serious-discussion

[proud olive]

[fervent pebble]

[arctic grove]

eulers number?

[proud olive]

Oh i actually didn't consider that

[arctic grove]

im too math pilled to consider e as something else

[deep mango]

HelLO!

[proud olive]

Hi ryc!

[arctic grove]

hey ryc

[deep mango]

Hi

[proud olive]

How's life in Italy?

[deep mango]

Uhhh

[arctic grove]

drunk

[deep mango]

It was a very good day

And now I am slightly drunk

In a not super fun way

but fine enough

My plan was to make it fun

but

my phone will not connect to the internet

[proud olive]

Being drunk is fun af

[fervent pebble]

L

[proud olive]

But only if you're around other drunk people

[fervent pebble]

rycie

how r u

[proud olive]

Being drunk alone sucks balls

[deep mango]

No that's perfectly fun too imo

I realized this sadly last time i was high

Like

I like being drunk so much better

[proud olive]

Being on discord doesn't count as being alone

[deep mango]

And that's very sad

But no one else is drunk here!

[proud olive]

Gah fair

[deep mango]

Also when i'm not on discord I talk to myself

(while drunk)

[proud olive]

I've never been drunk alone

[deep mango]

actually i do that while not drunk too if i'm totally alone

[proud olive]

I would probably do the same

[deep mango]

You haven't like

walked home from the bar or something

and gotten ready for bed

[proud olive]

Yeah i do that too from time to time

[deep mango]

It differs from person to person but oftentimes 2 drinks is the minimum to start to feel a light buzz and 3 drinks is the minimum to start feeling a proper kind of drunkenness

For me, 4 and above is where I am properly drunk

But it depends on the kind of drink too

[proud olive]

Wow

How much you weigh ryc?

[deep mango]

Like 70-75 kg? I don't know exactly atm

[proud olive]

Oh

Maybe i just got a low tolerance

[deep mango]

Which, by the way, is VERY NICE

Don't let people tell you it isn't

[proud olive]

Yeah it's not that low tbh

[deep mango]

Less money for you to spend

[proud olive]

I weigh 80 kg so i need a little too to feel it

[deep mango]

I see

[proud olive]

But I feel it like after only one box

That's when i start to get tipsy

[summer sandal]

I weigh 92 kg so maybe that’s why 1 drink is not enough.

[proud olive]

Probably not

Also just depends from person to person

[summer sandal]

I wanna try all the drink I have seen in movies.

Vodka, wine etc.

[proud olive]

Wine is good

Vodka is neat if you only want to get drunk

[arctic grove]

@proud olive explain

[proud olive]

No!

U can do it shy

What kind of traits does that e have?

[arctic grove]

its red

[proud olive]

Ya

So it's a ...

[arctic grove]

red e?

[proud olive]

Ya!

It's a red e

[arctic grove]

oh wait

||Ready, Set, GO!||

[proud olive]

bingo!

[arctic grove]

[deep mango]

It's fun to try different drinks, some are really interesting

My recommendation is that if you have the opportunity to go to a wedding with an open bar, take advantage of it to try some interesting cocktails.

Because otherwise you have to spend like 12 bucks on something that could be gross

I found out at a wedding how good white russians and tequila sunrises are

and that i don't like whiskey sours

[proud olive]

Open bar??

The dream

[deep mango]

Oh I mean as a mod my recommendation is to not drink and take care of your body! Especially if you are under the legal drinking age in your country. Or something.

[deep mango]

There was also an open raw bar

[proud olive]

What's a raw bar?

[deep mango]

I had so many oysters and so many cocktails

Various raw seafoods

[proud olive]

Damn jelly

[deep mango]

Like oysters, clams, and such

There were shrimp but i don't think those were raw

[fervent pebble]

0/10 mod

[deep mango]

What I did my job perfectly!

[fervent pebble]

why no blushysully then

nami would want you to add it

[dense belfry]

Asking the real questions

[deep mango]

Uhhhh...

[fair mural]

if nami wanted it he would have added it

[fervent pebble]

nami wants to let ryc feel like he's doing smthn

bc nami's nice that way

[wild lantern]

Maybe nami wants it but wants other people to add it?

[fervent pebble]

bruh nami can't do everything here

[fair mural]

ryc does stuff

[fervent pebble]

gotta let other ppl feel accomplished smtimes too

gotta let other ppl feel accomplished smtimes too

[bright hill]

Oh

It's the Nico girl

Cringe.

[willow finch]

I sure could use a vacation from these freaks

[deep mango]

If nami were nice he wouldn't have nominated me for worst user!

[leaden torrent]

no i dont

sussysullybutred on the other hand

banger emote

[deep mango]

Sussy sully but red is at best marginally better

[fervent pebble]

he's just being honest nami wouldn't lie to you

[fervent pebble]

liar

[fervent pebble]

true

[deep mango]

So he would lie to you, but not to me...

[fervent pebble]

yes :(

also ryc i just realized

[leaden torrent]

i would happily lie to ryc

[deep mango]

Then how am I the worse user!?

[fervent pebble]

you dont get to see my pfp??

[deep mango]

oh

Ofc I don't

[fervent pebble]

wow

[deep mango]

Well I do on mobile

[fervent pebble]

hm

[deep mango]

Checked your pfp

it's dumb

as expected

Screencap from a vn?

[fervent pebble]

HOW DARE YOU

stfu pigeon boy

i got it off pinterest

[leaden crown]

Is anyone good at financial math problems? i need help

[bronze pelican]

Pigeon boy LMFAO

Chalkbird pidgeon boy

[deep mango]

[ancient flame]

HI RYC

[tender tulip]

Random math time.
A matrix in GL(n,R) generates a Bravais lattice via the matrix acting on Z^n, and is thus effectively isomorphic to Z^n. However, the subgroup SL(n,Z) acting on Z^n is automorphic, thus for some matrix M in GL(n,R) and a matrix N in SL(n,Z), both M and MN generate the same lattice

not finished you dippy

Now, we can essentially say that the (modified to be a true lattice) dual lattice for a lattice generated by M is the lattice generated by M^-T

(the dot product between vectors the lattices is always an integer)

So lets assume we want a lattice that is self dual, so the lattice generated by M and M^-T is the same

But M and M^-T are not the same matrices, but because they generate the same lattice and due to the properties mentioned above, we can say M = M^-T * N for some N in SL(n,Z)

and from there we can say that if M generates a dual-lattice-invariant lattice, then M^T * M is an element of SL(n,Z) (and is also symmetric)

Lets say that a matrix M is crystalline if M^T * M is in SL(n,Z)

Well, let M = KA, where K is an orthogonal matrix (KK^T = I), well then M^T * M = (A^T * K^T) * K * A = A^T * A, so A is also crystalline. The set of crystalline matrices is invariant under the action of the Orthogonal matrix group S(n,R)

[The set of crystalline matrices does lack a group structure btw]

Lets add an equivalence relation to the set of crystalline matrices such that:
A ~ B if there exists a matrix C in O(n,R) OR a matrix D in SL(n,Z) such that A = CBD.

