00:00 - 21:0021:00 - 00:00

12:00 AM
@Victor, I give up trying to get a rigorous statement of what you want to prove
@Victor: You need to write down what you want to prove into a mathematical statement and only then one can use mathematical proofing methods to proof whether your statement is true or false.
I kinda know what you mean but I'm not at all good at writing that down in a mathematical statement.
I would have liked to help you but you're making it too difficult
@QED - What is the difficulties on?
@Victor, trying to get a precise formal statement of what you want to prove
@QED - is that very diffiucult to prove the theorems in different dimensional?
12:54 AM
Anyone know how i can plot $$z \geq \sqrt{x^2 + y^2}$$ ?
Do it by hand... It's a cone standing on its tip in the $(x,y)$-plane and whose sides are at an angle $\pi/4$ from the $z$-axis.
I know
But I am doing my hand ins in latex...
I was thinking of just drawing a xy plot and a xz plot
Not quite sure how though
you can just make a blank box, and draw it on after printing
I might do that, plotting is hard
1:18 AM
@Srivatsan It means that I expect you to understand that only the closed ball has a chance to be compact unless the vector space is zero.
ok.
Wait, what? // Nevermind. I'm not sure I'm reading it properly, but nevermind now.
1:34 AM
@Srivatsan could you please fix the title of the post you just edited (countinuity)?
och, too late: Byron already jumped in :)
Byron and continuity -- there's a long lost connection. =)
How do one prove that $$|a+b|^2 = |a|^2 + 2 a \cdot b + |b|^2$$
I know I have learned this quite some time ago, I just cant remember how right now.
That seems wrong. Are a,b real or complex?
ops
a and b are two vectors.
$\|a+b\|^2 = (a+b) \cdot (a+b)$. Multiply out.
1:46 AM
OK. Hint: $\| x\|^2 = x \cdot x$.
-so simple...
I seriously need to fix my sleep schedule
Up 7 AM
down 3 AM
Well I guess 4 hours sleep a night is a tad too little.
6-7 Is good. Even 5
2:49 AM
Gee, it feels kinda lonely here. A sleeping Asaf and no-one else around...
3:18 AM
@tb, great!

3 hours later…
5:50 AM
Is there a degree $n$ polynomial $p(x)$ such that $\gcd(p(1),p(2),...,p(n)) \not = \gcd(p(1),p(2),...,p(n),p(n+1))$?
Found one $x^2+3x+8$

3 hours later…
8:32 AM
@MartinSleziak Nice answer, +1 from me.
@tb Awww... : (
I found out that what I wrote is all given there.
But thanks for the upvote anyway.
Did you see that Wikipedia counts finite ordinals as example for regular cardinals? You exclude them in your answer.
I wrote my answer before I checked the Wikipedia article. I did not notice that.
I am not entirely sure this is standard.
hi all
Hi Rajesh.
8:35 AM
have you seen this
0

While reading some things about analytic functions earlier tonight it came to my attention that Fourier series are not necessarily analytic. I used to think one could prove that they are analytic using induction Let $P(n)$ be some statement parametrized by the natural number $n$ (in this case: ...

