Mathematics - 2012-01-05 (page 2 of 4)

@tb I am quite happy that I have finally solved the following problem: if $(X,d)$ is a complete metric space and ${A_n}$ a countable collection of proper non-empty dense subsets of $X$, then there is point of $X$ that is not in any of the $A_n's$

t.b.

What do you do if $A_n = X$?

Benjamin Lim

@tb I am dumb, it should be nowhere dense and not dense

t.b.

Or on a slightly less silly note $A_n = X \smallsetminus \{x_n\}$ for an arbitrary sequence of non-isolated points $x_n$ with $x_n \neq x_m$?

QED

I guess, I've been wanting to learn some mathematics for a while but I haven't managed to get into it properly

t.b.

8:15 AM

For example $A_n = \mathbb{R} \smallsetminus \{n\}$?

Benjamin Lim

what was I thinking

sorry, I should be having this of the top of my head

@QED start with the baire category theorem?

Asaf Karagila

Please Read: Chat Rules

6

Benjamin Lim

@AsafKaragila who is this addressed to?

QED

@AsafKaragila, maybe shorten it

Asaf Karagila

@BenjaminLim If you have to ask this, then it is also addressed to you.

Benjamin Lim

8:23 AM

@AsafKaragila Do you know a mathematician called Amnon Neeman?

Asaf Karagila

@QED Maybe. Maybe I break your legs, eh? ;-) Also, what did you have in mind?

t.b.

@AsafKaragila plus 1 especially for point 3

QED

lol

t.b.

@BenjaminLim I do, of course (by name).

Used some of his work for my thesis.

Benjamin Lim

Ahhh, he's pretty famous

I've met him in person once :D

t.b.

8:25 AM

He sure is.

Asaf Karagila

@BenjaminLim Do you know a mathematician called Uri Onn?

Benjamin Lim

@AsafKaragila no

@tb He told me the first 3-4 chapters of AM were easy

Asaf Karagila

@BenjaminLim He's a very nice person.

t.b.

@BenjaminLim what's AM?

Benjamin Lim

atiyah macdonald

t.b.

8:26 AM

Well, easiness is in the eye of the beholder

Benjamin Lim

@AsafKaragila I don't think I've been to any talks by him and I've never been to israel

t.b.

@Asaf: could you please unpin one or two of your thingies? // thanks

Benjamin Lim

you would expect for someone of the caliber of amnon neeman for that book to be easy

Daniil

Hello.

QED

hi

Asaf Karagila

8:27 AM

@BenjaminLim Well, your loss. He taught me one of the courses in linear algebra, Galois theory, representation theory; and he's very nice.

Hi @Daniil

Benjamin Lim

@AsafKaragila Hopefully one day I can meet him :D

@AsafKaragila Although I met Paul Baum in person and first thing he said to me was that I am very tall!

Daniil

Asaf, can I ask you a question regarding your answer?

Asaf Karagila

@BenjaminLim Come to Israel. He does $p$-adic stuff, or so.

@Daniil Obviously.

Benjamin Lim

I did not know he was the Baum in "Baum - Connes"

t.b.

@BenjaminLim so you're the guy on the right of your picture?

Benjamin Lim

8:28 AM

@tb yes

t.b.

But in comparison with Paul Baum almost anyone is tall, isn't it?

Benjamin Lim

ah hahahahahahahah

but man I got to say

he was dressed in a very relaxed manner

suspender belts, flip flops, t-shirt, shorts

Daniil

@AsafKaragila I do not understand how you can construct an infinite chain "taking all the elements comparable with x0 instead", since there might be infinitely many elements comparable with x_0, but they do not have to be comparable between themselves.

t.b.

he always was when I saw him.

Benjamin Lim

he was so cool!!

and you know what

he came into a talk my friend who's doing honours gave

he asked a lot of good questions too!