[essentially any hyper-volume preserving transformation, along with the existing same-lattice generating matrix]

Now, lets assume n ≤ 8

It's a well known fact that there is only one unimodular lattice in R^n (n < 8) up to isomorphism, the integer lattice Z^n. So, essentially, in n < 8, every crystalline matrix should be equivalent.

But in n = 8, there is also the E8 lattice. Thus, there should be TWO equivalence classes here.

I wonder if there is an actual way to prove this without going through the nuttiness of proving it using properties of lattices unrelated to matricies [including norm vectors and shit]

All of this I kinda bullshitted to myself during work today so it's almost entirely unfounded

[tender tulip]

The lattice generated by this matrix is:
{v in Z^n union (Z + 1/2)^n : sum of components is even}

but is this lattice like, isomorphic to Z^n

[tender tulip]

THis is wrong, ignore it

Also changing the name "crystalline" to "integral"

Looking up some terminology, essentially M^T * M is the Gram Matrix

[ancient flame]

[fresh stone]

[hollow sundial]

[hollow ginkgo]

Which finite groups are isomorphic to the automorphism groups of symmetric graphs?

[neat lintel]

Well all $S_n$ are isomorphic to $Aut(S_n)$ except for n = 2 and n = 6.
$S_n$ is a complete group (except for the two mentioned cases earlier). And every complete group is isomorphic to its automorphism group $Aut(S_n)$ because it has a trivial centre and trivial outer automorphism group.
In case of n = 2, the center of $S_n$ is non-trivial, and in case of n = 6, $S_n$ has outer automorphism group.
Except those, all other Symmetric groups can be the example here

[fathom swallow]

Pencil/Idris

[neat lintel]

Hi det

[placid quartz]

hewwo

[arctic grove]

valley........
i thought u were based........

[bronze pelican]

Yeah

I have some slides on this

[neat lintel]

Ooo

[bronze pelican]

Its also explained in Joseph J. Rotman.
An Introduction to the Theory of Groups.

[neat lintel]

I see

[iron mulch]

Hello everyone !
Now the school year is over so I would like to focus on maths and especially on topology and differential geometry
Please, do you know which basis I need to study these topics ? Thanks !

[arctic grove]

what math have u done already

[sleek wing]

[topology basis joke]

[iron mulch]

Not a lot of things sadly

I mean I learn quite fast and I have a good math "intuition"

[sleek wing]

have you ever taken a proof-heavy course

[iron mulch]

First year of university lets say

[iron mulch]

If I understand what you mean, yes

[sleek wing]

if you've done proofs then you don't need much else for (point-set) topology

[iron mulch]

Ow really ? Nice !

[arctic grove]

doing analysis would be recommended

tho u dont need it

[sleek wing]

hahhahahah

[arctic grove]

for differential geometry tho

[sleek wing]

oh for diff geo yes

[arctic grove]

u do need analysis and linear algebra

[sleek wing]

diff geo is an absolute beast compared to intro topology

[arctic grove]

and a lil topology wont hurt as well

[iron mulch]

Okay ! But until which point ?

[iron mulch]

Thanks !

[arctic grove]

a first course in real analysis

[sleek wing]

I recommend topology without tears for a good intro to topology

[arctic grove]

it will help if u have some idea about continuity, convergence and all

i recc Intro to topological manifolds

it has such pretty diagrams

[sleek wing]

that wasn't a joke

[arctic grove]

thats an actual book

Topology without tears

pretty popular

[iron mulch]

Ow okay ! Such a funny name!

[sleek wing]

yeah cause it's freely available online

[iron mulch]

Yes I think it is fine for this !

[arctic grove]

true

[iron mulch]

That s a very good point

Thanks for all your good advices ! I am quite excited !

[sleek wing]

good luck out there

[arctic grove]

feel free to ask questions in advanced channels

check #get-advanced-access

[iron mulch]

Advanced ? University channels arent sufficient ?

[arctic grove]

Not really

Since analysis often isnt early uni

[iron mulch]

Thank you !

[arctic grove]

and at times linear algebra stuff can just be group theory in disguise

[iron mulch]

That is quite interesting ! In France it is studied quite early

[arctic grove]

oh u are from france?

[iron mulch]

That's funny !

[arctic grove]

france is kinda cracked at maths

[iron mulch]

Yes !

[arctic grove]

not fair to compare it to other countries

[iron mulch]

Cracked...is it good or bad ? lol

[arctic grove]

it means very good

[iron mulch]

Okay !

[sleek wing]

topology isn't, I've yet to encounter a uni that does not do analysis in first year

[arctic grove]

u are in the uk wew

go see american unis

thank u

[iron mulch]

In middle and highschool we are really not good at all
But our universities have good level !

[arctic grove]

i see

[arctic grove]

its not like u cant do analysis in first year

every uni i want to go to also does analysis first year

(im not in the us)

[sleek wing]

who cares about america then

[arctic grove]

chrew chrew

[sleek wing]

"often isn't" = "is done everywhere except america" now

[arctic grove]

yes.

[iron mulch]

But what do they do first in America ? Analysis for me is really the basis

[arctic grove]

they do calculus

from single variable to multivariable

and diff eqs and liner algebra

something like that

[ancient flame]

y'all do analysis before calculus??

[arctic grove]

(i should clarify not everyone has to do this, but a lot of math majors do)

[sleek wing]

no we just do calc in hs

[arctic grove]

calc is hs stuff

[ancient flame]

a lot of people do calc in hs too

but not everyone

[arctic grove]

yea

[ancient flame]

and especially not calc 2 or 3

[sleek wing]

we do up to what I think is calc 2 in hs

and calc 3 at uni

[ancient flame]

not many people get to calc bc

[iron mulch]

Okay I will appear quite idiot but what difference do you do between analysis and calculus ? For me analysis implies differentials and calculus...integrals maybe ?

[ancient flame]

I don't think most schools offer calc 2 other than the AP class and not a ton of people take that

[iron mulch]

In France I think we quite mix both

[ancient flame]

calculus is basically "what is the derivative of this function" and analysis is "ok let's take a closer look at what's going on"

[arctic grove]

Analysis usually means calculus but proof based

[iron mulch]

Okaaay !

