Mathematics - 2012-04-12 (page 3 of 3)

robjohn

23:04

@BenjaminLim is it?

@Henning: how are you feeling?

Henning Makholm

Gah! Why are people so dead set upon cleansing MSE of computer science?

@robjohn Angry.

robjohn

@HenningMakholm the faq says that math related software is on-topic

Henning Makholm

@robjohn That's little help. What about the entire mathematical theory of computing and programming languages?

robjohn

@HenningMakholm such as? What is being claimed off topic?

t.b.

@robjohn Henning is referring to this thread

Henning Makholm

23:09

@robjohn People in this meta thread are very adamant that if they don't understand questions about type theory, then ipso facto those questions must be off-topic.

anon

tb asked me if I thought that was off-topic (we were in chat). at first I said it looked off-topic but then I recognized it as appropriate.

t.b.

And I agreed.

anon

Okay, you did :)

t.b.

I think it's really not a particularly good question in that posting a screen grab and asking what's this? hardly makes a question, but I think we're lenient enough for all kinds of nonsense, so this one wouldn't stand out, except that it has to do with computers.

Henning Makholm

I mean: "Somebody somewhere wrote an XML parser with the same name as the OP's professor's toy language; therefore the toy language is more like Fortran than it is like, well, say, a diff.geo. professors favorite example manifold". Sheesh.

@tb Oh, I agree that is is not a very well posed question. That doesn't make its topic off, however.

t.b.

23:15

@HenningMakholm I completely agree that computer science should by no means be off topic. I upvoted your question and voted to re-open the question, btw.

Henning Makholm

@tb Thanks.

Also, somebody edited my meta thread starter to prevent me from calling the ghetto a ghetto. Hooray.

anon

It does have racial connotations in some places.

Rob

@anon They are two members of triplets or quadruplets or etc.

@MarianoSuárezAlvarez Hi.

anon

Just thought of a question. Can mods see edits to comments either on the main site or in chat?

Jonas Teuwen

Good night, ding ding ding!

t.b.

23:22

@robjohn: could you maybe help out in this thread? I was pretty sure we isolated that mathjax inserted some garbage when we discussed that smiley-breaking phenomenon a while ago. However, I've been unable to reproduce the problem, but what joriki reports seems related to me. Given that you figured it out, you can maybe say more.

Mariano Suárez-Alvarez

Hello @Rob

robjohn

@tb I will look

t.b.

Thanks

anon

odd bug

robjohn

@tb There is an extra character between the two nines.

t.b.

23:27

@robjohn Yes, but joriki swears he double checked that he didn't enter that.

And given that he knows his way around computers, I'm pretty sure that it must have been added later on, which is what happened with the smileys, too.

Jonas Teuwen

Good night guys.

t.b.

Good night, Jonas

Jonas Teuwen

Thanks.

t.b.

@robjohn and that these odd characters appear after 79 positions seems a bit too much to be coincidental. But I don't insist.

robjohn

@tb the processor does enter line breaks after a certain number of non-break characters, but these are 200B and 200C characters (zero width space and zero width space non-joiner)

I have never seen anything add characters that high in Unicode

but I don't think he added them with any program unless he did it intentionally

t.b.

23:35

@robjohn The smiley here has exactly the same &zwnj; stuff added.

Hi Brian

Brian M. Scott

Hullo!

Benjamin Lim

Hey guys

robjohn

@tb I fixed that by adding a space to the LaTeX. However, nothing was automatically added to the LaTeX in the emoticons. These 200B and 200C are added to the LaTeX source.

Benjamin Lim

@tb @BrianMScott I have a small topology question

Brian M. Scott

Go ahead; I’ve a few minutes before I have to leave.

Benjamin Lim

23:40

So let me first say that this is an assignment question but I have done it the usual pedantic way via sequences

I'm trying to do all my assignment questions with topology (which is not allowed to be used because the course is metric spaces)

So it goes like this

Suppose $E \subset X$ is dense

show that $\overline{f(E)}$ is dense in $f(X)$

the closure is taken in the subspace

robjohn

@tb Did he copy the string from the formatted output and paste it back into a LaTeX source?