Asaf Karagila

8:30 AM

@Daniil If all elements are comparable with all-but-finitely-many take $x_1$ comparable with $x_0$, then there are only finitely many incomparable with both (intersection of two co-finite sets) then we can find a third, and so on.

t.b.

@BenjaminLim oh, he definitely is a nice guy.

Benjamin Lim

@AsafKaragila In a few years I hope to be able to visit Israel!

t.b.

Although I don't know him that well. Spoke to him only once.

Asaf Karagila

@BenjaminLim Sounds like a plan.

Benjamin Lim

thick glasses :D

@AsafKaragila Do you know that some countries in the world ban their citizens from entering Israel?

Daniil

8:31 AM

hm, I see, thanks.

@BenjaminLim countries like Iran?

Benjamin Lim

For example I have a friend at university who is from malaysia and on his passport it says: Valid for all countries except israel

Asaf Karagila

@BenjaminLim Clearly... Iran, I presume.

Benjamin Lim

don't mean to make this into a discussion on politics

Asaf Karagila

I think Zhen Lin once said that his passport is such passport.

Benjamin Lim

yes

@tb Did you stalk my profile to check again if I was the guy on the right??? 8)

t.b.

8:34 AM

what do you mean?

Benjamin Lim

it was a joke :D

t.b.

No I didn't.

Benjamin Lim

@tb Can't you tell from my surname that I am of asian descent?

t.b.

Sure I can, but I've seen weirder things than people of asian descent with slightly brighter hair than black... (the other person's face isn't visible)

Benjamin Lim

ah ok, that picture was taken on the ferry from Cronulla to Bundeena, Sydney

t.b.

8:38 AM

Sounds nice. I never was there. My brother spent about two years in Australia, but you don't just go there and visit for one or two weeks...

Benjamin Lim

@tb You could come visit Amnon Neeman :D

t.b.

A friend of mine did do that. But he's more into algebraic geometry and homotopy theory than I am.

Benjamin Lim

your research is in algebraic topology?

t.b.

(and that friend lived in Singapore when he visited him, that's a bit closer :)

Asaf Karagila

You can't spell "homotopy theory" without "top".

Benjamin Lim

8:41 AM

your research is in algebraic topology?

Perhaps you know Vigleik Angelveit?

t.b.

No. No I don't.

Benjamin Lim

apparently we have a few people coming to the math department

Skullpatrol

@tb Sir, have you ever seen the symbol for "such that" that looks like sort of like this " |."

Benjamin Lim

One of them I heard would be david smythe

@skullpatrol woaah that was out of the sky!!!

t.b.

@Skullpatrol No, I haven't. I've seen a single vertical stroke for that, but the period seems off.

@AsafKaragila ?

Skullpatrol

8:43 AM

@tb Yes, the period should be rised

@tb !

@AsafKaragila .

@tb "

@AsafKaragila /

@tb \

8:45 AM

you win.

Asaf Karagila

Huzzah! :-)

Skullpatrol

@tb Also the backwards epsilon is used. I was wondering is one "such that" symbol used in math and the "vertical stroke raised period" used in logic?

t.b.

@Skullpatrol I'm not really an expert on notation issues in logic (why do you ask me?). I never used a special such that symbol in math, a colon did always do the job for me. Neither did I use "therefore" and "because" and siblings. I don't like to hide ideas behind impenetrable symbols.

Okay, enough procrastination for now. See you guys later!

Benjamin Lim

@tb à tout à l'heure

QED

9:24 AM

iirc there's a pretty simple formula to calculate the fractal dimension of IFSs

Asaf Karagila

Oy vey. The Russian roulette thing is gonna turn up bad.

QED

"impossible to get a real gun in the UK" - not true, some guy just shot a bunch of his friends then himself

Daniil

reddit.com/tb/o2m6d that's pretty impressive

QED

there is some kind of "gun license" you can get here, not what the value in it is

kind of a dumb non-mathematical question

Nikhil Bellarykar

@Daniil haha funny

QED

9:42 AM

wow why has it got 56 upvotes?

who reads this site

trivial probability question with a story and picture behind it: 50 upvotes

:/

Asaf Karagila

Because the general crowd likes "easy" questions, no one cares about forcing and large cardinals and the negation of the axiom of choice anymore...

