Mathematics - 2012-07-20 (page 1 of 5)

Ali

00:01

Can someone please help me with editing the following statement to look mathematically/grammatically sound? "Luckily, the limit in Theorem 1 rapidly converges to the exact result, such that letting j = 30 is sufficient to have
t within 0.01% of the exact solution.

So, Theorem 1 suggests that t = \lim_{j \to \infty} f(j).

Gigili

@Ali Chi mikhay begi kollan? ghesmate akharesho nemifahmam.

Jonas Teuwen

Oh, sweet Asaf.

Gigili

@Ali You could say "convergence of the limit is rapid, as [blah]." But it is grammatical as it is now except the last part of the sentence that I don't get.

Henry T. Horton

Che barfii!

Gigili

Oh?

Ali

00:12

@Gigili: So, Theorem 1 expresses some quantity 't' as limit of a function of some variable 'j' when it goes to infinity. I'd like to say that the limit converges to the exact solution real quick such that the value of f(j) for j = 30 to infinity is almost about the same.

Gigili

@Ali The limit converges so rapidly that for "j=30" you almost have the desired result or something like that.

Henning Makholm

@Ali The only edit to your original formulation I would consider about the convergence is to put "rapidly" after" converges". But both choices are grammatical, I think. For the rest, I feel that "have t within" might be a bit too loose for mathematical writing...

Gigili

@Ali Also, I thought you could speak Per according to your profile so I asked that question.

Henning Makholm

How about just "setting j=30 produces t to a precision better than 0.01%"?

@Ali Are you sure that "suggests" is what you want to say here?

Ali

@Gigili: Thanks. Yeah, I do know Persian, but there are people here who don't.

robjohn

00:20

J.M. has gone for a fractal gravatar.

Ali

@HenningMakholm: Thanks. I am not sure about the latter. What would you suggest, instead?

Gigili

@robjohn Wow, shiny.

robjohn

@JonasTeuwen what has he done now?

Jonas Teuwen

@robjohn Mailed me :-).

Gigili

@Ali Obviously, the former doesn't contradict the latter.

robjohn

00:21

@Gigili It is a change for him. He has been doing constant curvature surfaces for a while.

Ali

@Gigili: I meant a substitute for word "suggest", by latter.

robjohn

@JonasTeuwen He never replied to the emails I sent him. :-(

Henning Makholm

@Ali Not sure. Depends on what you want to say. (I had a professor who lectured for years until someone told him that "suggests" and "implies" are not the same (or rather, their equivalents in Danish)).

Jonas Teuwen

@robjohn Oh, just send them again, he can handle that 8-).

robjohn

@HenningMakholm like "hints" and "commands" are not the same

Jonas Teuwen

00:24

@HenningMakholm Mmm, but I hope that only means he didn't understand the words, and not their meaning 8-).

Ali

@HenningMakholm: Hmm, I see. In mathematics, every word has a very particular meaning, and unfortunately, I am not familiar with most of such terminologies.

Jonas Teuwen

If you are too lazy to type all results and to make exercises, just state the theorem, don't give any exercises and name those "Further results".

robjohn

@JonasTeuwen It has been since he left chat. I know he got them, so there would be no point in resending.

Jonas Teuwen

@robjohn Might have as well thought "I will reply later on" and forgot. Happens to me all the time.

Gigili

@robjohn Oh, dear. Maybe just forward them to me and I'll reply to all of them.

robjohn

00:27

@Gigili maybe later ;-)

Henning Makholm

@JonasTeuwen Well, he's an American working in Denmark, and he had just looked up "imply" in a general English-Danish dictionary. Unfortunately the gloss he selected on was the one that matches the everyday "suggest" sense of "imply".

Jonas Teuwen

@HenningMakholm Ah! :-). (Btw Asaf broke my dream by stating that given HB you have non-measurable sets :-()

Henning Makholm

@Ali Well, to be precise: If the therorem makes it completely certain that t ist the limit, then "suggests" is too weak a word here, and you need "implies" instead. However, it it is possible that the theorem could be true and t still differ from the limit somehow, then "suggests" might be a good choice.

Jonas Teuwen

Good night guys.

Henning Makholm

Goodnight. Wait, is it 02:30? Time to call it a day.

