can anybody think of any more tags i should put on this question?

is it a measure theory problem, or something?

@AlexanderGruber No clue! =D

@user1

@MarianoSuárez-Alvarez Are you there?

@AlexanderGruber Nice drawings, by the way.

HI GRUBBY

@PeterTamaroff thanks, hopefully somebody will be inspired to answer it. :p

@Charlie hiya charlie :)

@PeterTamaroff Hi

@AlexanderGruber You take nice photos.

@GustavoBandeira thanks :p i just got back from asheville.

@AlexanderGruber wassup?

@AlexanderGruber I missed heavy ofensive mathematical rhymes at that photo.

@Charlie just got back from a weekend of group theory / punk clubs in north carolina

@GustavoBandeira im going to have to write some group theoretic hip hop

@user1 I have a question, don't know if you can answer it. It is set theoretical.

@AlexanderGruber Really? If you do that, I do the music.

@PeterTamaroff Ah, I am not sure either, but you should ask anyway.

You don't even need to sing. We can use google translator to sing.

@GustavoBandeira seriously, it's a deal. ;)

@AlexanderGruber But you need to do it involving mathematics and some neglected social reality.

@AlexanderGruber hmmm

@AlexanderGruber group theory and punk clubs?!

@user1 Well, it's about defining certain sets with certain sentences.

@GustavoBandeira of course. :)

@Islands yeah buddy!

Yes. Punk grouptheory too.

@Charlie how about you?

@AlexanderGruber I'm fine

@Charlie What's that punk celtic band again?

@PeterTamaroff ok

the south is awesome. i can't wait to move further in.

@PeterTamaroff dropkick murphy

@user1 For example, to prove that a continuous function $f:[a,b]\to\Bbb R$ is regulated, I fix $\epsilon$ and define $P_\epsilon(y)$ to mean "There exists a step function $s:[a,y]\to\Bbb R$ such that $|f(x)-s(x)|<\epsilon$ for all $x\in[a,y]$" and the look at the set $$A=\{x\in[a,b]:P_\epsilon(x)\}$$

Actually it should be something like $P(f,\epsilon,y)$, yes?

I mean, the sentence depends on those elements.

Hello all

The question is: How can I be sure I am not falling into absurdity when using those sentences?

@cyclochaotic hello

@PeterTamaroff Use quantifiers, you have just a formula $P$ with free variables $f,\epsilon,y$.

To make it a sentence, you have to use $\exists,\forall$.

@user1 Right, so there is no doubt of its validity.

@PeterTamaroff There is none, since $f$ was "fixed" at the beginning, right.

@user1 See this

(For a display of such idea)

This is a test $\sum_{n=0}^\infty\binom{n}{k}x^n=\frac{x^k}{(1-x)^{k+1}}\tag{1}$

@PeterTamaroff I have not read the whole sketch, but it never good to reuse variables when you are unsure of the logical validity of something.

@user1 "Reuse variables"?

You fixed $\epsilon$, then you go on to define $P_{\epsilon}$ for all $\epsilon$

@cyclochaotic \displaystyle

Cool got chatJax work'n

@user1 Oh, yes, silly me. Hehe, thanks. Of course $\epsilon$ is fixed throughout the proof.

Oh, but you're reading it wrong @user1

@user1 I edited, maybe it is clearer now? More of a punctuational thingy.

@PeterTamaroff You can start with assuming $f$ is given, then define $P_{\epsilon}$, then fix $\epsilon$.

Otherwise, you are putting a quantifier before a bounded variable.

I do think I understand what you mean though.

@user1 OK. Good.

See here, the set $A(\epsilon)$

(PROOF1)

This is a test FLT

@PeterTamaroff Technically the second use of "Let $\epsilon>0$" there is extraneous, but it does no harm (in fact it is helpful to the reader).

@user1 Hmm, true.

Both.

Thanks for the quick reply! THANKS SO MUCH!

@cyclochaotic You mean $F\ell T$!

@Raindrop As Richard Feynman, who won the Putnam said "Know how to solve every problem that has been solved."

@PeterTamaroff Yes, my bad :)

lol

@skullpatrol hi

@Charlie hi

@Charlie How are you?

@skullpatrol fine, and you?

@Charlie Fine thanks.