[arctic grove]

it doesnt concern with calculating integrals or derivatives mostly

[iron mulch]

Thank you ! So yes in France it seems we do not separate both

[ancient flame]

damn

[iron mulch]

Or I didnt notice it which is also a possibility !

[ancient flame]

lol

[viscid pecan]

Analysis is gauging into the rigorous study of functions

Two semesters of calculus is vaguely showing you what functions can do but doesn’t explain them really

Which is dumb

[iron mulch]

Ow calculus could be what we call "calcul infinitésimal" but yes, for us it's analysis

I see

[viscid pecan]

Oh here’s some more basic algebra, now just arbitrarily use these methods you’ll take for granted with your basic algebra skills

[iron mulch]

So analysis is like...higher level calculus ?

[viscid pecan]

It’s calculus the way it should be taught to people who are interested in mathematics

I don’t really see the benefit of taking a watered down class that doesn’t really teach you anything.

You’ll vaguely understand what a slope and an area are still after you wasted a semester or two if you ask me 🤷‍♂️

It’s like crazy that students ask if they should take linear algebra or multivariable calc. I tell them, why the hell is linear algebra an option here?

You SHOULD have that linear algebra foundation. Bloody hell

[sleek wing]

it's an absolute methhead arrangement that people can do multivar before lin alg

[iron mulch]

I didnt realize how important it was !

[cold needle]

yeah idk how but my school has calc 3 before linear alg

its so

oog

[viscid pecan]

Well we deal with dimensions all the time and linear algebra is how we approach the abstraction of dimensions early on

[cold needle]

its ok in my analysis class we saw a little bit of Rn calc but whatever

[viscid pecan]

So a customer asked me if I knew anything about noneuclidean geometry and I told him I very vaguely understand Riemann Surfaces 😂

If vaguely understand counts as understanding at all.

But I sort of visually understand some things

[iron mulch]

Yes I understand what you mean ! It is quite funny and...maybe satisfying !

[viscid pecan]

That stuff is probably more complicated than some QM stuff out there

You can have coordinate planes superimpose eachother like origami

[iron mulch]

That seems very beautiful

[viscid pecan]

It breaks your brain at some point too I think 😂

[iron mulch]

😂😂

Thats why mathematicians are a little bit crazy

[viscid pecan]

Being human is crazy

[velvet dagger]

Didn't I tell you to change the curriculum there? Smh

[open aspen]

Can you stir fry pork loin? Almost every recipe i see calls for tenderloin

(If not like shoulder or butt)

[hollow ginkgo]

I don’t see how that disqualifies S₆.

Actually, what about K₆?

[eager flame]

Heya

For someone who knows how to play sudoku, why would 4 be a mistake in the highlighted box. I don't comletely understand the rules.

[frail kiln]

Because one square should not have two of the same number, there are two 4s in that top left square.

Also, each row and column shouldn't have 2 of the same number.

[eager flame]

Oh right.

Thanks

[frail kiln]

No problem!

[fathom swallow]

kangaroo rat

[signal lintel]

a sudoku player

i didnt know people still play sudoku i thought i was the only one

[open gorge]

Last time I said that on this server I got crucified

[fervent pebble]

i would never crucify shyshy

[arctic grove]

Loll

i mean, its not exactly correct either

but it explains what analysis is pretty simply

I can also just analysis is inequality spam

and no one can say shit to me for saying that

[neat lintel]

~~Basically there exists an outer automorphism of S6 that doesn't preserve the structure of S6.

Aut(S6) is a semidirect product of S6 and C2. Hence, its order is 6! . 2.
By Lagrange's Theorem, |Out(S6)| = |Aut(S6)|/|Inn(S6)|
And Inn(S6) is isomorphic to S6, since the center of S6 is trivial (because any symmetric group of order ≥3 is non-abelian), and we know isomorphism preserves orders. Hence |Inn(S6)| = 6!
Hence |Out(S6)| = 2.6!/6! = 2, which implies that it is non-trivial, hence not complete, and implies Aut(S6) is not isomorphic to S6~~

Another great argument is that isomorphism is one-to-one and onto, and hence must preserve orders, but |Aut(S6)| = 2.6! ≠ 6! = |S6|, and hence no isomorphism exists between them.

[hollow ginkgo]

1. How is S₆’s exceptional outer automorphism relevant?
2. What about K₆?

[neat lintel]

For 2, I'm not really sure about that

[neat lintel]

Hmmm okay I changed my mind, I believe the second argument is more relevant here.
Because every complete group G has Aut(G) iso to G, but converse isn't always true (Aut(D8) is iso to D8 but D8 isn't complete, a counterexample)
So for 1, that exceptional outer automorphism is not really relevant here
@hollow ginkgo you may use my second argument why Aut(S6) is not iso to S6

[tender tulip]

Let V be a vector space of (field F acting on abelian group A)

Let B be the set of all bases of A, (all with the same cardinality, the dimension), and there exists a matrix that maps each base to another base. Does this mean that the general linear group of the vector space acts transitively on the set of bases?

[sleek wing]

yes

[odd narwhal]

Didn't you already ask this

[tender tulip]

yeah but didn't get an answer

it is transitive, I checked the def

[odd narwhal]

Im pretty sure you did

Anyways

Linear maps that send a basis to a basis are isomorphisms

And a linear map is defined by its action on some basis

[tender tulip]

I asked if it was free. Afaik it isn't

[odd narwhal]

It's not

Wew answered that

Iirc

[tender tulip]

I was going to use it at some point in the question I'm gonna try to answer in #linear-algebra

[muted totem]

I wasn't quite sure where to put this, so I decided to try here. Suppose we wanted to find maxima or minima on a function $f:\mathbb{R}^2 \rightarrow \mathbb{R}$. Does the following procedure relate in some way to "partial derivatives"? I understand they can be used to do the same thing.