Ali

00:31

@HenningMakholm: Cool! Then, I think "implies" is the right word for my purpose here.

Jonas Teuwen

@HenningMakholm In three hours.

Henning Makholm

@JonasTeuwen So you're in UTC-01? Iceland?

Jonas Teuwen

@HenningMakholm No, in three hours it is "day" 8-).

Henning Makholm

Ah.

BenjaLim

@JonasTeuwen all night here?

leo

00:36

higgs boson

?

Jonas Teuwen

@BenjaLim Yep. Bye.

BenjaLim

oh crap

9 hours on chat

why was makoto's meta question reopened?

leo

@Gigili nice!

quite sad but nice

Gigili

@leo What about it?

leo

@Gigili your gravatar

Gigili

00:39

Ah thanks, but what about Higgs Boson?

leo

@Gigili it was discovered

Gigili

Umm, I know.

Well, the question mark. Never mind then.

leo

@J.M. nice!

J. M.

The way I see it, if you manage to piss Arturo off, you're a real piece of work...

@leo I haven't done anything yet... :)

Bill Dubuque

@J.M. Not true, many folks have bumped heads with Arturo on sci,math. He even has his own stalker from one of the mexican newsgroups iirc.

leo

00:46

@Gigili the question mark: does it really is the Higgs boson?

J. M.

@BillDubuque Even petty stuff?

leo

@J.M. it doesn't matter (your gravatar is great!)

Bill Dubuque

@J.M. All kinds of stuff. sci.math has always had problems with egos clashing, besides the usual cranks, trolls, etc.

leo

zeenews.india.com/news/space/…

J. M.

@BillDubuque Ah, I remember encountering that one about the stalker when I was searching about Arturo... people are weird.

@leo Oh, that. Heh. I was expressing disappointment that the logo we proposed for the mathematica.SE site was not kosher with Wolfram, hence the gravatar...

@BillDubuque Maybe it's in the past. I haven't seen Arturo lose his shirt over petty stuff on math.SE, and in some cases he seems to have been remarkably patient with people I'd have punched in the mouth in real life...

leo

00:52

@J.M. I see, yours is better I think

Bill Dubuque

@J.M. Alas, I wish I could agree with you on that.

leo

I did not know that there is a faq tag for the main site

J. M.

@leo Some questions just keep popping up, y'know...

Bill Dubuque

@J.M. For example. But hey, we're all human... Some people do not tolerate fools well.

J. M.

@BillDubuque This is the tail end of a long and protracted argument that degenerated, I gather...

Bill Dubuque

00:57

@J.M. It get's worse elsewhere. My jaw dropped. But I will stop there.

J. M.

(On that note, I was a very young and green fool the last time I ever said "fuck you" with serious intent...)

@BillDubuque I understand. :) Thanks.

Gigili

@BillDubuque What a nice thread! (what the hell) I couldn't have learned so many $$%*&^ words at once in any other ways.

Bill Dubuque

@Gigili Obviously you've never lurked on sci.math. You can find it all there...

J. M.

I've lurked on sci.math back in the old days, but clearly I never saw the gem Bill showed. Likely because I was as picky back then as I am now with reading stuff...

Bill Dubuque

The crank there thinks he has invented a new system of numbers (polysign numbers). He's very annoying, but harmless.

J. M.

01:04

@BillDubuque ...it is probably a good thing that math.SE only had one guy inventing a new system of numbers (if memory serves), and that got dealt with...

@BillDubuque There wasn't anybody to wrangle people back then, right?

Bill Dubuque

In fact in one of those threads I think he was coming to my defense, after the crank was being extremely disingenuous. But as anyone knows, I can defend myself (well, actually, I was much more reserved on sci.math). I only spoke up so much on meta since I didn't want to see us make the same mistakes.

Gigili

@BillDubuque Well, I ... don't think I need to find them! They'll find me eventually like this case.

Umm, perhaps this is why he went bananas

"One" of the reasons ...

Bill Dubuque

@Gigili What about that?

Gigili

Three downvotes, offensive comments and whatnot.

J. M.

I'm loathe to class that user as a "crank" (my being an amateur likely disqualifies me from making such pronouncements), but really, the user is not even trying to be conciliatory... yecch.