@skullpatrol good

I am very tempted to answer this using an overly complicated approach. Must... resist... the... temptation.

Did you all here that the ternary Goldbach conjecture is probably solved. T.Tao like the preprint.

*likes

@user1 yes.

@user1 it's okay i do that all the time

@cyclochaotic Thanks for the info :)

Hi all. Is there a name for the set of invertible upper triangular matrices?

@skullpatrol could you watch this?

@skullpatrol your welcome

If we take 3 away from all odd numbers larger than say 15, can not the ternary Goldbach be applied to evens?

@AlanH hmm, I am not aware of a shorter name than that. Or do you mean a standard notation?

@cyclochaotic the ternary does not say that 3 will always be one of them

@Tobias something like SLn(R). So I suppose standard notation.

@AlanH in that case sometimes $B_n$ is used (though that is also used for other things)

@Charlie 7.59$\mp$0.05

and some might well use it to mean the lower triangular matrices instead

@skullpatrol I liked the animation

@Tobias Do you know if the elements of those matrices have to integers? No, right?

@Charlie I'd give the animation a 8.5

@skullpatrol yes, the animation is really good.

@AlanH you can write $B_n(A)$ to be more precise, where $A$ indicates what coefficients you allow

I think some people might use $T_n$ instead (T for triangular). But that might be confusing as $T$ is often a torus

@Charlie they could call that anim'et = animation + ballet

@user1 do it with FLT + strong induction

@AlanH in any case, the notation is not standard enough that it does not need to be explained

@cyclochaotic :D

@cyclochaotic it's a contemporary balet

@Tobias k, thanks

@Raindrop i liked problem solving through problems

@Charlie do you like ballet?

@Charlie I enjoyed it

@AlexanderGruber I LOVE

:)

@cyclochaotic :D:D:D:D:D:D:D:D

I'm watching this over and over

@Charlie watching

14:48

@AlexanderGruber I was also considering proving that it is equivalent to a property on a functor between two categories and then verifying that property by induction on a well-ordered set of categories.

@AlexanderGruber a scene from one of my favorite movies of al time

Yo @Argon wazzup?

@skullpatrol Hey Skull! Not much, how about you?

@Argon Chillin like a villain.

@argon HI!

@skullpatrol Hehe nice

@Charlie HI

@AlexanderGruber Did you meet Arturo yet?

@Charlie Later

@skullpatrol Later :)

@Charlie What ya doing?

@GustavoBandeira just a little thing

@Charlie A dot?

@GustavoBandeira yes

@Charlie You should dance ballet.

@GustavoBandeira I don't have time, or age, should have started a long ago

or weight

it requires lot of passion

not just be an amateur

@Charlie Nope. That's completely wrong.

@Charlie It requires that if you're going to presentations and competition, etc.

You can do it "for fun".

For example: Piano - All the greatest pianists started with 2yo.

I've started it with 19.

I'll never have the proeficiency of, say, my teacher.

But it'll be fun to perform some accessible music.

that's not enough

some accessible music?

@Charlie Yeah. Piano music is organized in tiers, some are easier, some are hard as fuck.

so

The good thing is that there is beauty in some of the easy stuff.

you should aim to be able to make hard as fuck music

@Charlie Yeah, I should but it'll take time.

@AlexanderGruber did you watch? :)

@Charlie Also: It's important to notice that there are a lot of roles in life. You don't need to be a professional russian ballerina, helping others to achieve that and thinking about new stuff is also important.

:/

Most people seem to be devoted to the protagonist kind of actor.

yes

In piano, for example - the requirements for being a player are so high that you can only choose to compose or to play but not both.

it's frustrating

i have to live knowing that there are things i simply cannot do

@Charlie I suffered and suffer a lot from this.

I do, a lot

It is as if we were taught that supermen do exist.

We're a lot smaller than what we think we are.

yes...

@Charlie I really believe that if you like ballet, you should download some classes, something like that.

@GustavoBandeira it's not enough

@Charlie Get happy with small stuff. Every step counts.

it requires more than just watch

If you don't do it, it'll be impossible to figure out this stuff that is beyond watching. =)

@GustavoBandeira I watched a royal ballet class

@Charlie One of my biggest dreams is to be able to extend my capacities: A brain upgrade would be nice. :P

hehehe

i need a better brain

@AlexanderGruber Are you alive?