[fathom swallow]

person2709505

[muted totem]

We'll use $f(x,y)=\cos xy$ as an example. First, consider the general "cross section" of $f$, which contains the point $(x,y)$, runs in the direction $\theta$, and is parametrised by $t$. We abuse notation a bit and call the cross section $(f \circ L)(t)$, where $L(t)=(x,y)+t(\cos\theta, \sin\theta)$. We find $f \circ L$ to be $\cos(xy+t\sin\theta + yt\cos\theta + t^2 \cos\theta\sin\theta)$. Differentiating with respect to $t$, we get that $\frac{d(f\circ L)}{dt} = -\sin(xy + xt\sin\theta + yt\cos\theta + t^2 \cos\theta\sin\theta)(x\sin\theta + y\cos\theta + 2t\cos\theta\sin\theta)$. At $(x,y)$, we have that $t=0$, so we get the expression $-\sin(xy)(x\sin\theta + y\cos\theta)$. This expression, which we'll use more abuse of notation to call $m(\theta)$, gives the slope in the direction $\theta$ at the point $(x,y)$. At a max or min, we will have that $m(\theta)=0$ for all $\theta$. Clearly, any $x,y$ satisfying $xy=2n \pi$ or $xy=\pi + 2n \pi$ $n \in \mathbb{Z}$ meet our criteria. We therefore conclude that f must have either local maxima or local minima at $xy$ coterminal to $-1$ or $1$.

[fathom swallow]

person2709505

[muted totem]

Sorry that should be "coterminal to 0 or pi" in the last sentence

[hollow ginkgo]

And how is any of that relevant?

[mint patio]

sotrue

[neat lintel]

Because we are trying to prove that isomorphism exists between Sn and Aut(Sn)
But this is not true for n=6.
S6 is a semidirect product of S6 and C2. Hence its order is |S6|.|C2| = 6! . 2

But order of Sn is 6!
If we map Sn to Aut(Sn), we see that the order is not preserved, and hence no isomorphism exists when n=6

[hollow ginkgo]

Why?

[neat lintel]

In isomorphism, order is preserved

Here it is not happening

[hollow ginkgo]

Why do we care about S₆ not being isomorphic to Aut(S₆)?

[pearl moth]

why wouldn't we care about that?

[hollow ginkgo]

What does it have to do with graph automorphisms?

[pearl moth]

dunno

are we only allowed to care about things that have something to do with graph automorphisms?

it does appear to be relevant, though

in a complicated way that i can't claim i understand

[hollow ginkgo]

That’s what my original question was about…

#serious-discussion message

[pearl moth]

yeah, but you don't get to decied what the discussion covers

once the discussion starts, it's the property of the community and can go wherever the community desires

[hollow ginkgo]

What was being discussed?

[pearl moth]

and in any case the exceptional case of S_6 is completely relevant to graph automorphisms, based on my very brief reading

[hollow ginkgo]

How so?

[pearl moth]

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

there's a section on there that applies this to graph automorphisms

i think, not sure, still seems cogent

[ripe wasp]

when reading textbooks, at what pace do yall read?

[surreal sapphire]

vastly depends on the book?

[ripe wasp]

i mean it ofc depends on the section length and difficulty but like generally

[surreal sapphire]

on a good day maybe 10 pages

[neat lintel]

depends

[ripe wasp]

do you spread out exercises and just reading evenly so like you read a bit then do some exercises or do yall have things like "reading days" then just "exercise days"

[neat lintel]

i go proof then skim exercises

cause some of the exercises only test for "knowledge"

particularly directly after the proof

when i find a hard problem i do it

[bright hill]

bruh

10 pages is more like a max imo

[surreal sapphire]

oh, exercises take longer
i havent considered this, because i dont do them anymore

[neat lintel]

Hello

[surreal sapphire]

i think its good to do exercises while reading the text but its hard to judge whether you already have the tools

[neat lintel]

the proof is left.

[surreal sapphire]

i did say on a good day

[brittle socket]

Lol this is so true

That the pace of reading a math book isn't really fast

If I reach the exercise part of a chapter it depends how long I need to spend. Its been quite a while since I've started on Spivak Chapter 2's exercises and I still have like 2 left which I want to try as they seem quite interesting

I have like 40+ pages of latex for Chapter 2's exercises alone lol

Perhaps even 50

(for just like 10+ qns, maybe around 13-ish)

[toxic gale]

Yeah I've been able to speed through lower level math books but once you get to the real stuff things grind to a halt. Content becomes so much more densely packed.

[viscid pecan]

Really hard books I’m working thru my strategy is to try to do half the exercises per chapter and try not to be too bogged down otherwise

Cuz if you can do about half the exercises, you should know enough to move on

Like especially if the exercises seem challenging to you, you probably should do them

[pearl moth]

it's been a while since i looked at a textbook, other than to look up something from a previously used book to refresh my memory

[wooden flax]

how to get active role

i have like 5k messages but no blue role

[bright hill]

you swear at @polar panther until it complies

[fervent pebble]

be better 😎

[bright hill]

like this:

@polar panther bitch, where very active???

[deep mango]

[deep mango]

Active roles are weighted by channel value

[wooden flax]

hm

i mean my chill ratio is .1

[bright hill]

stop sullying me

(╯°□°）╯︵ ┻━┻

I sully YOU!

[wooden flax]

[neat lintel]

adding active/very active roles was a mistake

[deep mango]

Gimme colors!! Gimme colors!!!

Imagine if helper were uncolored

Wow

[fervent pebble]

agree

[deep mango]

Valley why do you have that vile number as your name

I hate 91

[fervent pebble]

dami

• too lazy to change it

you can if u want

[bright hill]

why is 91 so vile?

[deep mango]

Should be prime

[bright hill]

oh

[fervent pebble]

$\frac{\mathbb{Z}}{91\mathbb{Z}}$

[fathom swallow]

13 x 7 = 91

[fervent pebble]

.> is that notation correct

[bright hill]

I don't think I've ever seen this notation

do you mean Z/91Z?

[neat lintel]

it was just a sully in the public discussion channel, discord

[fervent pebble]

oh right no mathbb

[fervent pebble]

lmfao

[bright hill]

[deep mango]

Z/91

[neat lintel]

writing quotient spaces as actual fractions is sometimes done. the notation is technically G/H, but you will confuse no one

[bright hill]

@sleek wing

[neat lintel]

G/H coming from the fact that it consists of left cosets and the G is on the left of H

but nobody cares

[deep mango]

No

[fervent pebble]

ryc cares

!

[deep mango]

I am having an espresso at 11 pm

[bright hill]

wtf is wrong with you

[deep mango]

They didnt give me 3 drinks

[bright hill]

that's the worst thing you've ever done

[deep mango]

These are the consequences of their actions

Im not letting tonight die that easily

[bright hill]

ryc, I'm disappointed

not only did you commit this heinous crime

[deep mango]

Im a bad boy

I do what the fuck I want

[bright hill]

you aslo failed to take reponsibility

[deep mango]

And no one can tell me what to do. Especially not you darq

[azure nymph]

What's wrong with espresso at 11 pm

[fervent pebble]

what abt shin

[deep mango]

How dare you

[bright hill]

[deep mango]

Uhhh sleep??