What I mean, I believe there are usually excluded from both - they are understood as neither singular nor regular.
I see.
I didn't know physicists are not too okay with mathematics
Ok, see you later folks.
8:39 AM
If we use the same definition, 2 would be singular - it cannot be written as union of 1 singleton. And 3 is regular. There is - in my opinion - why finite numbers should be considered in two different classes w.r.t. cofinality. I think the best possible way is not to consider them at all.
Anyway, these notions are usually important only for infinite sets.
Good morning.
Morning Asaf.
How your talk went? Is it some kind of seminar, where you talked?
No, I was teaching one of my classes.
(I just noticed that the other day I answered a question of a PhD student.)
Due to a strike I had to give extra lessons for the ones they missed.
8:43 AM
@MartinSleziak Then I have it all wrong. I thought that a cardinal is regular if it is equal to its own cofinality.
I have to give the same topic today. I just want it to be over and start predicate calculus.
@Matt Exactly the opposite.
So you are already teaching, Asaf? We still have "exam period" here. (I do not know the correct English term, but I guess it's clear what I mean.)
Then I messed up things?
You were correct.
I think your answer is right and you didn't mess up anything.
8:47 AM
Yes I mentioned $cf(\alpha)=\alpha$ as equivalent to singular....
Rookie mistake :-(
Thanks a lot for noticing it Matt.
I had overlooked that so don't thank me : )
9:05 AM
@MartinSleziak We are still in the fall semester.
Phew that was a long answer.
I thought it will be shorter :D
BTW the guy mentioned he learns from a Chines textbook, but John does not sound like Chinese name.
I cannot understand how someone can ask about an $\omega_1$-Lindelof space and whatnot and not understanding what is a regular cardinal.
I did not have time to get back to C(X) and AC, but I promise I'll get back to it later. I'm not sure how much later it will be.
Or worse, $\bigcup x^+$.
@MartinSleziak Ditto :-P
Oh, it's the same guy which asked about $G_\delta$-diagonals and that stuff?
9:09 AM
Yes.
@AsafKaragila yeah, but he already didn't manage to check continuity of something extremely simple. BTW: his MO handle is now Diagonal :)
hi @tb
@tb Yeah, I saw that change in MO names ;-)
Hi Rajesh
how have you been monseur
9:11 AM
BTW as cofinality was mentioned, I remember that Todorcevic and others had some results about cofinal types of *directed sets*. I can imagine this can be useful, I did not studied those things is detail. Is any of you familiar with this?
This is mostly directed to @Asaf and @tb.
Not verily.
ok
So never mind than.
I had slight feeling that there might be kind of relation between these results and Alexei's question about two types of subnets. But I am not sure about this. (First of all because I do not know those results about cofinal types in detail.)
One more question tagged under cardinals and I've got myself a specialist badge.
@tb : request you to sort things out for OP on this
@AsafKaragila You've got an upvote from me. In connection with your last paragraph, wouldn't Easton's theorem be worth mentioning? At least by giving some links, perhaps Wikipedia or MO thread. (or both)
Well-deserved upvote I would say.
9:19 AM
@MartinSleziak Easton's theorem has nothing to do with that. It has to do with power sets. If anything, Prikry forcing has to do with changing cofinalities without changing the cardinals. However this requires a measurable cardinal.
@MartinSleziak Thanks.. :-)
yes but i am puzzled with his latest edit
please suggest me something i could do
Amazing how more than 25% of the questions in are related to me somehow :-D
I mean, unlike the AC tag which is small, this tag is big.
@AsafKaragila You're right about that Easton thing. Sorry, my mistake.
9:23 AM
@MartinSleziak No harm :-)
Hi!
@tb : I somehow want to cajole him to read about uniform and non-uniform convergence of function sequences
That transitive set thing should or ? I would say the first, but I'm not entirely sure?
@MartinSleziak I'm not sure either.
Ok, so let's leave it as OP posted it.
9:25 AM
elementary I'd say.
Sweet Zombie Jesus! It's 12 degrees Celsius outside.
And quite windy!
Finally, some winter.
12 more than here :)
@tb I thought that the division is not made by the difficulty of question (from this viewpoint it's elementary), but by the topics. According to tag wiki e-s-t is for the sort of material covered in "Chapter 0" of undergraduate texts and in undergraduate set theory texts. This was the reason why I thought s-t is better.
I know, I know. I should come to Israel. But telling me about 12 degrees doesn't give much incentives...
It's a week of the year.
We're like co-Norway, where there is only one week of "summer" which is really just a nice spring day here. In Beer-Sheva we have like one week of "winter" which is really just a nice autumn day in Norway.
9:28 AM
@MartinSleziak But the first sentence for set theory reads "This tag is for set theory topics typically studied at the advanced undergraduate or graduate level"
@tb In ETH I'd guess this counts as anything non-naive ;-)
Probably...
Anyway, in doubt I leave it to OP's choice.
But I would say that most tags are much more problematic when deciding what goes where than these two.
Except the whole idiotic "if it has sets of statistical data about rock bands, then it's set theory!"
Ok, I'll see you later, I guess if I stayed logged in here, that would be too much distraction from what I am supposed to do today.
Have a nice day!
9:33 AM
Hah. I know how that's like.
You too.
See you, Martin
@AsafKaragila have you looked at the OP's profile of the question you closed a few minutes ago? More than half of the questions are of this kind... Kind of frightening.
We could go on a deletion spree, because it's such a lovely day, perhaps!
yesterday i've seen a strange thing happening to me on SE, i am not able to find a correct explanation for it
Wow... I just need to offer and give a bounty on someone else's question and then I have all the bronze badges except Precognitive, Peer Pressure and Tumbleweed.
It showed that i got an announcer badge for a question's link which points to a page which says that the question was deleted by the OP (me)
9:39 AM
Deleted things are not really deleted.
They changed announcer/booster criteria yesterday and then a lot of people got badges for that.
@AsafKaragila, is it possible to talk to you tête-à-tête atm?
okay...thanks @Asaf
@AsafKaragila not bad, I'm still missing 8. Although it's quite unlikely that I'm gonna get any of those... :)
@Daniil Yeah, I have an hour or so.
Why the other room?
It's not like the chat is active here.
Well, I thought we could talk in private.
If it is OK with you
9:43 AM
These rooms are not private, though.
Everyone can join them, and whatnot.
Or at least view the transcript.
Ah, well.
I am sure you are aware of the site Twitter. There is a guy John Cook, he has several interesting accounts on there.
Basically he posts several interesting facts from different areas during the week: johndcook.com/twitter
I saw his name in MSE or MO before, methinks.
I was thought, if you are interesting, about creating a similar account, but with tips and facts about set theory
I can code and host a bot
9:46 AM
Nah. I am not a big fan of these things.
Ok
I often consider starting a blog, but I know that very quickly this is going to be left alone and closed.
@Daniil Thanks for the offer, though. It is somewhat flattering. :-)
:D
10:03 AM
Well, I am going to get ready to the uni, got a long process today... trimming the beard, trimming my nails, etc etc.
Howdy @Srivatsan
10:47 AM
And now to the university.
See you folks later, much much later.