Bill Dubuque

01:12

@J.M. After much thought I think it is essential to keep tension off of main. If you see stuff flaring up there please flag it asap and/or steer people to meta. Most of these matters are much easier to handle as sparks, before they become flames.

J. M.

@BillDubuque I'll keep an eye, as always, but thanks for the reminder.

Bill Dubuque

@J.M. The "you" was meant to be royal, i.e. a request to everyone.

J. M.

Okay, but it was linked to my message... :)

Bill Dubuque

@J.M. Take it is a compliment if I refer to you as every mathematician!

J. M.

Fine, fine. :)

Bill Dubuque

01:19

@Gigili I think there is worse than that. After the rude way he has been treated, I'm surprised he has kept his cool. I had hoped we would be able to handle this more tactfully.

J. M.

BTW @Bill, your avatar is a modular form in the complex plane, yes?

@BillDubuque I think it's more of the theory you proposed a few days ago, something about him just being unfeeling.

He can't empathize.

Bill Dubuque

@J.M. Yes. Perhaps we are guinea pigs in the ultimate Turing Test.

Gustavo Bandeira

Does a function of $x$ in the terms of $y$ means that $x=x$ and $y=f(x)$?

Bill Dubuque

@J.M. See here for more

robjohn

@J.M.: I see you have swerved from the surfaces of constant curvature.

J. M.

01:25

@BillDubuque Aha, the Klein invariant. Thanks for the link!

Bill Dubuque

@robjohn Now we're both off the wagon!

Gigili

@J.M. Whoa, 50k? Congrats!

J. M.

@robjohn Well, I'm celebrating the graduation and expressing sadness that our proposed logo wasn't Wolfram-kosher... :)

@Gigili That's site-wide rep (rep over all sites added up); don't put too much stake into it... ;)

@Gigili It'd be a miracle if I can hit 50k here...

robjohn

@J.M. Oh? Did Wolfram complain about it?

J. M.

@robjohn Yes, sadly the lawyers feel that a hyperbolic pentagon is too near in appearance to a hyperbolic dodecahedron for their taste... :)

Gigili

01:28

@J.M. I know, I know. Still a big number.

robjohn

@J.M. Have you decided on a new logo?

Gigili

@J.M. Won't take too long, you're a 30k user here.

robjohn

@J.M. It's still like 43k just from Math and Mma

J. M.

@robjohn The one currently up on the newly graduated site is a stylized heptagon...

@robjohn If you put it that way... :D

Gigili

43k? Bah.

robjohn

01:32

@J.M. and I'm still struggling to get to 32k ;-)

@BillDubuque: don't get all worked up, it was a joke, not a plea for points :-p

J. M.

@robjohn Your past few days weren't that dry... :)

Bill Dubuque

@robjohn I will compose a 10000 point bounty question requiring strong Bezoutkas. Will that work for you? But you'll have to sacrifice your gravatar and red flyer. Deal?

J. M.

Bill, just so I can understand your position: you've never had to write an answer that required Bezout? :)

Bill Dubuque

@J.M. It's just a long running joke. Bezout works fine in some contexts. It started when Rob fired a big Bezouka at the rational root test. It's on whim.org somewhere

robjohn

@BillDubuque My red flyer!? Never!!

Talk behind my back. I'm off to the park.

Bill Dubuque

01:45

@J.M. In fact Rob even compliments me when I fired a Bezouka at the Rational Root Test. (thanks Rob!)

Bill Dubuque

02:02

@robjohn That's sly Rob, you took everyone to the park so I couldn't tell tall Bezout tales while you're gone...(no one else is here now).

Kannappan Sampath

I am still in a dilemma whether I should start hammering more CWs and quit or start contributing to the site. I am still irritated and worried people will continue to downvote me for no reason as they did on that last post I ever wrote for the site in the past two months.

Mark Dominus

Did J.M. get a new avatar?

J. M.

@MarkDominus Yes.

Mark Dominus

It is very handsome.

J. M.

I'm taking a break from constant-curvature surfaces for now, because of the newly-graduated mathematica.SE...

(and the "pentaflake" is nice.)

@KannappanSampath How many downvotes did it get?