@Charlie yes! i had a visitor

we both watched

it was fantastic.

@AlexanderGruber oh, forgive me

@Charlie I guess he went to compose the lyrics of our offensive mathematical gangsta rap.

@AlexanderGruber incredible!

@Charlie that part around 1:43 was so cool

@AlexanderGruber Yes!

@Charlie do you like other dance, like lindy?

@AlexanderGruber hmm...

i like ballroom dance

@Charlie i am learning salsa.

@AlexanderGruber ah, nice!

@AlexanderGruber I had some short lessons in the past.

I was in a hispanic presentation for school.

~16yo.

@GustavoBandeira like a presentation on hispanic culture?

Yeah.

it's been a long time i don't dance

neat, i was just learning it to hit on girls.

my goals were not so noble as a presentation :p

@Charlie why not?

I don't know

@AlexanderGruber Well. Some of the moves revealed interesting points of view of my partner...

@GustavoBandeira dat toss.

@Charlie i only started recently myself

@AlexanderGruber good, good

@AlexanderGruber Was trying to elevate your nobility while downing mine - Altruism/Teamplay.

haha

@Charlie Not even alone? I dance a lot alone.

it's not nice

?

it doesn't look cool

gangling

expressionless

What doesn't look cool?

my dance

@Charlie Who cares?

Just do it.

i care

@Charlie Apple?

:/

@Charlie E aí? Tá fazendo o que?

reading

@Charlie What?

something

@Charlie C'mon, Charlie.

You're a little more descriptive.

math

@Charlie Down one level in the hierarchy.

?

@Charlie Math comprises a lot of subjects.

yes

I need to learn a proof of the binomial theorem with non negative integral coefficients.

hmm

@Charlie i bet it looks pretty cool.

have you ever seen this?

@AlexanderGruber don't bet...

@AlexanderGruber We should learn the dance of the manwhore.. Deal?

@GustavoBandeira i know that dance.

@AlexanderGruber XD

@AlexanderGruber cool!

@AlexanderGruber I've read somewhere that there was a connection of group theory and dance. Has anyone really studied that?

@GustavoBandeira i do, every friday night.

soon i will have a paper on the well-known Texas $\mathbb{Z}_2$-Step

Good night, gentlemen

'twas a pleasure

night

@AlexanderGruber thanks for watching the video

@GustavoBandeira banoite

@Charlie welcome i loved it

goodnight cha li

Just started reading "Algebra, ch0" and the function decomposition theorem is wonderful. I can already see it is going to be useful. Not sure if I will be able to pull my eyes away from ch0 to read any of the other books I have planned (not sure if that is good or bad).

@Bageer The book seems interesting.

@Gustavo So far it is (and I havent even gotten to the algebra).

@Bageer What page?

The theorem I was talking about is on page 15 (Thm 2.7) and I am working through the problems on section 2 (same chapter as the theorem).

@Gustavo Sorry I couldn't type out my answer more quickly (to your question) ;-)

@amWhy Relax.

After I received the answers, I'm perplexed by how stupid I am.

@GustavoBandeira You're not stupid...we ALL overlook simple things...at times. Anyone who claims otherwise is LYING!

@Bageer I couldn't make some exercises on page 8. =/

Have you read the chapter?

@Gustavo

@amWhy Yeah. But no problem with that - gonna try to make better mistakes tomorrow.

@Bageer Yes.

I've looked the book three times.

If f(x) is multiplicative, $$\sum_{d\mid n}f(d) \leq e^{\sum_{p\mid n} f(p)}$$

@GustavoBandeira There you go! ... Oops, I did it again: "there you go" ;-)

The first time I looked at that book, the second time. Now it's almost english!

My number of questions and the number of upvotes in my three first questions is the same! I should earn a badge for that.

@Gustavo Hah. Yah you might just be getting ahead of yourself.

@Gustavo I have been typing my answers (so far...) so If you would like I could send them to you I could, plus I love talking about math, so if you are ever working through it I am pretty sure I would be willing to discuss it.

@Bageer Yep.

I'll talk about it in a min.

brb

@Bageer I'm back. U there?

@Gustavo Yup.