1 hour later…
11:54 AM
Actually, what's wrong with asking 5 questions within 2 hours?
12:06 PM
@Matt and see the comments here and tell me if you still think that there's nothing wrong with it...
Using the site for having ready-made solutions at hand in case he gets stuck... Oh, well, il a du culot...
12:25 PM
@tb One of the 3 up votes on your amusing comment is mine! This guy isn't being told off for asking 5 questions in 2 hours he's told off for posting homework verbatim without even having had a go at it first. No, I don't see anything wrong with even asking 20 questions in 2 hours.
Now he's changed his name. : D
@tb Good job the König isn't here otherwise he might consider giving you a good spanking for using a language other than English. On top of that one that's mouth rape if spoken. : P
@tb How did you find out the source of his exercises? did he mention them somewhere?

1 hour later…
1:48 PM
@magma The user mentioned it in the expanded comments here.
I'm really confused about how my university/library doesn't seem to have full access to everything on SpringerLink. Here I was thinking, for all its faults, at least it should be rich enough to afford some good subscriptions...
@ZhenLin What paper are you looking for?
I was curious about the paper "Scott is not always sober" and wanted to have a look, but it seems the library doesn't have a sufficient subscription.
It's not important.
It's just 2 pages. I can access it. Wonder if there is a way to transmit it =)
2:04 PM
@ZhenLin If you wish to do so, see my profile page to get to my email.
I can send you the paper.
Nah, as I said, I didn't really intend to read it.
Ok, no need to to that then.
Sober spaces - was it some condition about closure of one-point sets?
What is the Jury Duty room for? Is it an affiliate of this chatroom? =)
I can guess what it is for. My main question is the second one.
The intention was that calls for close votes and similar things will not get lost here among other things. But I don't think it really works.
@Martin: A sober space is one which has a unique generic point for each irreducible closed set.
The reason why they are interesting is that everything you could want to know about them is encoded in the lattice of open sets.
2:08 PM
@MartinSleziak Because nobody uses it: and the room was not advertised in chat here (perhaps you could've used the "notice board" to the right for advertisement =)).
I went there just now seeing you and tb visited it recently.
@Srivatsan It was starred here for some time.
@MartinSleziak Oh, I didn't know that. Not sure how I could've missed it =)
I am not sure it's really needed, but since t.b. posted there today, I thought I could try it too.
I like the idea, let's see..
2:14 PM
BTW thanks for the edit of my answer Srivatsan.
No problem.
I've noticed that we have a moderator here in the chatroom - this does not happen too often.
I've seen moderators of other sites in this chatroom!
@MartinSleziak The moderator is fading away... like the Chesire cat.
That's correct. But from Math.SE I thing I've only seen here Willie Wong.
2:18 PM
What exactly is the difference between and ? Or are they synonyms?
I would think that vector-space tag is a subset of linear-algebra. But I did not see it used much.
I feel the same. Perhaps we could just make it direct to linear-algebra as a synonym..?
OK.
Maybe you can ask J.M. about his opinion, when he is around.
2:24 PM
Right, thanks. I posted it in the Jury Duty room. I don't see JM around here these days anyway.