[bright hill]

that might be true

but I'm disappointed still

[fervent pebble]

what abt nami

[deep mango]

Nami has no sway over me

Neither does shin

[fervent pebble]

what abt dami

[deep mango]

Hes just usually right when i dont understand what im talking about

[azure nymph]

It's like a hot chocolate or tea before bed nice warm drink to relax

[bright hill]

kenshin

[deep mango]

What

Ok

[bright hill]

what's wrong with you

[deep mango]

This is why warm milk exists

[fervent pebble]

kenshin has a crippling caffeine addiction ofc

[deep mango]

But yeah hot choccy is great for before bed

[fervent pebble]

.

[bright hill]

dami being scary is just a meme

[deep mango]

Valley you started with the most embarrassing one and you're moving down the embarrassment chain

[bright hill]

get a grip

[azure nymph]

Admittedly I have to have a large cold brew or dopio to really feel caffeine

[deep mango]

Dami could not possibly get me to do something

[fervent pebble]

we aint even at the bottom yet boi

what about slurp

[bright hill]

@neat frost you've been summoned

[deep mango]

Slurp also is incapable of getting me to do things

[fervent pebble]

what about alex

[deep mango]

Unfortunately you are moving further and further away from people who historically have had any sway

[hardy vessel]

valley enumerating everyone in the server

[fervent pebble]

what about skid

[deep mango]

[fervent pebble]

no answer means yes btw

[deep mango]

What if we had a real conversation

[fervent pebble]

what's that

[bright hill]

lmao

[fervent pebble]

jkjk what do you want to talk abt mr bad boy

[azure nymph]

So what is everyone studying these days

[deep mango]

Well my espresso just got finished

So now I will head home

And not have any wifi during my walk

[bright hill]

haskell, mostly

[deep mango]

Or internet access whatsoever

[fervent pebble]

a tragedy

[azure nymph]

Ew

[deep mango]

Its very nice

I had a fun day

[fervent pebble]

gj

[bright hill]

haskell is ok, come on

[fervent pebble]

!

[deep mango]

I am excited for tomorrow morning where I will learn about how someone is studying gravitational waves from LIGO data

[azure nymph]

I have heard many bad things about haskell though admittedly I don't know any code

[bright hill]

[maiden vapor]

where can i get help for addmath

[fervent pebble]

for what?

[maiden vapor]

trig

[bright hill]

anyone I know that knows even a tiny amount of haskell seems like they want to suck its dick

this is news for me

[azure nymph]

Really my professor said he always got really annoyed with it

[bright hill]

is he a mathematician?

[azure nymph]

Yes

[bright hill]

bruh

[azure nymph]

He does like modeling and computation in mathematical biology

But he learned a ton of languages

[neat frost]

Untrue.

What does ryc need to do?

[sleek wing]

ban

[neat frost]

WEW

[sleek wing]

slurp

[neat frost]

WEW

[sleek wing]

how's it hanging homedawg

[neat frost]

Not well

And you?

[sleek wing]

very well

[neat frost]

I’m sure

Wew do you live by yourself?

[fervent pebble]

L

[sleek wing]

most of the time

[neat frost]

Mmm

How do you afford your own place?

[sleek wing]

I'm rich

[neat frost]

But like serious-type time

You strip?

[fervent pebble]

LMFAO

[wooden flax]

LOL

[sleek wing]

no I don't STRIP

jesus..

it's called POLE DANCING?

[neat frost]

Mmm

[sleek wing]

IT'S AN ART?!

[neat frost]

Aha

[sleek wing]

you wouldn't understand it slurp

[neat frost]

So is stripping my friend

[fervent pebble]

honestly slurp ur kinda insensitive

[fervent pebble]

speaking from personal experience?

[neat frost]

Some might even say stripping is a more complicated art

[neat frost]

Maybe, maybe not

[sleek wing]

I strip when I go in the shower (except my swimming goggles and spongebob swimming trunks)

[fervent pebble]

based

[sleek wing]

sometimes I even bring in one of those inflatable ring things

[fervent pebble]

pool noodles?

no

wait

the little floaties?

[sleek wing]

no like

one of these

[neat frost]

Aha

How much money do you make?

[sleek wing]

in the shower? not much

[neat frost]

Pole dancing

[sleek wing]

it all gets wet and mushy by the time I pocket it in my spongebob swimming trunks

[sleek wing]

I'm not from poland I haven't danced with anyone from there

[neat frost]

No silly that’s pole dancing

I’m talking about pole dancing

[sleek wing]

OHHHHHHH

I don't get it

[neat frost]

Ofc you wouldn’t

Pole dancing wew, pole dancing!

[sleek wing]

oh why didn't you just say so slurp

640 morrocan dirham per hour

[neat frost]

,w 640 Moroccan dirham to NIS

[fathom swallow]

Results provided by WolframAlpha

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

Requested by Slurp#0155

[neat frost]

Mmm respectable!

[sleek wing]

wait slurp why have you converted it to israeli shekels

u want it in euros

[neat frost]

As a flex

[sleek wing]

tbf the currency symbol is swag

[neat frost]

Obviously I memorized the exchange rate from NIS to euro

[bright locust]

,w 640 Moroccan dirham to USD

[fervent pebble]

is that an aleph i see

[neat frost]

No

[sleek wing]

no

[neat frost]

₪

[fathom swallow]

Results provided by WolframAlpha

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

Requested by % Openglobe %#3085

[neat frost]

It’s a stylized שח

[fervent pebble]

hmm

[neat frost]

Which stands for new shekel

[fervent pebble]

looks like an aleph

[bright locust]

Ok I guess

[neat frost]

Your mom does

[sleek wing]

yo mama lookin like an om nee cron

[neat frost]

Wow

[velvet dagger]

What is going on

[bronze pelican]

what a donut

[sleek wing]

don't eat it

[plucky zodiac]

Is there a differential equations section for this discord

[primal seal]

#odes-and-pdes

[deep mango]

so many pings

[ancient flame]

starting to learn linear algebra!

but

the author uses a horrible notation for dot products

$u^Tv$

[fathom swallow]

gmod

[ancient flame]

like what

these aren't transposed matrices what are u doing

[summer sandal]

I guess R^n for them is R^(1 * n).

The space of all 1,n matrices.

[leaden torrent]

these aren't transposed matrices
yes they are

this notation totally makes sense if you associated 1x1 matrices with scalars

i'd prefer a \cdot but there's merit in how they present it

[summer sandal]

My fault I meant R^(n * 1).