@Bageer I'll try to re-do some of the exercises now. I guess I have a question on one of them

@Gustavo Okay, which one.

@Bageer this one

I'll try to answer that question now. My mathematical O.S. is a little more sofisticated now (almost like a windows 95).

Also: Isn't his book more like category theory?

@Gustavo Well it is taking the approach that algebra should be taught from the category theory perspective (at least that is my impression).

Also you might want to look at the errata: math.fsu.edu/~aluffi/algebraerrata/Errata.html

It makes that problem possible :)

Well, somehow I was understanding relation as equivalence relation.

@Bageer Read the question, read 1.5 - I'm stuck in the same way I was.

@Gustavo Did you do 1.2 and 1.3?

I'm doing 1.2

@Gustavo Having a good idea of 1.2 and 1.3 will be useful for 1.5.

The weird part for me is that it asks for a proof, but whenever I try to prove it, the only thing that comes to mind is writing the given definitions.

Well a big part of mathematics is definitions, and since you are proving things about definitions it would make sense to start there.

@Bageer I'm reading Brian's answer now.

You want to show that P_~ is in fact a partition, so you will want to start with the definition of P_~ and show that it is a partition of S.

@amWhy I've seen this now:

Did I write that?

@amWhy I guess so.

I don't know why I would have? I wouldn't have knowing it was you, maybe I just didn't look closely at the "OP" user name (your name), since I have no worries about your acceptance rate...hmmmm

@amWhy I believe the answer to your question lies in the comments on this question.

My gosh..."Did" (shake my head). I don't get him, I don't recall having seen that comment thread before.

I upvoted your question there...Why is Did such a "dick" sometimes?

@amWhy Dunno. At first, I guess he thought I was lying.

(at that's quite true)

But as he wanted to make a deep search on my intentions, I decided to reveal it.

I'm not a big fan of asking a lot about stuff people answer me - mostly because I study only elementar stuff. I don't want to bother them.

For example - You know at what math level I am, can you imagine if I'm going to ask about the Riemann Zeta Function at that mathematica.se question?

@Bageer What does he do with the errata? Won't he update the text?

@amWhy Oh, and also as an addendum to the reasons I've given - sometimes I overasked stuff to people and they treated me weird.

@amWhy Thanks for the vote.

@Gustavo When new additions are released (I would think). If you are using the digital version (easily found online), I don't it's a legit one put out by the author so he probabably does not release a new digital version every time he fixes errors.

@Bageer Did you print/buy the book?

@GustavoBandeira You should never feel weird about asking: I'll come beat up anyone who makes you feel weird, or stupid, about asking.!

@amWhy Haha Thanks.

@Gustavo Not yet. I am using the digital version, I will be buying it though. Math books are about the only thing I buy, its an addiction.

@Bageer Kinda the same here. But the printed version is damn expensive.

Oh, it's a hardcover book... Every hardcover book costs + 40U$D than the paperback.

I believe these covers are made of gold.

@Gustavo Hah. No they are actually made out of rare baby tiger leather.

@Gustavo Make me happy before I head for bed : $\;\Large \checkmark\;$ ;-)

@amWhy Where? The binomial question?

If you're up to it...but no pressure...accept what you'd like to accept :^)

@amWhy Oh. I've accepted Zev's answer because it was the first question that made me understand it. I thought it was fair

Althought I know that your answer tells it better.

@amWhy How can I tell if a source is "Academic/Peer Reviewed"?

I feel ashamed of switching.

@GustavoBandeira No worries.

There's another question of mine that I accepted one answer, but then another great answer (that told me a lot more than the previous one) appeared.

You have the right to switch; it happens all the time, actually...but do what works for you.

@amWhy I know. I'm just afraid of attracting hate. Specially after that chat with Did...

@GustavoBandeira what happened

@GustavoBandeira no one hates you! Did hates everyone! ;-)

@amWhy XD

@GustavoBandeira ?

Well, I think I'll head for bed...seeing as I'm not appreciated, ;-)

@Ethan I am not entirely sure but I think the the review typically happens during submission to a (peer reviewed) journal.

@amWhy What?

