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8:00 AM
Ok, can I continue with what I said earlier?
actually now that I am aware of that fact I said I may have a new problem on my hands...
 
what is it?
 
that if we have $x \in G_1 \cap G_2$
then choose $\epsilon$ so small that $\overline{B_\epsilon (x)} \subsetneqq G_1 \cap G_2$
 
\subsetneqq
 
thanks
but then the problem comes when I take $G_1 \cap G_2 \cap G_3$
this is not empty too, say it contains $y$
but then there is no guarantee that I can choose a delta so that $\overline{B_\delta (y)} \subsetneqq E_1$
@tb BIngo
 
@BenjaminLim yes. Choose $\varepsilon$ so small that $B_{2\varepsilon}(x) \subset G_1 \cap G_2$.
Don't look at $G_1 \cap G_2 \cap G_3$. Look at $E_1 \cap G_3 \subset G_1 \cap G_2 \cap G_3$ and proceed from there.
 
8:04 AM
@tb bingo, got it
now I got it
you have given me the mother of all hints
 
:)
so, can you complete the argument now?
 
definitely, I already have a canned theorem in the bad :D :D :D
@tb On another point I am very pissed with myself
I asked such a n00b post on hausdorff spaces
I totally forgot that if $E$ is open in a topological space $X$
 
Yeah, I got your ping. :) Such things happen...
 
that for every point $x \in E$, there is a neighbourhood $U$ such that $x \in U \subset E$
@tb In fact remember that day we were talking about largest and smallest topologies?
It's kicked into me now why the closure of a set $A$ is the smallest closed set containing $A$
and why the interior of a set $A$ is the largest open set contained in $A$
 
Sorry, I'm a bit lost...
Hi, QED
 
QED
8:10 AM
hi
 
you were trying to explain to me that day something about how the intersection of all topologies containing a topology $\mathscr{T}$
 
Oh, right.
 
is the smallest topology containing $\mathscr{T}$
@QED Hello
 
QED
hi
 
what brings you here?
 
QED
8:13 AM
I'm not sure
 
@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 $A_n's$
 
What do you do if $A_n = X$?
 
@tb I am dumb, it should be nowhere dense and not dense
 
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
 
8:15 AM
For example $A_n = \mathbb{R} \smallsetminus \{n\}$?
 
what was I thinking
sorry, I should be having this of the top of my head
@QED start with the baire category theorem?
 
@AsafKaragila who is this addressed to?
 
QED
@AsafKaragila, maybe shorten it
 
@BenjaminLim If you have to ask this, then it is also addressed to you.
 
8:23 AM
@AsafKaragila Do you know a mathematician called Amnon Neeman?
 
@QED Maybe. Maybe I break your legs, eh? ;-) Also, what did you have in mind?
 
@AsafKaragila plus 1 especially for point 3
 
QED
lol
 
@BenjaminLim I do, of course (by name).
Used some of his work for my thesis.
 
Ahhh, he's pretty famous
I've met him in person once :D
 
8:25 AM
He sure is.
 
@BenjaminLim Do you know a mathematician called Uri Onn?
 
@AsafKaragila no
@tb He told me the first 3-4 chapters of AM were easy
 
@BenjaminLim He's a very nice person.
 
@BenjaminLim what's AM?
 
atiyah macdonald
 
8:26 AM
Well, easiness is in the eye of the beholder
 
@AsafKaragila I don't think I've been to any talks by him and I've never been to israel
 
@Asaf: could you please unpin one or two of your thingies? // thanks
 
you would expect for someone of the caliber of amnon neeman for that book to be easy
 
Hello.
 
QED
hi
 
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
 
@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!
 
Asaf, can I ask you a question regarding your answer?
 
@BenjaminLim Come to Israel. He does $p$-adic stuff, or so.
@Daniil Obviously.
 
I did not know he was the Baum in "Baum - Connes"
 
@BenjaminLim so you're the guy on the right of your picture?
 
8:28 AM
@tb yes
 
But in comparison with Paul Baum almost anyone is tall, isn't it?
 
ah hahahahahahahah
but man I got to say
he was dressed in a very relaxed manner
suspender belts, flip flops, t-shirt, shorts
 
@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.
 
he always was when I saw him.
 
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!
 
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.
 
@BenjaminLim oh, he definitely is a nice guy.
 
@AsafKaragila In a few years I hope to be able to visit Israel!
 
Although I don't know him that well. Spoke to him only once.
 
@BenjaminLim Sounds like a plan.
 
thick glasses :D
@AsafKaragila Do you know that some countries in the world ban their citizens from entering Israel?
 
8:31 AM
hm, I see, thanks.
@BenjaminLim countries like Iran?
 
For example I have a friend at university who is from malaysia and on his passport it says: Valid for all countries except israel
 
@BenjaminLim Clearly... Iran, I presume.
 
don't mean to make this into a discussion on politics
 
I think Zhen Lin once said that his passport is such passport.
 
yes
@tb Did you stalk my profile to check again if I was the guy on the right??? 8)
 
8:34 AM
what do you mean?
 
it was a joke :D
 
No I didn't.
 