Kannappan Sampath

02:11

@J.M. I don't remember but irritatingly many of them.

J. M.

@KannappanSampath That's not exactly "everybody", right? Just keep contributing anyway.

robjohn

02:32

@BillDubuque And why would I not? :-)

Bill Dubuque

@robjohn I can't imagine squeezing everyone into the red flyer. But hey, with all the recent talk of AC, I'm sure you know how to do all sorts of funky decompositions, stuff that would even drop the jaw of Banach and Tarski

Chuck Fernández

hi can you give me a function $f$ $X\rightarrow Y$ such that $f(A_1 \cap A_2) \neq f(A_1) \cap f(A_2)$ where $A_1, A_2 \subseteq X$?

woops

you get the idea right?

robjohn

@ChuckFernández You can fix that by typing up arrow a couple of times

@ChuckFernández much better :-)

Chuck Fernández

@robjohn thanks

robjohn

$f(x)=x\bmod3$

$A_1=\{1\}$ and $A_2=\{4\}$

Chuck Fernández

02:37

thanks

Kannappan Sampath

@robjohn If I may ask, did we make any progress on the Euler's totient? I am getting nowhere.

And I wish you a pleasant evening.

robjohn

@KannappanSampath I thought about it, but had to give up. I will think some more tonight after dinner.

Kannappan Sampath

Any breakthroughs or short lemmas? (not that these intersect in null set)

robjohn

@KannappanSampath not of any import. I showed that $3^{n+2}\,|\,10^{3^n}-1$, but that is nothing earth shattering.

Kannappan Sampath

@robjohn This holds for all $n$, but did you have to prove it in this context?

anon

02:53

@ChuckFernández See this question: math.stackexchange.com/questions/170725/…

Kannappan Sampath

I can't see any embellishments on the site. No icons showing up, no arrows! :(

(arrows: the one that you use for voting.)

anon

I would prove it via $3\mid\Phi_{3^k}(10)$ for all $k=1,\cdots,n$.

And $3^2\mid\Phi_{3^0}(10)$.

Peter Tamaroff

03:19

Hello peoples of the math.

Henry T. Horton

Peter? What are you doing here?

Peter Tamaroff

@HenryT.Horton What are you doing here?

Henry T. Horton

I'm not here. This isn't happening.

Peter Tamaroff

@HenryT.Horton Wait. Should I be elsewhere?

@HenryT.Horton I refuse to enter into a philosofical debate.

J. M.

@PeterTamaroff Which of you two is the particle, and which one is the anti-particle?

CLarue

03:25

Please, do not interact in deciding that, though.

Peter Tamaroff

@CLarue LOL

Henry T. Horton

But... I just want to hug him

J. M.

@HenryT.Horton I'm sure the results will be spectacular...

Peter Tamaroff

@HenryT.Horton Oh, so you have seen my picture.

I tend to have that effect on people. Sorry.

@J.M. What is your new gravatar?

J. M.

@PeterTamaroff It's a "pentaflake" fractal, but I used the logo we proposed over at mathematica.SE instead of the usual pentagon.

Peter Tamaroff

03:31

@J.M. Oh, OK.

The logo here at SE is pretty cool IMO

J. M.

@PeterTamaroff The logo for math.SE?

Peter Tamaroff

@J.M. Yes.

J. M.

Ah. Jin has good taste, so he's the one to thank...

Peter Tamaroff

@J.M. Who's Jin?

J. M.

@PeterTamaroff He's the guy who designs the look-and-feel for all the SE sites.

anon

03:34

Someone should take the MSE logo (with the usual optical illusion) and change the cubes to multicolored platonic solids. I guess it'd have to be in a pentagonal arrangement though.

which would be slightly sad, because hexagons are cooler than pentagons

or hotter, if Mario Party 2 taught me anything

J. M.

@anon :D

Most of the space-tessellating polyhedra that aren't cubes look somewhat elaborate, though...

Peter Tamaroff

How do you write this "phonetically"?

Φιλομαθέω

I'm getting

Philomatheo

J. M.

@PeterTamaroff "philomatheo".

anon

i<3maffs

J. M.

That's an omega, not a terminal sigma.