[velvet dagger]

Ryc go clean your room

[ancient flame]

oh

well I gave up on that book after I realized it was geared toward engineers

"applied linear algebra"

no ty

[leaden torrent]

that explains the conflation of scalars and 1x1 matrices

if the only spaces you work in are F^n for a field F, there's no danger in doing so.

[ancient flame]

makes sense

[pearl moth]

i see that a lot, both in texts for engineers and also in content for machine learning

vectors are nx1 (or sometimes 1xn) matrices and scalars are 1-vectors and thus 1x1 matrices

[leaden torrent]

conceptually it is perhaps a bit weird that associating vectors in the definition-of-a-vector-space sense with "row/column vectors" (i.e. 1xn or nx1 matrices) is totally fine, but associating 1-vectors with scalars can be problematic

like the distinction is easy enough if you know how vector spaces are defined formally

"matrices are built from vectors, whereas scalars are just a completely separate object"

but i can see why it's weird for learners

scalars "aren't really" 1-entry vectors, but vectors ARE really 1-column matrices?

¯_(ツ)_/¯

[pearl moth]

yeah

[neat lintel]

Don't do 1 vectors have seemingly same properties as scalars

[peak tide]

not always.. for example, if $v$ is an $n \times 1$ vector and $c$ is a scalar, then you always have $cv = vc$. On the other hand, if $w$ is another $n \times 1$ vector, then $w^T w$ is a $1 \times 1$ matrix, but but you don't have $(w^T w)v = v(w^T w)$; the multiplication on the left hand side is invalid as the dimensions are incompatible

[fathom swallow]

OurBelovedBungo

[neat lintel]

Okay that's actually a good argument

in practice everyone identifies 1 x 1 matrices and scalars anyways

Yea

so while this is technically right, who cares lol

(maybe "who cares lol" is a bit harsh given the original question, it is still a good point)

[peak tide]

generally true, but the above shows that you can run into trouble if you aren't paying attention, and it's not just a silly hypothetical example, this kind of stuff shows up sometimes when doing extended calculations involving matrices and vectors (things like deriving kalman filter equations and such)

"aha, that's a scalar, so I can slide it over here to simplify..."

"oops, wtf, now the dimensions don't make sense"

[neat lintel]

So depending on context of calculations, you can "interchange" the concepts of 1 vectors and scalars
But in general, they're not the same

[peak tide]

yeah, fair characterization, you can treat them the same in many cases but not always

[ashen pike]

3b1b made a video on the duality of the dot product with a column vector and n*1 matrices I think

[sick burrow]

Does anything actually go wrong if you treat 1x1 matrices as scalars

[sick burrow]

Like this comment. What other spaces would that be a problem in?

[storm sage]

Well as they pointed out above, you can multiply a scalar times an nx1 vector but not a 1x1 matrix by a nx1 vector

So you have to be tricky with the notation

[sick burrow]

Well yeah so it doesn't work in the 100% formal sense but also does that matter

[storm sage]

I mean it always matters if you're trying to prove something or if you're doing a calculation and all of a sudden you notice the dimensions don't work out

Practically it's useful to identify 1x1 matrices with scalars

But identification is not the same thing as they're always the same

[sick burrow]

Yes I'm aware they're different objects

I was more referring to Namington's comment

if the only spaces you work in are F^n for a field F, there's no danger in doing so.

Like what changes here with infinite dimensional spaces?

[static loom]

probably the nicest thing imo about this is using it to write a projection matrix onto the vector v, $$P=\frac{vv^T}{v^Tv}$$ it's pretty straightforward to show $P^2=P$

[fathom swallow]

Merosity

[ancient flame]

interesting

[static loom]

I suppose I should also mention, I-P would then remove the component of a vector in the v direction, which is also handy, and you can combine more things to remove more components or to make a plane etc

[ancient flame]

I see

[heady fog]

Does anyone here have interview experience from a European, non UK quant job?

Im wondering if it is reasonable to expect the same type of questions as one might get in the US

[leaden torrent]

consider, say, ℝ over ℚ

[sick burrow]

Wait why is that a problem

[leaden torrent]

the 1x1 matrix [π] obviously doesnt correspond to any scalar

[sick burrow]

How is that a matrix though

Or a 1x1 matrix

The entries of a matrix have to be in the scalar field right?

[leaden torrent]

no? they just need to come from a ring

oh i see your concern

yeah theyre not matrices in the sense of being compatible with the linear map structure of the vector space

since this is an equivalence you can only make for finite dimensional vector spaces

(since you need to fix a basis)

so the direction that fails is going from scalars to matrices

[sick burrow]

How do matrices work in infinite dimensional spaces anyways

[leaden torrent]

they dont

like you can talk about matrices by just considering them as arrays of numbers from some ring

[sick burrow]

I forget do linear maps have to send basis elements to finite linear combinations of basis elements?

[leaden torrent]

but

they have no relation to the linear maps of the space

theyre just an extra thing you can talk about

if you wanted matrices to correspond to linear maps, your matrices would need to be infinitely large

[sick burrow]

Is that a problem though?

[leaden torrent]

well, not necessarily

the existence of such "matrices" in most contexts requires the axiom of choice though

[sick burrow]

Yeah but doesn't half of analysis require that also

Or all of analysis?

[maiden bear]

there are some special cases where it does make sense to talk about infinite dimensional matrices as maps between infinite dimensional spaces

[leaden torrent]

yeah like

its a totally sensible thing to do

but its not usually as useful as finite matrices are for finite dimensional spaces

since obviously you cant really use them computationally

good luck diagonalizing an infinite matrix lmao

[maiden bear]

lol

well a bunch of LA goes down the drain with those i guess

Lartomato gave me a lil excurse about R^inf and GL_inf some days ago when we talked about infinite dimensional matrices there

[stone ferry]

Proof that the series converges to sin(x): dude just look at it, what other function can it be?

[static loom]

same that's what I do when I look at $x \prod_{n \ge 1} \left(1-\frac{x^2}{n^2\pi^2}\right)$

[fathom swallow]

Merosity

[velvet dagger]

Okay but actually though

What is a suitable "calculus way" to define sin(x)?

Like if you just define the power series and prove stuff about it, its geometric nature/importance are unclear

I guess real/im part of the exponential?

[neat lintel]

spivak's "calculus" gives a definition of the trig functions based on integration

i don't remember it off the top of my head and i don't have the pdf on my laptop

where

[velvet dagger]

Yeah I know that one but that feels like

Completely scuffed lmfao

[neat lintel]

it is and it is god awful to work with

especially when you're a first year calculus student fresh out of highschool (where "opposite over hypotenuse" was good enough)

[velvet dagger]

I think the differential equation might be the strat tbh?

