Mathematics - 2015-01-27 (page 1 of 3)

Gato

12:02 AM

@PedroTamaroff good point! ;p

Pedro Tamaroff

@Gato So, do you know how to start with this?

Gato

not really @PedroTamaroff

Pedro Tamaroff

Where did you get this problem from?

(Perhaps you can find some inspiration there, you see.)

r9m

@robjohn Nice!! :-)

Gato

In fact I was trying to prove that $exp(in \theta)$ is dense using Ted's idea : "I prefer to suppose there's an open interval U in the circle that contains no power of e^iθ, @Gato, knowing that the circle has finite measure."

robjohn

12:07 AM

@r9m I don't know if one would call it slick, but I thought it was worth posting.

Pedro Tamaroff

@Gato OK. And did that get you anywhere?

Also, what is $\theta$? An irrational number?

r9m

@robjohn I was trying to prove $e^{x-x^2/2}+e^{-x-x^2/2} \le 2$ in that form too .. ! :-) It's a nice proof :)

Gato

Only if for an infinite group of $S^1$ there is an accumulation point

robjohn

@r9m I am still trying to think of a way that doesn't require taking a derivative.

@r9m Yours is the only one so far

Pedro Tamaroff

@Gato If you know that for each $n\neq m$, $e^{i\theta n}\neq e^{i\theta m}$ you can deduce this sequence has an accumulation point in $S^1$; since $S^1$ is compact.

But this accumulation point doesn't necessarily fall into the interval you assume is disjoint from this sequence.

r9m

12:13 AM

@robjohn I tried Jensen for a long time ... couldn't manage to use it without having to use double derivative ..

robjohn

@PedroTamaroff There is a pigeonhole argument that can be used.

Pedro Tamaroff

@robjohn Yes, yes. We're letting Gato think.

Gato

@PedroTamaroff since multiplying is continuous every point is as well an accumulation point right?

Pedro Tamaroff

@Gato But not of the original sequence.

You're changing the sequence when you multiply (I assume you mean rotate by an appropriate point.)

Gato

Right (yes it's why I meant..)! I know we can prove the density using additive subgroup of $\Bbb{R}$ but Ted's idea doesn't need this and I don't know how can I do so..

@PedroTamaroff

Pedro Tamaroff

12:18 AM

@Gato Perhaps @robjohn can help you only slightly with the pigeonhole idea.

Do you know about the pigeonhole principle, @Gato? It is a very important principle!

Gato

@PedroTamaroff I have already heard that name somewhere..

Pedro Tamaroff

@Gato The principle is very simple: if you have $m$ pigeons and you must distribute them in $n$ boxes, and $m>n$, there must exist a box with at least two pigeons. You can make this more complicated and precise, but this is the simplest form of it.

Gato

As stated is just logical, I need this for the density?

Pedro Tamaroff

@Gato Yes.

What you want to think is about $nt-\lfloor tn\rfloor$ when $t$ is irrational.

These are numbers in $[0,1]$.

Mike Miller

@Pedro Do you need a hint, pal?

Pedro Tamaroff

12:23 AM

@MikeMiller Oh, you asked me something about $S^1$ too.

I am doing one thing and I'll think about it.

Gato

@PedroTamaroff Okay thanks I will think about it.

I need to sleep now, good night all!

robjohn

@Gato Take a look at the pigeonhole argument in this answer, and see if you can adjust it to your needs.

$$\left|e^{ip}-1\right|=\left|e^{i(p-2\pi q)}-1\right|\le|p-2\pi q|$$

Mike Miller

12:44 AM

PEDRO

N3buchadnezzar

@robjohn heya

robjohn

@N3buchadnezzar how are things?

N3buchadnezzar

@robjohn Just back from vacation, you?

robjohn

@N3buchadnezzar work is busy, but I can escape here :-)

N3buchadnezzar

;-)

Samuel Yusim

12:57 AM

when I'm trying to use the universal property of tensor products to prove that some module $Q$ is isomorphic to the tensor product of two other modules $M$ and $N$, what I try to do is as follows: I take a bilinear map from $M \times N$ to some module $P$, and show that it must uniquely factor through $Q$

however I always get stuck on uniqueness, it seems

e.g., I have to prove $F^{mn} \cong F^m \otimes_F F^n$ where $F$ is a field

so I take a bilinear map which sends (u, v) to P somehow

and I notice that I have a nice map from $F^m \times F^n$ to $F^{mn}$ (which I view as $m \times n$ matrices over $F$ by $\Phi(u, v) = uv^T$

forgot a right bracket after "over F"

now it should be true that for any bilinear $L : M \times N \to P$ there's a unique $\hat{L}: F^{mn} \to P$ such that $\hat{L} \circ \Phi = L$, but I don't know how to prove it

my intuition screams that it's true but I just can't figure out how to say why

Pedro Tamaroff

@SamuelYusim Well, here you can simply use that tensor products distribute over direct sums.