@tb Can't you tell from my surname that I am of asian descent?
 
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)
 
ah ok, that picture was taken on the ferry from Cronulla to Bundeena, Sydney
 
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...
 
@tb You could come visit Amnon Neeman :D
 
A friend of mine did do that. But he's more into algebraic geometry and homotopy theory than I am.
 
your research is in algebraic topology?
 
(and that friend lived in Singapore when he visited him, that's a bit closer :)
 
You can't spell "homotopy theory" without "top".
 
8:41 AM
your research is in algebraic topology?
Perhaps you know Vigleik Angelveit?
 
No. No I don't.
 
apparently we have a few people coming to the math department
 
@tb Sir, have you ever seen the symbol for "such that" that looks like sort of like this " |."
 
One of them I heard would be david smythe
@skullpatrol woaah that was out of the sky!!!
 
@Skullpatrol No, I haven't. I've seen a single vertical stroke for that, but the period seems off.
@AsafKaragila ?
 
8:43 AM
@tb Yes, the period should be rised
 
@AsafKaragila .
 
@AsafKaragila /
 
8:45 AM
you win.
 
Huzzah! :-)
 
@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?
 
@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!
 
@tb à tout à l'heure
 
QED
9:24 AM
iirc there's a pretty simple formula to calculate the fractal dimension of IFSs
 
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
 
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
 
@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
:/
 
Because the general crowd likes "easy" questions, no one cares about forcing and large cardinals and the negation of the axiom of choice anymore...
 
Are you talking about that Russian roulette question?
 
Yeah.
 
If I recall correctly there was also some really stupid "batman equation" question
which got immense number of upvotes.
 
Yeah, that was linked all over the internet.
 
9:44 AM
But it is horrible as a question, really.
 
QED
ugh
 
Yeah...
 
314 votes on an answer...
 
QED
that'll be reddits influence
 
9:49 AM
Well, some of the comments are witty, on the other hand :P
 
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?
 
@ZhenLin No, not yet. I'm still too tired from the night, I'll do it later.
 
@ZhenLin Do you know, off hand, who came up with this "set builder" notation Zhen?
 
No.
 
@ZhenLin Do you care?
 
QED
@Skullpatrol, did you study that chapter I recommended yet?
 
10:35 AM
@Zhen Either way, the filter is a predicate on the CBA, it's a "second order" operation, so to speak.
 
@Skullpatrol: Not really, no.
@Asaf: Sure, but it's idempotent, which greatly restricts the class of modal logics it can be used for.
 
Also, have you seen the top pinned message? Chat rules and whatnot.
 
@QED No, I've been too busy, maybe in a couple of weeks.
 
QED
what have you been wasting your time doing?
:)
 
@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.
 
10:36 AM
@QED Recovering from the holidays
 
@Asaf: That's just the symbols. What are the axioms?
 
QED
I think you're missing out on some good stuff
 
@ZhenLin $\square (A\to B)\to(\square A\to\square B)$, $\lozenge A\leftrightarrow \lnot\square\lnot A$.
 
QED
incredible
 
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.
 
@QED I think it is a bit over my head, but I'll give it a try on your recommendation.
 
I don't think this system can prove $\Box A \to \Box \Box A$.
 
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
 
@JM Howdy!
 
10:41 AM
@QED OK
 
hey, hey Asaf.
 
@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.
 
@Zhen I suppose these rules can be replaced by equivalent ones, I'm just thinking about how the system should behave ("logically")
 
@Asaf: The thing about modal logic is that there are many, many axiom systems, each with different purposes/interpretations in mind.
 
Is there a mathematical use for logics without a deduction theorem?
 
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.
 
@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. :-)
 
Ah, I think it's mostly non-mathematicians who are interested in the other forms of modal logic...
 
@ZhenLin Yeah, I think they also added obligatory operator or something like that.
@JM There is a plethora of standing closing votes.
 
One at a time, Asaf... :)
 
QED
annoying I got downvoted
for not providing full proof
I was just giving a starting point
 
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
 
@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
 
Not only that, when I later "corrected" the answer, the downvoter did not undo his vote.
 
11:02 AM
ahoy guys
 
@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.
 
11:19 AM
a deletion request (see last comment)
 
Voted, @JM you're up.
 
@tb what do we do; flag it?
 
@robjohn can you vote to delete it already?
 
@tb Ah, is it beyond my paygrade? :-)
 
I think it's too soon for non-trustees.
 
11:22 AM
@robjohn Possibly.
 
@AsafKaragila that explains why I could not see a way to vote.
 
Should I add rule no. 6: Speak English, not l33tglish, and not Inuit either. Unless of course, it's a part of a joke.
 
@robjohn you should see a delete link next to the reopen link
 
@tb Not unless it's too soon for him to vote on that.
 
@tb nope. It is indeed beyond my abilities.
 
11:23 AM
@AsafKaragila I always had this delete link. Strange.
 
@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.
 
@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.
 
