Mathematics

Thorgott

12:12 AM

Are you asking for a concrete procedure?

Akiva Weinberger

12:37 AM

An algorithm

Tay

1:18 AM

Hey! If I'm reading a paper that has an intermediate result that I can't understand, where can I ask for clarification? Would it be fine to ask on the main site if I put a relevant excerpt from the paper and also include a link? Or is it okay to ask in chat?

Thorgott

1:29 AM

Both are fine. You can ask pretty much anything here and if no one here can help, you can post a question on main, which will be fine as long as you include the relevant context.

Tay

Thanks!

Here's the paper. I'm confused about the proof of the Theorem 25. On page 18 there's an inequality (63), which if you consider the inequality (61), should have the coefficient 3/2 and not 3 in front

This seems basic, but I can't understand why the author would pick a larger coefficient than required

And no amount of context helps

DRP

2:27 AM

Is there a way I can delete a question of mine here?

After a while just shows flag for moderator

anakhro

3:26 AM

Unless it is profane, I don't see why you'd want to delete it.

user76284

4:11 AM

en.wikipedia.org/wiki/Graphon generalizes immediately to directed graphs if the graphon is asymmetric, right?

Akiva Weinberger

4:29 AM

Feb 10 '17 at 21:45, by Akiva Weinberger

Graph theory game http://treksit.com/?thegame

Semiclassical

5:12 AM

@AkivaWeinberger so basically planarity.net but with background effects

Semiclassical

5:30 AM

also, the bonus area is creepy af

Mary Star

6:06 AM

ok, for that we have:

Let $\epsilon>0$. We want to show that there is a $\delta>0$ s.t. if $0<|x-0|<\delta$ then $|f(x)-1|<\epsilon$.

We have that $\left |f(x)-1\right |=\left |\frac{x}{x}-1\right |=\left |\frac{x-1}{x}\right |=\frac{|x-1|}{|x|}$. How can we continue?

Shootforthemoon

6:29 AM

@Semiclassical I see, thanks. No, the question was a little different from the other, since I did not ask for mathematical proofs but for an intuition (also physical) of what was going on. I see that with the system of expansions everything fits well, but I cannot explain that in terms of lengths for example, and I imagine like 0.999... is just a point immediately before 1.

@Semiclassical And also my problem is about the limit XD 1 divided by ten infinitely many times will tend to zero, but it's not zero (imo)

The limit of that procedure is zero, but since whenever we divide we get still a smaller quantity, if I imagine the steps repeated all over the time, we will never reach zero, but something like 0+

Or maybe @Sem we could say in terms of measures smthg like no points can be found between 0.9999... and 1, hence the two coincide?

Shootforthemoon

6:52 AM

But so, if we could also represent in some way the point immediately before 0.999... , that is "0.999...8", then this must coincide as well with 0.999... We could repeat (via an imaginary limit) such procedure for any point, and conclude that every point is the same.

Akiva Weinberger

@Semiclassical Adding to my reading list: arxiv.org/abs/1308.0066

Here's a paradox

which I shared before, a while ago

A finite game is a game which cannot last an infinity number of steps

(Assume two players)

The Master Game is defined as follows: Player 1 suggests a finite game, and then they play it with Player 2 going first

Is the Master Game a finite game?

On the one hand, yes: because they select a finite game, it will eventually end.

On the other hand, no: If it were a finite game, then we can play like this: Player 1 suggests they play the Master Game. Player 2 suggests they play the Master Game. Player 1 suggests they play the Master Game. etc. This can last forever, contradicting our assumption that the Master Game is a finite game.

So, is the Master Game a finite game or not? Where's the flaw in the reasoning?

Rithaniel

7:09 AM

Anyone familiar with proving the Nine Lemma via diagram chase? I'm doing the case when the top two rows are exact and trying to show that the bottom row is exact.

I'm having some difficulty showing that the bottom row is exact in the middle.

I've shown that the image of the injective side is contained in the kernel of the onto side, but the other containment is giving me a headache

feynhat

7:40 AM

@Rithaniel So, you have shown that the last row is a chain complex.