$F^m\otimes F^n \simeq F\otimes F^n\oplus\cdots \oplus F\otimes F^n\simeq F^n\oplus \cdots \oplus F^n \simeq F^{nm}$.

Using universal properties is not really optimal here.

Julian Rachman

1:18 AM

Hey everyone. I had a question regarding topics in mathematics: What are some mathematics topics that have a small, warm community?

Pedro Tamaroff

@JulianRachman Perhaps your internet failed? I've deleted the duplicate message just some minutes ago.

user1111

@Pedro Let him keep the question

he seems to want to know the answer

Julian Rachman

Oh. Ok. Thank you. It probably did @Pedro

user1111

Of course, though, i'm not the mod

@Julian I think number theory would be a good community

Julian Rachman

@user1111 but it is a HUGE community of people.

user1111

1:21 AM

why do you say that?

do you have any stats?

Pedro Tamaroff

@JulianRachman Yes.

Julian Rachman

@user1111 No, But I have heard.

Pedro Tamaroff

But the message stays in the history for other mods, IIRC.

Julian Rachman

@Pedro Can you delete all my comments from January 19 and 20 jsut ot be safe? I made a mistake

Pedro Tamaroff

@JulianRachman What's the problem?

user1111

1:23 AM

@Julian sorry for interrupting, but who did you hear it from?

Samuel Yusim

@PedroTamaroff I appreciate that, but it's just one of a set of similar problems, so a direct answer would still be helpful

r9m

@robjohn I'm waiting for probability theorists to have a look at that inequality :-) .. I think I learnt about the Hoeffding Inequality from one of Jack D'Aurizio's answers .. someone or the other is going to spring that I suppose .. :)

Julian Rachman

@Pedro It is just that I said some things that really was not good and I would like to take them back.

Pedro Tamaroff

@SamuelYusim How is my answer not direct?

Samuel Yusim

I want to know how to show uniqueness of the $\hat{L}$ maps

Pedro Tamaroff

1:24 AM

@JulianRachman Can you link to the discussion and delete the comment? I don't want to be looking for stuff.

user105491

@Pedro Please do not do that. He had made some rude comments about me

Julian Rachman

Ok. No pron

user105491

and therefore he wants to delete them

Pedro Tamaroff

@SanathDevalapurkar If the comments are offensive, they should be deleted.

user105491

@Pedro Yes, I agree with you on that

user105491

1:25 AM

But did not contain bad words

Julian Rachman

Thank you. I appreciate it.

Pedro Tamaroff

It's good that Julian is apologizing, too.

You two should try to avoid getting into discussions here or in comments in main. It seems you go to the same school, so you can probably discuss such things personally.

user105491

@Pedro I understand that.

user105491

And that is precisely the reason he wants them deleted

Julian Rachman

I am truly sorry... @Pedro Thank you for understanding. It was my fault in the first place

I got my lesson so I appreciate it @Pedro

Pedro Tamaroff

1:27 AM

@SanathDevalapurkar I think I've already told it is not nice to smother Julian. Sometimes you seem to get obsessed with something and press on him too much.

Just give each other air, Julian and Sanath.

user105491

@Julian It's no problem. But it seems like you're apologizing more to Pedro than to me. :-P @Pedro I did not realize I was doing that. I apologize, @Julian

user105491

and thanks for the advice, @Pedro!

Julian Rachman

I did appoligize to you. I will knee if I have to because i am sincere

user1111

@Julian I know I'm being very very inappropriate, but I am pretty interested in knowing from where you got the stats that number theory is a huge community

user105491

@Julian And as I said, i apologize to you too. So we are even.

Julian Rachman

1:29 AM

Oh. I heard for certain opinionatic places.

user1111

@Julian what do you want to study then?

Julian Rachman

@Sanath I jsut want us to get along.

user1111

because that general field will help narrow down this broad question

Julian Rachman

@user1111 Idk. There is a lot! and I am young

just curious

user1111

I know that

that is why i'm asking you what you are generally interested in

I recall that you said that you wanted to do homotopy theory, in the chat thing that you linked to

Julian Rachman

1:30 AM

I currently am working with topology. But know very little. But find it sort of interesting.

user1111

@JUlian do you know any algebra at all?

or analysis?