@GustavoBandeira Just teasing you...though I do feel kind of bad...I'll get over it :-)

@Bageer this doesn't have anything to do with math

@amWhy =(

@Bageer My english teacher wrote "you need atleast 3 peer reviewed sources"

@GustavoBandeira =)

@Ethan Well what I said is not restricted to mathematics, also if you have access to a library (that has access to journal databases) there is normally an option to search only for peer reviewed articles.

Lol I have to finish it today

What is it on

?

How can I tell if a source is 'academic or peer reveiwed'

@Bageer the war in Vietnam

I was looking through the resources at the bottom of en.wikipedia.org/wiki/Vietnam_War

But I am not sure which are and aren't peer reviewed or academic

Well you can say someone on the internet skimmed whatever article you found, therefor peer reviewed.

@Bageer I think some other connotations might be associated with 'peer reveiwed' rather then being reviewed by a single person

@Ethan Anything specific on the war in Vietnam?

@Bageer Somthing about the causes of the war, the event itself, and some of the effects

Or somthing like statistics on death rates would be ok

@Bageer I appreciate the help btw lol

I am going to have to do a presentation..

Usually I can make people laugh, but not with somthing like this

lol

@Ethan No problem. Try google scholar. If you find an article there that you can't get I can check if I have access through my library and I won't ;) send you the pdf of the article.

@Bageer Is MLA format single or double spaced?

@Ethan Pretty sure its double spaced, don't take my word for it though I forgot all that stuff the moment I only had to write math.

Lol they don't bother with all this shit when you write math do you

@Ethan Nope just a sensible LaTeX setting for the most part.

Judge work by its content not by the way you can dress it up in different formats and fonts

One more Project Euler problem down. One more to go for 200. Problem 429 was a gift.

Hmm... "See below for guidelines." Nothing's below. Am I missing something?

@Mike I think it is refering to the etiquette guidelines. It is below the pictues of avatars and "there are other rooms...": meta.math.stackexchange.com/questions/3890/…

Is that thing permanently stickied there or something?

Probably, not sure why it is not just in the paragraph with the "See below for guidelines" though.

@Mike the stickiness where's off every monthish, so one of me or robjohn has to repin it every once-in-awhile

@Bageer unfortunately the room description does not allow inline links (it just puts down the whole url in text), which made the description very ugly

it is also not too unreasonable to ask that new users "see below" as suggested, or perhaps expect they can Ctrl+F the word "guidelines" if they don't look hard/cleverly enough

@anon Ah, I see.

err, meant to say "wears," not "where's"

most seem to not even read anything on the right at all, so it doesn't seem to make too much difference :)

True. A bit like assigning reading in class, nobody does it.

...unless they're really, really bored.

I have a question, mostly it is just to check that my answer is making sense.

Ask away. Then we'll see if anyone can answer it.

The problem is saying: With notation as in example 2.4, explain how any function $f:A \to B$ determines a section of $\pi_A$. $\pi_A$ is the projection and example 2.4 is a diagram with $A\times B$ and two projections coming off of it (to $A$ and to $B$). My thought is that a section is a right inverse $A \to A \times B$, so the image of the section could be the graph of $f$. Or in other words the function that makes the diagram commute.

I guess I am just not sure if that is what the question is actually wanting. So do you guys think it is a decent answer?

The more I think about it the more I think that is what the problem is wanting, but I am a little afraid I am missing something.

Can somebody suggest me a good book about inequalities ?

@D3r0X4 cauchy-schwarz master class

When I want to prove that the product topology on $\mathbb R^n$ with repsect to the euclidean topologies on every factor is the n-dimensional euclidean topology, is it enough to show that the norm on the product topology equals the euclidean norm?

@Montaigne You would have to define the norm and show that the topology has the open balls wrt this norm as a base, then it would be sufficient to show that this norm is the same as the euclidean norm.

@Montaigne I would show that the set of open balls wrt the Euclidean topology is a base for the product topology and then that the base given by the factors in the product topology is a base for the Euclidean topology.

Visually, you put a box in a sphere in a box.

Yes this is the way I would do it also, but I am inetersted in the "non-topological" approach. Do you know any reference where it is proved that the maximum norm is induced by the product topology

The same way as the user ncmathsadist did it here: math.stackexchange.com/questions/162535/…

@Montaigne I cannot suggest any references though it sounds pretty standard (as if I have seen it before in, say, Munkres' text).

terrytao.wordpress.com/2011/05/24/…