Daniil

Are you talking about that Russian roulette question?

Asaf Karagila

Yeah.

Daniil

If I recall correctly there was also some really stupid "batman equation" question

which got immense number of upvotes.

Asaf Karagila

Yeah, that was linked all over the internet.

Daniil

9:44 AM

But it is horrible as a question, really.

QED

ugh

Asaf Karagila

Yeah...

Daniil

184 votes, 178k views... math.stackexchange.com/questions/54506/…

Asaf Karagila

314 votes on an answer...

QED

that'll be reddits influence

Daniil

9:49 AM

Well, some of the comments are witty, on the other hand :P

Zhen Lin

10:29 AM

@Asaf: I suspect the best chance for interpreting modal logic using boolean algebras would require you to interpret the modalities as unary operators on the algebra. Have you looked at Kripke models yet?

Asaf Karagila

@ZhenLin No, not yet. I'm still too tired from the night, I'll do it later.

Skullpatrol

@ZhenLin Do you know, off hand, who came up with this "set builder" notation Zhen?

Zhen Lin

No.

Skullpatrol

@ZhenLin Do you care?

QED

@Skullpatrol, did you study that chapter I recommended yet?

Asaf Karagila

10:35 AM

@Zhen Either way, the filter is a predicate on the CBA, it's a "second order" operation, so to speak.

Zhen Lin

@Skullpatrol: Not really, no.

@Asaf: Sure, but it's idempotent, which greatly restricts the class of modal logics it can be used for.

Asaf Karagila

Also, have you seen the top pinned message? Chat rules and whatnot.

Skullpatrol

@QED No, I've been too busy, maybe in a couple of weeks.

QED

what have you been wasting your time doing?

:)

Asaf Karagila

@ZhenLin Well, prior to this morning I didn't even know that there were different kinds of modal logic. I only thought there was one type. The classical modal one with necessary and possible.

Skullpatrol

10:36 AM

@QED Recovering from the holidays

Zhen Lin

@Asaf: That's just the symbols. What are the axioms?

QED

I think you're missing out on some good stuff

Asaf Karagila

@ZhenLin $\square (A\to B)\to(\square A\to\square B)$, $\lozenge A\leftrightarrow \lnot\square\lnot A$.

Zhen Lin

Huh, who knew tuna could be so expensive?

QED

incredible

Zhen Lin

10:39 AM

OK, the first one is called the "distribution axiom" or "axiom K". The second one is the definition of $\Diamond$ in classical modal logic.

Skullpatrol

@QED I think it is a bit over my head, but I'll give it a try on your recommendation.

Zhen Lin

I don't think this system can prove $\Box A \to \Box \Box A$.

Asaf Karagila

Oh, we should probably add $A\to\square A$.

QED

@Skullpatrol, if you get stuck feel free to ask me about it - you'll be fine because it doesn't demand any prerequisites

Asaf Karagila

@JM Howdy!

Skullpatrol

10:41 AM

@QED OK

J. M.

hey, hey Asaf.

Zhen Lin

@Asaf I think that's the necessitation rule "N". But Wikipedia presents it as a deduction rule $\vdash A$ implies $\vdash \Box A$ instead.

They're not equivalent if the deduction theorem is not valid... and that might happen, but I'm not sure.

Asaf Karagila

@Zhen I suppose these rules can be replaced by equivalent ones, I'm just thinking about how the system should behave ("logically")

Zhen Lin

@Asaf: The thing about modal logic is that there are many, many axiom systems, each with different purposes/interpretations in mind.

Asaf Karagila

Is there a mathematical use for logics without a deduction theorem?