[fervent pebble]

you can easily get that from the power series def

which then gives some geometric structure

plus i bet you could define them in terms of polar integrals

.>

maybe

[cold needle]

the differential equation way is cool

really good exercises to get the other properties and all

[velvet dagger]

@fervent pebble the thing is

You just write down a power series and it's like

Okay cool

y tho

I think you need to start with the differential equation or say real/imaginary part of complex exponential

[fervent pebble]

hm

how do you get the power series def or the exponential def from the diffeq tho?

[velvet dagger]

So in calc unless you're doing complex number stuff early (but then it's weird since you're not really doing complex analysis exactly)

You prob just have to do the diff equation if you want it not to be scuffed. At least that has the oscillation-y intuition behind it

That's a good question, I know exactly what that story looks like for the exponential but hmm

[tall badge]

i mentioned it and a rando here called it "I need to touch grass" def, forever tainting my opinion of trig & DEs /s

[velvet dagger]

It's still a little bit unfortunate because I feel like differential equations are fundamentally a linear algebra idea but hmm

@tall badge sometimes you get got in life man

It's how it goes

[cold needle]

wdym the power series is just the power series solution you can get from doing like frobenius or whatever

right ?

i forgot how it goes tbh

lol

[velvet dagger]

I don't know differential equations lol

Yes I study spectral theory of the Laplacian

I don't see the problem here

[cold needle]

understandable

[tall badge]

the other grass

[brittle socket]

I am the grass

[fervent pebble]

touch grass 😉

[brittle socket]

[chilly hull]

https://media.discordapp.net/attachments/775154210777726987/991247671820042250/ezgif-5-f2850d50dc.gif

[fervent pebble]

holy shit

"woog" has been said over 30k times on this server

not counting pings

pinged over 15k

[tall badge]

poor woog

[static loom]

thats a lotta pings

[fervent pebble]

that's also not counting mod pings which i bet he used to get

[cold needle]

she

[fervent pebble]

she

and which i can't count

[wild lantern]

Isomorphism has only been said around 15k times?

[cold needle]

woog isomorphism

[fervent pebble]

but im gonna guess conservatively during when she was actively modding at least 5k times?

[static loom]

if you want to imagine the server prior to woog, you can in part imagine ann in charge

[fervent pebble]

so im gonna say total count of mentions/pings > 50k

probably more counting channels i can't access like ivory

[static loom]

that's not a metaphor lol

[fervent pebble]

if a mod looked it up they'd prolly see more results

[wild lantern]

Well I have seen old chill posts from Ann

[tall badge]

17.5k woog pings/mentions

[fervent pebble]

yeah that's about 2.5k more than i saw

so i imagine the casual mentions are even higher

[sick burrow]

why do people always forget woog is a girl

[wild lantern]

I think a lot people just default assume people are boys online unless told otherwise.

It's not really a fair assumption to make ofc.

[azure nymph]

That's why you go for the genius "they"

[wooden flax]

a cool pronoun is "ey" as a replacement for they

from the spivak calculus guy

[fervent pebble]

honestly on discord i would say it is

although i should be saying they anyways

[near temple]

???

[fervent pebble]

proportion of men on discord is >>>> vs proportion of women on discord

[near temple]

How do you know

[fervent pebble]

discord is mainly a gaming service, which is male-dominated

[near temple]

You say this on a Math server

[fervent pebble]

yeah

i do

math is pretty male-dominated too

[near temple]

But by how much?

[fervent pebble]

probably a lower proportion than discord

but a subcommunity is not necessarily representative of the greater community

[leaden torrent]

actually everyone here is female

under directive of the Biden administration, we are instituting mandatory femboyization for all our users

[odd narwhal]

Is it. It's been shying away from branding itself as a gaming service for years now

Like since 2018 even I think

[leaden torrent]

it doesnt brand itself like that anymore but it still carries the baggage

[odd narwhal]

Sure but it has gained a lot of new users who don't know of its dark past

[leaden torrent]

you can say the same thing about this server

[near temple]

What was it's Dark Past?

[leaden torrent]

g*mers

[near temple]

[odd narwhal]

That's true nami, you don't air out your dirty laundry in public often

[leaden torrent]

theres also just the whole nature of like, how online communities tend to polarize

[near temple]

Like how everyone eventually gets trapped in their echo chambers

[leaden torrent]

a space (a website, a server, whatever) pushes out 1 demographic, either intentionally or accidentally

and then that demographic ends up in another space

and they gradually grow more and more disjoint

even within discord, this much is obvious

anime servers have a radically different culture to the rest of this platform lmao

[near temple]

Well it's unavoidable since you can't cater to everyone

[leaden torrent]

it is like

weird

[near temple]

How?

[leaden torrent]

idk how to describe it

[near temple]

I've never been in one of those

It can't be THAT different?

[leaden torrent]

[near temple]

[leaden torrent]

theres a sort of like, forced positivity in a lot of them

its really hard to describe

ive been in servers that straight-up banned any emotes that didnt originate on their server

including global emotes

its fucking weird

[near temple]

[odd narwhal]

I feel like being horny is also less frowned upon in those spaces

[leaden torrent]

you say that as if #「ivory-tower-emeritus」 isnt constantly horny

[static loom]

as long as you hide it in your fur suit, it's fine

[near temple]

I feel like it'd be encouraged depending on the anime

[odd narwhal]

Talking about cum and being horny are not the same thing nami

I don't think ivory has been horny for at least like, a week

[leaden torrent]

i think this is homophobic

and theres plenty of servers out there that are just like

either openly racist or really not good at hiding it

naturally i am not part of any of them, at least to my knowledge

[odd narwhal]

Like uhh

[leaden torrent]

but

yeahhhhhhh

[odd narwhal]

that one

[leaden torrent]

and then theres like

trans discord

which i swear is a fucking alternate universe

such a different culture to the rest of discord

or even like, general LGBTQ spaces

nothing wrong with it or anything, just a cultural observation

[near temple]

How does it compare to this server?

[leaden torrent]

this server also has a pretty unique culture lmao

we try and make it feel less "arcadey" than most servers in general

[static loom]

future techno-anthropologists will study these messages

[leaden torrent]

so like

less focus on roles and shit

there's a reputation system technically but no one uses it lmao

no gimmick bots or whatever

the roles that exist are almost purely functional, except the activeness roles

[near temple]

Yeah some people have three different roles that don't seem to do anything

[leaden torrent]

and a lot of these functional roles have intentionally obscured names

[chilly coral]

One time i was inactive for a while then lost my blue name and I was devastated. I place the whole value of my existence on the color of my name

[leaden torrent]

like γ and ±

(no i will not answer questions as to what these roles do)

(but they do do something)

[near temple]

So "Role that does nothing" does something?