Julian Rachman

I do

'Analysis

I am taking a course in Real analysis at a college

user105491

how much analysis do you know?

Julian Rachman

'but I self studied before-hand for about 3 months

user105491

ok but how much analysis do you know?

user105491

1:32 AM

sorry if I sound inappropriate

Julian Rachman

Up until the continuity and the Topology on $\mathbb{R}$

user105491

i'm just trying to help @user1111 help you more

Pedro Tamaroff

@SanathDevalapurkar @JulianRachman I have gone through the messages. I don't find anything offensive. The only thing I find is me and Julian agreeing that Sanath might have made Julian think one should study mathematics in such and such way, which I think it is no the way to go.

user1111

@Pedro I agree with you. I can see that there is nothing offensive there, but such things can hurt @Julian and @Sanath's friendship

Julian Rachman

Ok I am sorry for saying this. But i sound like a bitch and I really an so sorry about it.

user1111

1:33 AM

so i mean, morally, it's the right thing to do

Pedro Tamaroff

@JulianRachman No, you don't.

user105491

@JUlian Hey, part of it was my fault too

user105491

So we can just be friends

user105491

:-)

user105491

Sorry i gtg

user105491

1:34 AM

bye

Pedro Tamaroff

But -- in my opinion -- you need to stop worrying about algebraic topology and homotopy theory (for now!) and start learning from the bottom up.

Julian Rachman

Please I will be glad to welcome you again and be great mathematicians. :)

user1111

@Julian what topology on R?

Julian Rachman

@Pedro I have already changed my mindset

Mike Miller

@user1111 I'm not going to back this up with statistics, but you could do so by looking at the database of AMS members. Number theory and number theorists, as a proportion of mathematics and mathematicians, is indeed quite big. Certainly I wouldnt call it small; if you want small, you start specializing. The number of people working on the applications of tensor triangulated geometry for the sake of p-adic hodge tbeory is probably quite small.

Julian Rachman

1:35 AM

And ahve gottne a lot of advice

user1111

@Mike Sorry, I don't have access to MathSciNet or anything like that

@Julian ok, how about algebra?

Alex Wertheim

Not to butt in, but I'd also agree with @Pedro. :)

Julian Rachman

abstract @user111

@user1111

Pedro Tamaroff

@AlexWertheim I love pomeranians.

user1111

do you know abstract algebra?

Sanath's website seems to show that he's teaching something like that

Alex Wertheim

1:37 AM

@PedroTamaroff: I love dogs. But I confess, this was actually a friend's choice of avatar. She had great amusement in picking it. =P

Mike Miller

@user1111 You don't need it.

user1111

and i presume you go to the same school?

Pedro Tamaroff

@AlexWertheim Though I just like the ones with round heads. Not the chihuahua looking ones.

user1111

@Mike ah, thanks

i never saw that before

@Julian

Julian Rachman

@user1111

yes

user1111

1:38 AM

WHat about that thing that Sanath is doing?

Julian Rachman

?

Pedro Tamaroff

user1111

that seems valuable if you don't know abstract algebra

@Pedro That's cute

Alex Wertheim

Awwww. What do you think of samoyeds, @Pedro? Now that's my kind of dog.

Mike Miller

@user1111 Actually, this is more direct. Note that it counts people more than once. Compare that against a count of total memvers if you can find one.

Pedro Tamaroff

1:39 AM

@AlexWertheim Those look pretty majestic.

Julian Rachman

@user1111 What does that mean?

Pedro Tamaroff

I like German shepherds for majestic. Or collies.

user1111

@Julian He seems to introduce abstract algebra from the basics

quoting his website:

Alex Wertheim

They are. :) I had one for many years.

user1111

"introduction to group theory, ring theory, vector spaces, and modules"

@Julian

@Mike as you go down the line the numbers kinda start to decrease :-P

@Julian hello?

r9m

1:43 AM

@PedroTamaroff Anyone who'd want to have those for dinner are simply monsters ...

Arkamis

Anyone available to clarify some language regarding sigma-algebras for me?

Pedro Tamaroff

@Arkamis Perhaps.

What is troubling you?

user1111

@Arkamis Can't guarantee anything, but i can try

Arkamis

the following wording from Folland:

user1111

@Julian are you still on are have you left?