Zhen Lin

10:43 AM

As a logician, you are probably interested in the systems to do with provability, or with the system JDH developed for forcing.

Asaf Karagila

@ZhenLin I could be. For starters I am interested in helping my girlfriend in her semantics homework when she needs help, and now they arrived to modal logics. Forcing should be fun too, though. :-)

Zhen Lin

Ah, I think it's mostly non-mathematicians who are interested in the other forms of modal logic...

Asaf Karagila

@ZhenLin Yeah, I think they also added obligatory operator or something like that.

@JM There is a plethora of standing closing votes.

J. M.

One at a time, Asaf... :)

QED

annoying I got downvoted

for not providing full proof

I was just giving a starting point

J. M.

10:49 AM

On another tack: where are all those votes on the Russian roulette query coming from?

QED

hordes of people that hang around and never upvote actual math

Asaf Karagila

@QED I got downvoted for writing the pairs $P_n=\{a_n,b_n\}$ and saying that the product $\prod P_n=\varnothing$, because "we can choose $a_n$ from every pair", and if we cannot then there is no business calling them that. I hate taking this sort of heat from people lacking experience with set theory and unable to distinguish between internal and external names for elements.

QED

mm

Asaf Karagila

Not only that, when I later "corrected" the answer, the downvoter did not undo his vote.

Nikhil Bellarykar

11:02 AM

ahoy guys

robjohn

@Matt or @QED: without using this link, can you find that comment? When I try to show the source of the answer, the source of the page is re-sent, but without the comments expanded.

t.b.

11:19 AM

a deletion request (see last comment)

Asaf Karagila

Voted, @JM you're up.

robjohn

@tb what do we do; flag it?

t.b.

@robjohn can you vote to delete it already?

robjohn

@tb Ah, is it beyond my paygrade? :-)

Asaf Karagila

I think it's too soon for non-trustees.

t.b.

11:22 AM

@robjohn Possibly.

robjohn

@AsafKaragila that explains why I could not see a way to vote.

Asaf Karagila

Should I add rule no. 6: Speak English, not l33tglish, and not Inuit either. Unless of course, it's a part of a joke.

t.b.

@robjohn you should see a delete link next to the reopen link

Asaf Karagila

@tb Not unless it's too soon for him to vote on that.

robjohn

@tb nope. It is indeed beyond my abilities.

t.b.

11:23 AM

@AsafKaragila I always had this delete link. Strange.

Asaf Karagila

@tb, @rob: There are many closing votes waiting for your attention on the "Today" tab in the mod tools page.

@tb The delete button appears two days after closure for 10kers and immediately for 20kers. You may have checked "old closed" questions before, and you have been 20ker for some time too.

t.b.

@AsafKaragila No. Maybe it's because of a script I have installed. I had the delete link and then one of those ugly yellow things popped up that I have to wait a few hours/days.

Asaf Karagila

Ah. Possible too.

robjohn

:-)

t.b.

@AsafKaragila I don't think there's any question I want to close for which I haven't voted, yet.

Skullpatrol

11:28 AM

@tb I found this link answering the question about the backwards epsilon symbol and also the single vertical bar which does not have a raised period; thanks for showing some interest in my query. math.stackexchange.com/questions/15455/backwards-epsilon

Asaf Karagila

@robjohn I guess you have to wait 6000 more points...

t.b.

@Skullpatrol thanks for the link.

Skullpatrol

@tb np

QED

hi

robjohn

@AsafKaragila Indeed. I had to look at the close votes on the mod tools page even to see that.

QED

11:31 AM

frustrated by the downvote and "where is the proof?" math.stackexchange.com/questions/96606/…

not sure who's upvoting that comment

Asaf Karagila

@robjohn As long as you're having fun...

robjohn

@QED that way lies madness :-)

Skullpatrol

@tb It appears that "Peano introduced the backwards lower-case epsilon for "such that" in his 1889 "Principles of arithmetic, presented by a new method," according van Heijenoort's From Frege to Gödel: A Source Book in Mathematical Logic, 1879--1931 [Judy Green]."