If you think of each row as a chain complex, you get a short exact sequence of chain complexes.

Rithaniel

Oh, that's meta

Thorgott

10:14 AM

@MaryStar you should rethink the "$|\frac{x}{x}-1|=|\frac{x-1}{x}|$"

Edward Evans

10:45 AM

0

Q: Submodule of $R$-Invariants for a Hecke Pair $(R,S)$

I'll just define a Hecke pair here for completeness: Definition: Let $S$ be a monoid and $R$ a group contained in $S$. We call the pair $(R,S)$ a Hecke pair if every $R$-double coset of $S$ is a disjoint union of finitely many $R$-left cosets of $S$. As an example, we have $(\operatorname{S...

Shootforthemoon

11:28 AM

Hi, I'm trying to prove by comparison the convergence of generalized harmonic series, of the form $$\sum_{n=1}^{\infty} \frac{1}{n^{a+1}}$$ where $a>0$. I proved this for $a=1$, showing that $$\sum_{k=1}^{n} \frac{1}{k^2}<1+\sum_{k=2}^{n} \frac{1}{k(k-1)}$$
but I'm not succeeding in generalize this for any $a>1. $

Any suggestion?

Alessandro Codenotti

11:46 AM

@EdwardEvans suggest me some cool metal

Edward Evans

12:02 PM

@AlessandroCodenotti what kind of Metal? Hahaha

Or rather, do you most often listen to metal? So I know not to recommend some obvious bands lol

Alessandro Codenotti

I'd say I listen mostly to prog rock and post rock, but I also listen to a lot of metal

@EdwardEvans Something heavy but technical maybe

Something that Balarka would like let's say lol

Lately I've been getting into Cult of Luna for example

Edward Evans

12:22 PM

Lol fair, I listen mostly to black metal, but do you know The Zenith Passage?

@AlessandroCodenotti the Song Deus Deceptor is cool af

Alessandro Codenotti

@EdwardEvans no, I'll check them out, thanks!

I'm not very familiar with black metal but if you have cool stuff to suggest I'm always looking forward to listen to something new

Edward Evans

Nice one, also Fallujah are great, check out Sapphire or Chemical cave from that album

Alessandro Codenotti

I will, thanks!

Edward Evans

And if you want some „post black metal“ which is more accessible then Numenorean are incredible, and møl

Hehe

Alessandro Codenotti

I know Numenorean, I listen to the last album when it came out and liked it

Didn't expect to see them mentioned here!

Edward Evans

12:40 PM

Yeah Numenorean are great, they played in Mainz recently

Alessandro Codenotti

Nice

There's a lot of interesting concerts in Köln, but they always happen while I'm in Italy somehow

There's a group from NRW that I really like, I missed them last year when they played in Bochum and I'll miss them again in April when they'll play in Köln, both times because I'm in Italy

But I'll go to a Snarky Puppy concert while in Italy in April so that's fine :P

Edward Evans

Nice, I’m seeing Helrunar tomorrow

Loka Lögsaga is Great

But black black metal lol

Edward Evans

2:32 PM

Yo @Lukas, I have a "general" Hecke theory question for ya if you're here :P

Lukas Heger

okay

Edward Evans

So suppose $(R,S)$ is a Hecke pair. Then an element $\sum_{s \in R\setminus S}a_s Rs \in \mathcal{L}(R,S)$ is $R$-right invariant iff for all $s, t$ such that $RsR = RtR$ the coefficients $a_s, a_t \in \Bbb Z$ are equal. Why then does

$$\sum_{s \in R\setminus S}a_s Rs = \sum_{s \in R\setminus S / R}\sum_{\substack{s_j \in R\setminus S\\ Rs_j \subseteq RsR}}a_sRs_j$$

lol

Lukas Heger

well, $R$ acts from the right on $R\backslash S$ and this yields a decomposition of $R\backslash S$ as a disjoint union of double cosets

Edward Evans

Ahhhhhhhh so I'm thinking of $R\setminus S / R$ as "$(R\setminus S)/R$" lol

Lukas Heger

yes exactly that

Edward Evans

2:41 PM

omfg

hahaha

Lukas Heger