was edited

horrifying

[blazing pawn]

MonkaS

[vivid halo]

oh man lmfaooo

[rancid meadow]

Tyler is my grad student. When he informed me that Shape Group is not standard terminology, I was a bit curious to how he could have come to that conclusion. While searching for a citation to prove him wrong I came across this entertaining discussion on StackExchange. If either Tyler (the original poster) or Pece (the other grad student who claimed this isn't standard terminology) would have taken the time to search the term 'shape group' on MathSciNet before posting on StackExchange they would have avoided wasting each other's time -- and mine. Typing 'Shape Group' into the search field of MathSciNet yields numerous paper on the subject. Since I've apparently already spent the time doing what they should have done, I think it would be appropriate for me to suggest that they look at these two papers written by people that Tyler has actually met, talked to and drove a van for not two weeks ago :

[blazing pawn]

Oh my god

[urban oracle]

wow, are you a professor?

[blazing pawn]

Oh my goddddd

That hurts to read

Nvm theyre kinda right

[rancid meadow]

yes. i sent this message on mse.

[blazing pawn]

This was pretty mean

[velvet dagger]

What a prick goddamn

[blazing pawn]

get ready for proofs

Ok way anyway

[rancid meadow]

guh i hate students who go into math classes and then whine about writing proofs

lmao

[urban oracle]

I feel like they should teach more proofs (especially during earlier math classes), so everyone doesn't immediately start crying

[rancid meadow]

[they] do depending on which courses you take

lol

some people just havent gotten out of the HS mindset of doing math

etc.etc.

[velvet dagger]

Probably depends on what type of class that is

If it's a class for math majors then grow up

[blazing pawn]

Im asking an MSE question about how to show that points above a k-rational point p in X in the base change to the algebraic closure have trivial stabilizer in pi_1(U_bar{k})

What should i tag it other than algebraic geometry

Actually let me just rephrase what should i tag questions about etale pi_1 as

[urban oracle]

like K-12 education lol

[vivid halo]

tag them as @vivid halo please help

[blazing pawn]

@vivid halo Pls help

[vivid halo]

okay

[blazing pawn]

do you want to see the full set up

ok let me post

[vivid halo]

yea so what are U and X here?

[blazing pawn]

let k be a perfect field, X a proper normal integral curve over k, U an open subset of X, p in U k-rational (my defn of this is that the residue field of p is k idk how standard that is)

let tilde{Q} be a point lying above p in the pro-etale cover tilde{X} of X

let bar{Q} be the image of tilde{Q} in X_bar{k} the base change to the algebraic closure

my goal is to show that the stabilizer of bar{Q} in pi_1(U_bar{k}) is trivial

[vivid halo]

hold up

[urban oracle]

I feel like majors like engineering should be taught actual math proofs though instead of trying to ignore proofs altogether so they roughly know where all the stuff comes from (although I know everyone will hate me)

[vivid halo]

I'm a little confused by the use of the pro-etale cover, I don't know that this is totally necessary

[blazing pawn]

Yeah idk this is how the book does it

[vivid halo]

yea so here's how I think about the exact sequence 0->π^et_1(X)->π^et_1(X_0)->Gal(\bar{k}/k)->0 for X_0 over k and X over \bar{k} (this is the notation I usually use so forgive the change of notation)

think about what each group classifies in terms of its finite quotients: Gal(\bar{k}/k) classifies finite extensions of k, π^et_1(X_0) classifies finite etale covers of X_0, π^et_1(X) classifies finite etale covers of X

[blazing pawn]

(i think i get the exact sequence, like the absolute galois group measures the extent to which etale maps over U lose etaleness when base changed to bar{k})

Like everything makes sense to me except the claim that the stabilizer is trivial

[vivid halo]

well right so what the sequence is saying is that there's a specified class of covers of X_0 that are just base changes of X_0 to a finite extension of k

these covers, once you base change to \bar{k}, all become trivial

[blazing pawn]

Yeah

Like pi_1(U_bar{k}) accounts for the etale covers over U that are just base changes

Right

[vivid halo]

right okay so now there's one additional piece of content, we haven't produced our splitting yet

shh

anyways

let me think about this for a second, I really don't like the proof that Szamuely gives for this

[blazing pawn]

I dont really get it tbh... like the claim is that if i take the compositum of all the extensions of K of the form K L where L | k algebraic any automorphism of that stabilizing bar{q} is trivial

[vivid halo]

yea this is written in such a stupid way

[urban oracle]

should this go in one of the advanced channels lol

[vivid halo]

nah it's fine

[blazing pawn]

No i am too based for those

If i use them it makes my score increase faster i have to stay here so its hard to tell that im a no lifer

The role is hidden by honor

Irrelevant

[vivid halo]

anyways my advice is to just move on and ignore the issue

[blazing pawn]

Yeah I did that

I went back to try to understand it but then I didnt understand it

guess ill just ask on MSE

[vivid halo]

well hold on

[brisk dome]

May I ask a question here?

[vivid halo]

sure yea I think the current conversation isn't going anywhere

[brisk dome]

Lmao

[rancid meadow]

#❓how-to-get-help

[brisk dome]

Posted my question in #help-9 if you wanted to look my good sir @vivid halo

[vivid halo]

@blazing pawn oh let me say a word about these splittings that don't come from rational points

[blazing pawn]

Wait

Now that I think about it maybe i am 4head

And I have things mixed up

does pi_1(U_bar{k}) correspond to etale morphisms over U that dont come from base changes?

because thats gonna be etale covers of U_bar{k} right

[vivid halo]

yes

these are the "geometric" covers