Peter Tamaroff

03:38

@J.M. Sorry, yes.

@J.M. What does it mean?

J. M.

@PeterTamaroff To be honest, I just read the thing phonetically. I don't know what it means. :D

Peter Tamaroff

@J.M. Hahah OK. Google is saying "love of learning" "curiosity" "learning spirit"

Steven Li

hello

Eugene

hello all. it's been awhile

Peter Tamaroff

@Eugene Euge, how's it going?

J. M.

03:41

@PeterTamaroff I see, that's why the "Φιλο-" prefix is there. "Loving".

Henry T. Horton

Huge Euge

Eugene

alright. and you?

Peter Tamaroff

@Eugene Can't complain.

CLarue

the μαθέω seems to translate to "battling"

Steven Li

is it appropriate to ask math question in this chat room?

Peter Tamaroff

03:41

@StevenLi Sure.

anon

yes

Steven Li

sweet

Henry T. Horton

I'm not even wearing a shirt. Anything goes in here.

anon

Legend says math was the original purpose handed down to this room.

Steven Li

lol. um im having trouble understanding metatheorem

Peter Tamaroff

03:42

@anon HEHEHE =D

J. M.

@anon But hey, who listens to the old guys? :P :D

Peter Tamaroff

General question: Just as we pair $\epsilon$ and $\delta$ together, what is the pair of $\lambda$?

Steven Li

im reading a thing called deduction for propositional calculus

J. M.

@PeterTamaroff $\mu$, often.

@HenryT.Horton That's nothing. Someone in this room used to chat pants-less...

Peter Tamaroff

@J.M. Great. $\lambda $-$\mu$ does pair sweetly.

Steven Li

03:43

i dont get how the "proof" works

anon

...

Peter Tamaroff

@J.M. And another one was an automated "Clever-Bot"-like programme.

Steven Li

is my question too vague?

Peter Tamaroff

Just like "isometry" is the cool word for "metrically equivalent", what is the cool word for "topologically equivalent" (for metric spaces)

@StevenLi I think you should provide more info.

anon

@StevenLi what question? I was under the impression you were leading up to asking it...

Steven Li

03:48

opps lol

Peter Tamaroff

"i dont get how the "proof" works" $\Rightarrow$ What proof?

Steven Li

sorry let me try again

Henry T. Horton

@PeterTamaroff "Topologically equivalent" (for any topological space) is called "homeomorphic"

A homeomorphism is a bijective continuous map with continuous inverse

anon

and if you have differentiability, you can say diffeomorphic

Peter Tamaroff

@HenryT.Horton If it is bijective then it has inverse. So we may just say "continuous bijection".

@anon You know topology?

Eugene

03:51

@PeterTamaroff but the inverse needs to be continuous as well

Peter Tamaroff

@Eugene I'm trying to think about a continuous function with discontinuous inverse...

Kannappan Sampath

@PeterTamaroff well you are asking Langlands if he knew anything about those automorphic forms.

Peter Tamaroff

@KannappanSampath Sorry?

Kannappan Sampath

@PeterTamaroff Google some obvious terms please :)

Peter Tamaroff

@KannappanSampath Come on....

Kannappan Sampath

03:55

@PeterTamaroff OK. Have you heard of Langlands Programme?

Eugene

@PeterTamaroff math.stackexchange.com/questions/68800/…

Peter Tamaroff

@KannappanSampath Nope.

Eugene

@PeterTamaroff it was a TV show on PBS that got cancelled due to low ratings

2

anon

I do not know topology like Langland's knows forms.

lol

Henry T. Horton

@PeterTamaroff $f: [0,2\pi) \longrightarrow S^1$, $f(t) = (\cos t, \sin t)$

Kannappan Sampath

03:57

@PeterTamaroff I am no expert on that but hope to become one some day. It is a grand unification theory that this generation of Mathematicians are heading towards.

@anon I know you also share similar interests, am I right?

J. M.

@Eugene "Automorphisms in the sky... I can go twice as high.."

anon

Yes. Things like Langland's and Moonshine are part of my life goals.

Kannappan Sampath

@anon Mine too. :)

Eugene

@J.M. "take a look... it's in 'the book'... reading rainbow"

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$Mathematics$ Mathematics