Arkamis

1:45 AM

"If $\mathcal{M}$ is the $\sigma$-algebra generated by $\mathcal{E}$, then $\mathcal{M}$ is the union of the $\sigma$-algebras generated by $\mathcal{F}$ as $\mathcal{F}$ ranges over all countable subsets of $\mathcal{E}$."

Julian Rachman

@user1111 sorry had to do something

user1111

@Julian no probs

Pedro Tamaroff

@Arkamis Yes.

Julian Rachman

i havent done that yep as to what you ahve described

Arkamis

What is meant by "as $\mathcal{F}$ ranges over all countable subsets of $\mathcal{E}$?"

user1111

1:45 AM

so what about sanath's thing?

Julian Rachman

isnt that done in topology?

@user1111

user1111

abstract algebra?

Julian Rachman

he does homotopy theory

user1111

no, it's not done in topology

@Julian I can see that from his website

Arkamis

Does that mean $\mathcal{F}$ is a family of sets, containing some number of countable subsets of $\mathcal{E}$?

user1111

1:46 AM

but abstract algebra is not done in topology

Julian Rachman

'And what about abstract algebra? this as a research fireld?

Pedro Tamaroff

@Arkamis No.

user1111

rather, they combine (kinda) in homotopy theory

Arkamis

I mean, I know what the theorem is trying to prove, but I'm stuck on the language.

user1111

no, it is not a research field

Julian Rachman

1:46 AM

yes I know @user1111

user1111

at least not as much as you might expect

i mean, there's (non)commutative algebra and stuff

Pedro Tamaroff

It means $\mathcal M$ is the union of all the $\sigma$-algebras of the form $\langle S\rangle$ where $S\subseteq E$ is countable.

Julian Rachman

So waht are we trying to get at?

Kevin Driscoll

@Arkamis They mean that F is some collection of countable subsets of E

Julian Rachman

I sort of dont want to copy sanath

user1111

1:47 AM

but basic abstract algebra, as he's teaching it, you can't do much research in

@Julian I understand what you're saying

Arkamis

I know that, @PedroTamaroff, I'm curious as to what the term "ranges over" refers to

@KevinDriscoll Ok, that's what I thought.

Pedro Tamaroff

@Arkamis It means "sweeps through" or any equivalent visual aid.

user1111

Sanath seems like a nice and hardworking guy but the way he reacted above seemed kinda harsh and protective

@Julian That is not to say he does not seem like a nice guy

Pedro Tamaroff

@Arkamis For example, $\Bbb N$ is the union of $\{i\}$ as $i$ ranges through the natural numbers.

user1111

But he works in homotopy theory, and homotopy theory contains a lot of every field

Arkamis

1:48 AM

Well, a $\sigma$-algebra generated by a set doesn't make sense unless you're implicitly either talking about a set of sets or the powerset of that set

user1111

@Julian

So the question is

Julian Rachman

@user1111 yes I understand. He can be a bit discouraging, but he still motivates me. :)

Mike Miller

@Pedro Have you solved the $S^1$ problem?

Pedro Tamaroff

@MikeMiller In part. I was doing something else.

Julian Rachman

Yes? the quesin?

user1111

1:49 AM

do you want to do math with intuition

or do you want math with symbols?

homotopy theory is kinda a combination of the two

Arkamis

thanks, @PedroTamaroff and @KevinDriscoll

user1111

i should know, i study htpy theory

Julian Rachman

I do like both

Pedro Tamaroff

@Arkamis If you need strict notation.

Kevin Driscoll

@Arkamis Well, F is the subset and then that generates the sigma algebra

Julian Rachman

1:50 AM

i mean i do what bothe @user11111

Kevin Driscoll

I think

Pedro Tamaroff

$\langle E\rangle =\bigcup\{\langle S\rangle :S\subseteq E,S\text{ countable }\}$, @Arkamis.

Julian Rachman

I do like symboles

user1111

@Julian then you can do algebraic geometry, but homotopy theory contains algebraic geometry

Arkamis

@PedroTamaroff I'm not stuck on that -- I know what the theorem is saying. I know what the statement means.

user1111

1:50 AM

like derived algebraic geometry

which is what it seems like sanath is doing.

Pedro Tamaroff

@Arkamis Then what is bothering you? I'm confused.

Arkamis

@PedroTamaroff The term "ranges over"

Julian Rachman

I like it! But i have ALWAYS had an interest in category theory ever since

@user1111

Pedro Tamaroff

@Arkamis What's your mother tounge?

user1111

why category theory?

@Julian

Arkamis

1:51 AM

I wanted to be sure it meant what I thought it meant.