[leaden torrent]

that one doesnt lmao

[static loom]

reminds me when I left the server I never got around to requesting my gamma role back cause I like the peace and quiet

[near temple]

[leaden torrent]

that one was just to test the role assignment system

and we kept it around because:

(a) some people really like their useless novelty roles

(b) being able to assign and unassign a role can actually be useful for debugging discord

like, we have a 10 minute wait period on new members

but every once in a while it breaks for someone and lasts forever

and they can fix it by assigning themselves a role

literally any role

[near temple]

Weird

[leaden torrent]

discord is a weird platform.

this server is simultaneously a lot more "regimented" than most servers and a lot less "restrictive" on where stuff goes

like, except for "dont post your questions in discussion channels (unless theyre interesting)" and "memes go in #chill "

we're not SUPER picky about like

#math-discussion going briefly off-topic for a bit

[near temple]

People do this all the time anyways lol

[leaden torrent]

if it lasts a while we'll try and turn it back around

i mean sure but its mostly new users who do it

i.e. users who havent interfaced with the server culture

[near temple]

That makes sense

[odd narwhal]

Come back to your hole mero

[near temple]

It's just that because there's a constant stream of new users it's noticable

[leaden torrent]

but like, ive been on servers where there are like

8 different "topics" channels

like theres a #food channel and an #anime channel or whatever

[static loom]

noooooooooooooooooooooooooooooooooooooooooooooooooooooooo

[leaden torrent]

and if you start posting about food in #general

[static loom]

ok maybe later but not tonight

[leaden torrent]

youll be redirected to #food

that isnt necessarily a bad system, it works for them

but we dont have anything like that

the closest thing are the "misc" channels

#chess-go-shogi and #latex-help

and #cats

[near temple]

Those are so random

[leaden torrent]

but you can still post about those topics elsewhere

[odd narwhal]

Except #❓how-to-get-help

[leaden torrent]

(though cat gifs should stay in #cats and #chill most of the time)

[static loom]

I think the good thing is there's a kind of "directedness" that math sort of imposes on stuff that gives enough structure that works well

[leaden torrent]

yeah, i mentioned this earlier

but i mean like

[near temple]

So Math gives the server structure?

[leaden torrent]

if youre intending to just discuss something

you can just throw it in a discussion channel

[static loom]

I get a similar vibe from any kind of technical help server, they have this sort of intrinsic help-helper system aspect

[leaden torrent]

hell, if you want to discuss analysis you can do it in like

7 different channels

not counting help channels

and each channel will have a different "target demographic"

[near temple]

I feel like #discussion and #chill are used for the same things a lot of the time

[leaden torrent]

talkign about it in #real-complex-analysis will probably result in people trying to help you with a specific question or concept

[static loom]

idk how other people use this server but I have all help channels muted then a handful of math subjects I'm not that interested in muted too, so I'm only ever seeing stuff pop up that is in subjects I'm interested in

kind of how I use MSE I guess too

[leaden torrent]

talking about it in ivory or advanced-lounge will probably result in people discussing work they did in that area, or maybe even extensions and generalizations and stuff

(ivory will also probably result in it being interrupted by the occasional shitpost)

[static loom]

like have watched tags and ignored tags

[leaden torrent]

talking about it in #discussion will probably result in a low-level discussion where people ruminate on their academic experiences

[near temple]

[leaden torrent]

also someone chimes in with "wow this looks soooo hard" every 15 minutes for some reason

as if that adds anything

[static loom]

it would be nice if there was some way to implement this sort of tagging system in discord to emulate this kind of experience:

[leaden torrent]

lmfao

i love that MSE has a collection of "bullshit filters" tags

like how arxiv has math.gm

[static loom]

haha

[leaden torrent]

479 questions, 6 asked this month

do i dare click

"hey MSE, solve the collatz conjecture for me"

[static loom]

aww poor kid, closed

[leaden torrent]

it seems this person simultaneously

• did not realize that a constructive answer was a solution to the collatz conjecture
• immediately recognized that it would be a solution when informed of such

which is like, a weird mix

[static loom]

big yikes

[leaden torrent]

there are some questions that are tagged with collatz-conjecture that make no sense though

is this actually related to collatz

[wooden flax]

RIP cv

[static loom]

it's probably some convoluted way they've tried boiling down how to solve it and this is their "key" step or something

[chilly coral]

What're the odds that, even if they proved this, it wouldn't mean anything cuz they made a mistake somewhere else

[leaden torrent]

100%

???

like i can see how this is maybe tangentially related but

weird af to give it that tag

[clear parcel]

maybe to draw more attention to it lol

[static loom]

haha

[leaden torrent]

im pretty sure the collatz-conjecture tag would just make people avoid it more.

[static loom]

well that's certainly how I use it

and it works great

[sick burrow]

I still want to find out what the gamma role does one day

like I get that's it's probably either some admin thing or access to some private channel, and in either case there's really no reason I should know

and I wouldn't particularly it's just that I am gamma

(ignoring the imposter that joined recently)

Nami is banach-alg a functional role or a shitpost role?

[fervent pebble]

active and very active were mistakes tbh

they should be removed

[ancient flame]

no

[neat lintel]

yes

[arctic grove]

bad take

[reef carbon]

@strong sphinx how are 4-digit question numbers 'seemingly infinite'? :P

[strong sphinx]

Every other book I've seen just restarts the question number for each section but Demidovich just keeps going. I have to respect it though.

[fervent pebble]

does anyone know a proof not by diagonalization that $|\bZ| \neq |\bR|$?

[fathom swallow]

13 x 7 = 91

[sleek wing]

yup

[fervent pebble]

would you like to show it to me

[sleek wing]

perhaps I would

can I do Q and R though since |Q| = |Z|

[fervent pebble]

yeah

[sleek wing]

ok so say you've got a countable list of every real number written out as their decimal expansions

[fervent pebble]

okay

[sleek wing]

then I start constructing a new number 0.(stuff). The first decimal of this new number is made by taking the first decimal of the first number and adding 1 to it, if that decimal is a 9 then I just set it to 0
I then construct the second decimal by taking the second decimal of the second number and doing the same operation as before, I then do the same for the third and fourth and fifth and so on

at the end of this process I now have a new number that is by definition different in at least one place to every number on the list

[fervent pebble]

[sleek wing]

so it's a number not on the list

[fervent pebble]

wew

[sleek wing]

thus R is not countable

[fervent pebble]

bad