Asaf Karagila

Like how Cantor received downvotes for set theory and went mad.

robjohn

@AsafKaragila And Didier was to blame!

QED

11:33 AM

@Skullpatrol, oh right "x in X" vs "x such that X"

what's the LaTeX for $\in$ backwards?

Asaf Karagila

$\ni$ \ni

QED

cool

$x \in X$ is the same as $X \ni x$, but you read them as "x in X" and "X such that x"

Skullpatrol

@QED The "vertical bar" symbolization comes in use with "set builder" notation

QED

what

Skullpatrol

@QED " | "

t.b.

11:38 AM

@AsafKaragila The knights of $\ni$?

Asaf Karagila

The knights who says $\ni$.

"No... not $\nu$, $\ni$!"

robjohn

@AsafKaragila Ekke Ekke Ekke Ekke Ptangya Ziiinnggggggg

t.b.

When you have found the shrubbery, then you must cut down the mightiest tree in the forest ... with a herring

J. M.

@AsafKaragila Done.

Herring? I'd have used halibut myself. Or a swordfish...

Asaf Karagila

@robjohn Maybe not Didier per se, but some other Frenchmen certainly downvoted set theory openly...

@robjohn I loved the knights who until recently said $\ni$...

robjohn

11:43 AM

@AsafKaragila I laughed so hard when I first saw that movie, that I thought for sure that I would pass out.

Asaf Karagila

I have the Extraordinary Special Edition DVD.

t.b.

@robjohn can you typeset that in MathJaX?

J. M.

I really wish that the protect bit shows up as soon as questions hit a certain number of views, as opposed to having to wait for two days...

Asaf Karagila

@JM Sounds like a valid feature request to me!

J. M.

If I get bugged enough, I guess I'll post something on meta.SO...

Asaf Karagila

11:47 AM

@JM Go post it on meta.SO

robjohn

11:58 AM

@JM I've bugged your phone and several houseplants. Is that enough?

J. M.

Won't work; the place is effectively a Faraday cage... :)

Asaf Karagila

With two lions?

J. M.

Nah, I had to let the two lions go; I ran out of assholes to feed them with...

Asaf Karagila

What about the tiger?

robjohn

@JM $\tiny{\text{oh, you don't say...}}$

Asaf Karagila

12:03 PM

@robjohn He did, actually, say that.

J. M.

@AsafKaragila I don't have any, apart from the one in my frosted flakes...

Asaf Karagila

@JM And he's Grrrrrrrrrrrrrreat!

t.b.

seen the paper linked to by deoxygerbe? quite impressive...

J. M.

Charming font... :)

robjohn

@AsafKaragila You mean he's G$\large{\text{R}}\Large{\text{R}}\LARGE{\text{R}}\huge{\text{E}}\Huge{\text{AT!‌}}$

Asaf Karagila

12:12 PM

No, he's Grrrrr-ate!

robjohn

@JM There should be an option for that font in $\LaTeX$

J. M.

Heh. Once upon a time there was this shareware that allowed you to turn your handwriting into a font. It came with a PDF that was a grid. You printed it out, wrote your stuff in the boxes, and scan it back in for the software to process...

Asaf Karagila

I like JDH's cardinals wiki.

J. M.

You're going to contribute to it?

Asaf Karagila

Already am.

I started carving AC related things :-)

J. M.

12:20 PM

Is Cantor's attic the hidden fun section of Hilbert's hotel?

Asaf Karagila

No, it's where the workers of the hotel live nearby.

t.b.

However, I don't think the post warrants downvotes as it's hardly fair to say you've never posted an answer without entirely reading a question (or maybe you have never, in which case you should give yourself a pat on the back).

?

!

)

12:22 PM

...

/

=

you win.

What's more equal than two sticks?

J. M.

++

t.b.