Pedro Tamaroff

Please be Spanish please be Spanish

Arkamis

@PedroTamaroff Terrible english.

Pedro Tamaroff

Oh, OK.

user1111

you don't know abstract algebra but are interested in category theory?

i'm confused

as heck

@jUlian

@Julian ever since when?

Julian Rachman

I like the diagrams?

LOL

user1111

1:52 AM

that is not a reason! :-)

Julian Rachman

sorry...

user1111

but honestly, category theory is very abstract

it requires a lot of effort

Kevin Driscoll

@Arkamis I though a sigma algebra generated by a single set does make sense?

Julian Rachman

ya. I really like abstract concepts

I want to THINK

user1111

i find it amazing that sanath did that when he was so young

@Julian yeah, i know

but every math field requires thinking

but the thing is that category theory requires you to spend a LOT of time understanding the abstract concepts and translating them to mean something intuistically

Alex Wertheim

1:54 AM

Ok. I'll bite. What is so wrong with calculus? Calculus is amazing. It's some of the most beautiful, important math ever done. There's plenty of thinking to be done in calculus.

user1111

@Alex haha, yeah

i mean you can do things in like analysis or something

like PDEs

and in fact that is what i was going to ask you about, @Julian

Do you have experience with differential equations

@Julian

Alex Wertheim

I just don't see the point of fluttering about in topology and analysis without having any idea why analysis and topology are so important in the first place. Which, and this is only my opinion, just seems beyond belief without a thorough, solid understanding of calculus.

Julian Rachman

Yes @user1111

user1111

@Alex exactly why i think @Julian you should spend some time studying calculus

Julian Rachman

I dont like analysis. and I can say that because I am taking it

user1111

1:56 AM

why not?

Julian Rachman

Yes. i understand

user1111

it's beautiful!

@Julian Let me give some advice

you seem to be so very concentrated on doing some research that you don't remember that the most beautiful part about math is the learning process

Alex Wertheim

How could you like analysis if you're trying to study it without knowing calculus? Analysis encapsulates calculus. That's like saying you don't enjoy french movies without knowing how to speak French. There's only so much you can enjoy if you don't speak the language.

user1111

@Alex precisely what I am telling @Julian

Julian Rachman

I have learned calculus

but on my own

user1111

1:58 AM

@julian introduction

sorry, integration?

Pedro Tamaroff

With the little perspective I have, I have to agree with something someone told me: one should study category theory once one knows a load of examples of concepts of category theory. It makes no sense to learn what a projective object is in a category, or what a terminal object is, or what a universal property is, or a kernel or an equalizer if one hasn't bumped into the obvious examples of such things in the practice.

5

Julian Rachman

some @user1111

user1111

@Pedro I love you. That is great. @Julian @Pedro's comment is exactly why you shouldn't want to do category theory simply for diagrams (im joking here)

@Julian Can I give you a question?

Additionally category theory simplifies many constructions as special exmples of things

for example (co)products as (co)limits, etc

@Julian Hello?

Julian Rachman

IDK anything about category theory. sorry. only an overview'

@Pedro thanks for the advice

user1111

@Julian Can you summarize what it is, then?

I mean, you shouildn't even be worrying about categoyr theory at this point in your education

it's a waste of time right now

Can I ask, slightly unrelated, on why you have a math genealogy profile? You are learning calculus!

Julian Rachman

2:03 AM

it has something to do with a collection of objects and arrows having morphisms, homeomorphisms, and etc. acting on it?

user1111

@Julian

@Julian what's a homeomorphism? Do you know?

Julian Rachman

@user1111 I am trying to get it removed. I did not know how professional it was until later

@user1111

user1111

ok

but why was it made?

Pedro Tamaroff

Guys you needn't ping each other all the time.

It is basically you two in the conversation at the moment.

user1111

Haha, yeah

i know. it's just fun though

jk

i'll stop

Ok @Julian (last ping) so what is a homeomorphism? Just want to know if you know what it is

because though you used it in the right context, knowing calculus does not mean you know what a homeomorhpism is

@Pedro and did i say i was a guy? :-)

Mike Miller

2:08 AM

Pedro solve the $S^1$ problem or you're in trouble

Pedro Tamaroff

@MikeMiller There's nothing to prove.

Done.

Mike Miller

"Is trivial!"

Not acceptable

Julian Rachman

@user1111 Sadly, i dont

user1111

you do not have to be sad

it is not necessary in the first place for you to know what a homeomorphism is at this point

but can i give you an integration question?