Ah. Possible too.
 
:-)
 
@AsafKaragila I don't think there's any question I want to close for which I haven't voted, yet.
 
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
 
@robjohn I guess you have to wait 6000 more points...
 
@Skullpatrol thanks for the link.
 
@tb np
 
QED
hi
 
@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
 
@robjohn As long as you're having fun...
 
@QED that way lies madness :-)
 
@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]."
 
Like how Cantor received downvotes for set theory and went mad.
 
@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?
 
$\ni$ \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"
 
@QED The "vertical bar" symbolization comes in use with "set builder" notation
 
QED
what
 
@QED " | "
 
11:38 AM
@AsafKaragila The knights of $\ni$?
 
The knights who says $\ni$.
"No... not $\nu$, $\ni$!"
 
@AsafKaragila Ekke Ekke Ekke Ekke Ptangya Ziiinnggggggg
 
When you have found the shrubbery, then you must cut down the mightiest tree in the forest ... with a herring
 
@AsafKaragila Done.
Herring? I'd have used halibut myself. Or a swordfish...
 
@robjohn Maybe not Didier per se, but some other Frenchmen certainly downvoted set theory openly...
@robjohn I loved the knights who until recently said $\ni$...
 
11:43 AM
@AsafKaragila I laughed so hard when I first saw that movie, that I thought for sure that I would pass out.
 
I have the Extraordinary Special Edition DVD.
 
@robjohn can you typeset that in MathJaX?
 
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...
 
@JM Sounds like a valid feature request to me!
 
If I get bugged enough, I guess I'll post something on meta.SO...
 
11:47 AM
@JM Go post it on meta.SO
 
11:58 AM
@JM I've bugged your phone and several houseplants. Is that enough?
 
Won't work; the place is effectively a Faraday cage... :)
 
With two lions?
 
Nah, I had to let the two lions go; I ran out of assholes to feed them with...
 
What about the tiger?
 
@JM $\tiny{\text{oh, you don't say...}}$
 
12:03 PM
@robjohn He did, actually, say that.
 
@AsafKaragila I don't have any, apart from the one in my frosted flakes...
 
@JM And he's Grrrrrrrrrrrrrreat!
 
Charming font... :)
 
@AsafKaragila You mean he's G$\large{\text{R}}\Large{\text{R}}\LARGE{\text{R}}\huge{\text{E}}\Huge{\text{AT!‌​}}$
 
12:12 PM
No, he's Grrrrr-ate!
 
@JM There should be an option for that font in $\LaTeX$
 
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...
 
I like JDH's cardinals wiki.
 
You're going to contribute to it?
 
Already am.
I started carving AC related things :-)
 
12:20 PM
Is Cantor's attic the hidden fun section of Hilbert's hotel?
 
No, it's where the workers of the hotel live nearby.
 
!
 
12:22 PM
...
 
/
 
you win.
 
What's more equal than two sticks?
 
++
 
12:23 PM
sheesh. And I wanted to do some work. See y'all later :)
 
Haha!
 
Work is such a real distraction from chatting... :D
 
Quite!
 
(On another note: I like that all my badge counts are multiples of three...)
 
I had powers of 2 recently.
 
12:26 PM
@JM the same with my gold badge count! amazing!
@JM Tomorrow, that will change.
 
@robjohn You're on 99 days now, no? Almost there...
 
How about you skip tomorrow?
 
@JM Indeed :-)
@AsafKaragila Sure. Why not? :-p
 
I have 520 consecutive.
 
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?
 
Yeah!
 
QED
"delete" just hides, really
 
@QED Nope. There's no such thing as a real deletion in the SE engine...
 
QED
boohoo
 
(Even deleted comments are still visible to mods.)
 
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
 
@JM ah
 
QED
12:50 PM
yes
 
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
 
@AsafKaragila For the better?
 
@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.
 
@AsafKaragila Will this magnet be mounted on your belt?
 
12:58 PM
@robjohn No. It will be in my kitchen, housing the bread slicing knife and the Arcos.
Well, be seeing you.
 
@AsafKaragila Okay; that's probably a more normal use.
@AsafKaragila later :-)
 
1:24 PM
@robjohn I don't see a way to view the comment in the source of the page, sorry.
 
@Matt Other than the link I provided.
 
I can't really look into this right now.
 
Okay
 
I just found out that the exam dates are out and that Futile Attempts is tomorrow in 3 weeks.
Maybe later.
 
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.
 
1:44 PM
@robjohn May I ask you a question?
 
@Skullpatrol You just did.
 
@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
 
@QED But I will die for your right to say that.
 
@Skullpatrol Do any of those etiquette suggestions seem unreasonable?
 
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
 
"as defined by the room owners"... it seems that Asaf has defined things.
 
@robjohn " When talking in a room, it's polite to stay roughly on topic for the room, as defined by the room owners. "
 
on topic means what is being discussed, if there is a discussion going on.
 
@robjohn on topic for the room
 
@Skullpatrol Asaf is the room owner. He can decide what is on topic for the room.
 

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