12:23 PM

sheesh. And I wanted to do some work. See y'all later :)

Asaf Karagila

Haha!

J. M.

Work is such a real distraction from chatting... :D

Asaf Karagila

Quite!

J. M.

(On another note: I like that all my badge counts are multiples of three...)

Asaf Karagila

I had powers of 2 recently.

robjohn

12:26 PM

@JM the same with my gold badge count! amazing!

@JM Tomorrow, that will change.

J. M.

@robjohn You're on 99 days now, no? Almost there...

Asaf Karagila

How about you skip tomorrow?

robjohn

@JM Indeed :-)

@AsafKaragila Sure. Why not? :-p

Asaf Karagila

I have 520 consecutive.

J. M.

Bah, he's just sourgraping that there's no badge for 500 consecutive days of visiting...

QED

12:29 PM

are moderators able to hard delete a post?

Asaf Karagila

Yeah!

QED

"delete" just hides, really

J. M.

@QED Nope. There's no such thing as a real deletion in the SE engine...

QED

boohoo

J. M.

(Even deleted comments are still visible to mods.)

robjohn

12:30 PM

@JM except for comments, no?

QED

I posted a pretty bad failed attempt at a proof, then deleted it and posted something better

robjohn

@JM ah

QED

12:50 PM

yes

Asaf Karagila

Hmmm. I just signed a check and it's amazing how my signature has changed over the past 12 years.

QED

I don't know

J. M.

@AsafKaragila For the better?

Asaf Karagila

@JM I don't know. My handwriting changed too, so it makes sense.

Well, I am going to buy some stuff. Gonna prepare a magnet to hold knives, and whatnot.

robjohn

@AsafKaragila Will this magnet be mounted on your belt?

Asaf Karagila

12:58 PM

@robjohn No. It will be in my kitchen, housing the bread slicing knife and the Arcos.

Well, be seeing you.

robjohn

@AsafKaragila Okay; that's probably a more normal use.

@AsafKaragila later :-)

Matt

1:24 PM

@robjohn I don't see a way to view the comment in the source of the page, sorry.

robjohn

@Matt Other than the link I provided.

Matt

I can't really look into this right now.

robjohn

Okay

Matt

I just found out that the exam dates are out and that Futile Attempts is tomorrow in 3 weeks.

Maybe later.

robjohn

I just was going to say that I got the URL by going to Didier's profile and then to his activity tab, selecting the comment tab, and finding the link to the comment there.

Skullpatrol

1:44 PM

@robjohn May I ask you a question?

robjohn

@Skullpatrol You just did.

Skullpatrol

@robjohn I see that there is an attempt to set up "Chat Rules" for this room, and I was wondering why should they be any different than those under "What can we chat about?" found in the "faq's" in the bottom right corner?

QED

this isn't a democracy

Skullpatrol

@QED But I will die for your right to say that.

robjohn

@Skullpatrol Do any of those etiquette suggestions seem unreasonable?

Skullpatrol

1:55 PM

These etiquette suggestions seem reasonable: What can we chat about?
This site is an extension of The Stack Exchange Network, so discussion should more or less revolve around the same topics you'd find at The Stack Exchange Network — but in an interactive, less strictly Q&A focused way. Do have fun, but please keep it professional and always be respectful of your fellow community members. When talking in a room, it's polite to stay roughly on topic for the room, as defined by the room owners. If you find yourself consistently veering into other topics, you should consider taking it to anoth…

robjohn

"as defined by the room owners"... it seems that Asaf has defined things.

Skullpatrol

@robjohn " When talking in a room, it's polite to stay roughly on topic for the room, as defined by the room owners. "

robjohn

on topic means what is being discussed, if there is a discussion going on.

Skullpatrol

@robjohn on topic for the room

robjohn

@Skullpatrol Asaf is the room owner. He can decide what is on topic for the room.

Transcript for

$Mathematics$ Mathematics