Julian Rachman

that is true

Pedro Tamaroff

2:11 AM

@MikeMiller Tomorrow noon I'll give you a solution.

Mike Miller

Noon what time?

Pedro Tamaroff

OK, closer to night. Like 6 or 7 pm. Or something.

Miguelgondu

3:02 AM

I have a question. Perhaps a silly one.

I was looking at this question math.stackexchange.com/questions/1087999/a-riddle-for-2015 , and I found myself asking: can every number up to 9! be written in that way?

Miguelgondu

3:16 AM

up to 1+9!, I mean.

Mike Miller

Probably not 9!-2.

Gato

6:43 AM

@robjohn Thanks!!+1

robjohn

@Gato You were able to show density?

Fargle

7:26 AM

I'm having trouble showing that a vector space cannot be the union of three of its proper subspaces. Can anyone nudge me gently in the right direction?

David Zhang

@Miguelgondu Hey! I'm the guy who did that computer search in the question you linked.

The answer is a resounding NO, there are tons of numbers between 1 and 9! that are not expressible in that form.

I mean, it is clear that no irrational number can be written that way. But even if we limit ourselves to just the integers, many of them are unattainable.

The first unattainable positive integer is 2284, after which there are 348862 more until 9!.

So 348863/362880 ~ 96.1% of integers between 1 and 9! inclusive cannot be written that way.

It might interest you to know that among the numbers which are attainable, there is enormous variation in the number of ways to express each one.

As shown in my post, there are 536 ways to obtain 2015. That might seem like a lot, but there are a staggering 648,265 ways to obtain 0, and 184,681 ways to obtain 1.

A Beautiful Mind

Hello @JayeshBadwaik

Mike Miller

@Fargle You need some more conditions. As is, that's false.

Jayesh Badwaik

@ABeautifulMind Hello, howz it going?

A Beautiful Mind

@JayeshBadwaik My mental problems have worsened. I am giving myself a few more years to get well and go to grad school.

David Zhang

7:39 AM

@Miguelgondu If you try to plot the distribution of the number of way to express each number, you get some rather interesting figures.

Jayesh Badwaik

@ABeautifulMind Sorry to hear that. I hope you get better.

David Zhang

That plot includes the full range of numbers which can be produced. You can see that points tend to cluster around the origin, with 0 and 1 huge outliers.

If I zoom in a bit closer and show only numbers between -1 and 1, you can see the behavior a bit more clearly. Most numbers can only be produced in a few hundred ways.

Mike Miller

How'd you make that figure?

Fargle

@MikeMiller Er, rather, a finitely generated vector space over an infinite field.

Mike Miller

@Fargle Infinitely generated won't work either, but infinite field is key. (Any $\Bbb F_2$-vector space of dimension greater than 1 can be written as a union of precisely 3 proper subspaces.)

David Zhang

7:43 AM

@MikeMiller These were all done in Wolfram Mathematica, after I had finished the original search.

Mike Miller

@DavidZhang Sure, but I was more curious about the code that produced it. Did you bound the denominator of the numbers in your plot below?

David Zhang

No, I didn't do anything like that. There are only a finite number of rational numbers which can be produced in this fashion, so I literally just produced them all and counted them up.

If you'd like to see it, I still have the frequency table stored as a text file.

Mike Miller

Sure, that'd be cool. I enjoyed your post.

David Zhang

It's about 5MB compressed. Can I upload files through Math.SE chat?

Mike Miller

Only images. My email is in my profile, if that's most convenient.

David Zhang

7:56 AM

@MikeMiller Sent.

Najib Idrissi

8:33 AM

The idiot who downvoted my posts on main every time I opened a meta post apparently deleted his account, I feel like I should celebrate

Is there a way to see what accounts were deleted recently?

Mike Miller

@NajibIdrissi Ah, it was my anti-Najib alt. They finally caught me.

Najib Idrissi

Ah, apparently "undownvote" in this manner actually means that the serial downvoting was caught, but there weren't enough questions affected to merge it as "serial voting reversed"

Seriously though, what do these people feel they're achieving? It's childish.

Mike Miller

Well, they're trying to condition you. They suspect that if they downvote you when you make meta posts you'll stop making meta posts. It's silly, of course.

A Beautiful Mind

Hello @MikeMiller.

Mike Miller

morning

Najib Idrissi

8:45 AM

It just makes me wonder which of the people who usually disagree with me are mentally 5yo

A Beautiful Mind

Most people stop growing mentally at 20.