Benjamin Lim

$f$ is a continuous function from $X$ to $Y$

robjohn

That would explain how the extra characters got into the LaTeX source.

Benjamin Lim

@BrianMScott Now because $f$ is a continuous function, we have immediately that $f(X) \subset \overline{f(E)}_Y$

Brian M. Scott

Okay.

Benjamin Lim

23:42

the subscript there is to indicate the closure is taken in $Y$

Brian M. Scott

Whoa! $f[E]$ is over in $Y$.

Benjamin Lim

Sorry

Sorry typo

Brian M. Scott

Okay; so you have $f[X]\subseteq\operatorname{cl}_Yf[E]$.

Benjamin Lim

So now I call the closure in the subspace $f(X)$ just $\overline{f(E)}$

but then we also have that $f[X] \subseteq \operatorname{cl}_{f(X)} f[E]$ too

Now from here I want to say something like because $f[X]$ is closed in the subspace $f[X]$ trivially

we must have equality the other way round too because I want to say something like $f[X]$ is a closed set in the subspace containing $f[E]$

@BrianMScott Sounds ok?

t.b.

@robjohn That I don't know. But something odd seems to be going on; joriki has added a few comments to his question on meta.

Benjamin Lim

23:46

@tb Hey I got my results for my analysis mid sem!!!

t.b.

The three exclamation marks indicate that you're happy with the outcome, right?

Benjamin Lim

yeah I have never got full marks in an exam at uni before...

Brian M. Scott

Okay: $\operatorname{cl}_{f[X]}f[E]=f[X]\cap\operatorname{cl}_Yf[E]=f[X]$, since $f[X]\subseteq\operatorname{cl}_Yf[E]$.

t.b.

Oh, great! Congratulations!

Benjamin Lim

@tb thanks.

@BrianMScott How did you get the last equality?

@BrianMScott Can I use the reasoning that I wrote above?

Brian M. Scott

23:49

@BenjaminLim See my edit.

Benjamin Lim

@BrianMScott I am stupid.

Brian M. Scott

Got it okay now?

Benjamin Lim

yeah

@BrianMScott You said it more succinctly than i did

@tb done.

huh?

@BrianMScott In my analysis course whenever they dish out an assignment I always try on the side to tackle it with results from general topology

so that at least in my heart I know that I can attack them in a more general setting

But then this has given me a kind of handicap

Brian M. Scott

That’s probably good practice; just remember that some things really will require metrizability, or at least first countability.

t.b.

I think it's good practice. :)

Benjamin Lim

23:54

@tb In the analysis exam for one minute I forgot what bounded meant!!! ffffffuuuuuuuuuu

t.b.

(what Brian said)

Benjamin Lim

@BrianMScott yeah sometimes we need to throw in hausdorffness or something to make the proof work

@tb Sequences, ugly as hell!!!

Brian M. Scott

But sometimes they really are the easiest way to go.

Benjamin Lim

I suppose yeah

t.b.

Is this the handicap you mentioned?

Benjamin Lim

23:56

@tb about the bounded thing?

Brian M. Scott

And when you’re working under time pressure, the best argument is the one that you can see and write down quickest, even if it’s not the most general or most elegant.

Benjamin Lim

@BrianMScott Yeah like in the exam they asked us to prove that if you have a countable collection of nested compact sets their intersection is not empty

I tried to recall a proof from rudin using open covers that attacked it more generally (the finite intersection property)

but then 1) I could not use open covers 2) I forgot the proof

So I just went "sequence"

t.b.

2) is a real handicap :)

Benjamin Lim

@tb hahahahahahahahahhahahahahahahahahahahahahahahahahahaahahahahahahahahahahahaha

t.b.

You just pass to complements and add that you want your compact sets to be closed (or add Hausdorff to the hypotheses)

Benjamin Lim

23:59

@tb Hey it was an exam ok lapses like that are excusable :D

Brian M. Scott

If their intersection were empty, their complements would be an open cover. Take a finite subcover; the closed sets that are complements of the open sets in the finite subcover would then have empty intersection. Can’t happen with a nest of non-empty sets.

Benjamin Lim

@BrianMScott oh wow

that's nice!!!

Transcript for

$Mathematics$ Mathematics