2 hours later…
4:32 PM
actually, not a bad question math.stackexchange.com/questions/98192/…
I think the answer is "no, doesn't exist"
but it's the kind of thing where you might be surprised
5:04 PM
0

An approach that is very effective but not quite elementary is given by nonstandard analysis (NSA). Essentially, epsilontics are delegated to some powerful set-theoretic machinery. There is a post by Terry Tao that explains how NSA does the epsilon management for you: Ultrafilters, nonstandard an...

is that true...?
a sequence is a function N -> R
he's lifting it to nonstandard numbers *N -> *R
I don't really know whether or not you can do that
yeah you can do it
so if x,y : N -> R are sequences and their lifts *x,*y : *N -> *R are real for hyperreal inputs (<=> the "limit" is defined) then *(xy) is real for hyperreal inputs so it's limit is defined?
is that correct? (it's a lot simpler than the answer given)
I guess it could be real but vary, rather than be constant..
so that's wrong
6:03 PM
Do you have any ideas for what other purposes could room like Jury Duty useful. I mean things that are not important enough to be starred (pinned to the noticeboard, so to say), but it would be good to have them separately somewhere, so that they do not get lost between smalltalk and other stuff and where they can be easily noticed at least for a few hours.
The original suggestion was to use it in connection with closing questions and similar things. (But we usually have enough jurors in the main chat very quickly.)
Maybe something like comments about tags, e.g. like the Srivatsan's comment? (Perhaps with link to the discussion in the main chat, if there was a discussion about it.)
Sorry to interrupt the NSA stuff, I just thought it would be useful to post something like this. Just wanted to make more people notice that room. (We should either start to really use it, or abandon it.)
6:34 PM
HAHA, the wifi at my institute connects finally to Math.SE
This question has a very nice kind of symmetry at the moment: 3 upvotes, 3 downvotes, 3 close votes.
@Martin A +1 suddenly come now?
Hm, symmetry has ben broken...
6:49 PM
or a counter
@Martin, I would say so, look at this answer: math.stackexchange.com/a/37156/21436
Here Didier explains this!
@AndreasSpÃ¶rl It could only be nicer if, in addition, it would have been 33333rd question.
0

Definition of Uniform Continuity A function $f$ is said to be uniformly continuous if to each $\epsilon >0$, $\exists~\delta >0$ such that whenever $|x-y|<\delta$, $|f(x)-f(y)|<\epsilon$. The following is just an "uninformed" intuition: If your function will have arbitrary lon...

Can any of you go over this answer and leave comments for me?
@KannappanSampath Well, it's not entirely clear whether in the newer question asks for intuition (in that case I would definitely say duplicate), or the OP just want to see how Jacobian is computed in this specific case. To be sure, I've asked here, instead of voting to close as duplicate right away.
7:37 PM
@KannappanSampath I strongly object to this kind of rude and non-constructive criticism. To be blunt, I find your comment obnoxious. Of course, there's always room for improvement but if you don't have any helpful thing to say please keep silent.
@tb I am sorry, if I was rude.
But, yours sincerely, I don't understand what the OP wants to say at all!
Isn't he just saying it's hard to read because of bad grammar?
7:52 PM
Yes, it is a bit hard to tell what exactly the question is, but obviously the OP invested quite a bit of effort to get his point across (and he may have failed badly). But just telling him that he should try to improve his grammar and write more clearly without pointing out what is unclear and where you have trouble following is not constructive or helpful at all.
@tb Yes I agree
What's up you guys?
I cannot edit it now!
hi
@KannappanSampath There is a little cross for deleting comment.
7:54 PM
And there is a larger cross for Jesus Christ.
@MartinSleziak Haha, it's gone now! Thank You, I have lost touch with site, Thanks to my institute
@AsafKaragila You are Humorous!
I try :P
I can't wait for the next semester. I won't have to teach the day after refill night! :-D
8:14 PM
Interesting I'm getting close to 200 points.
no, not interesting
wrong
question is good, vote up
I have a wee question that I wasn't sure should be on the board; more a chat question.
hello
And it's this: I want to know what experience folks here have with nootropics.
8:23 PM
noo...was?
lol
nootropics are what you might call memory enhancers, cognitive-ability enhancers, e.g. caffeine, &c.
ooh I have been missing a question on math and drugs
Smart drugs?
yes, smart drugs.
Euler used some heavy stuff I believe
8:25 PM
Oh really?
no sry erdos
I've been curious about them. I figure who better to ask than you all.
I have no personal experience with them, besides caffeine. I'm sure we all know a lot of people who use Adderall, but I can't vouch for it.
I'd also be interested in hearing from anyone about things you believe help your cognitive abilities, whether it's coffee or cheese, or some habit, whatever it is.
I believe in hard work
As I. And I'm not advocating otherwise :)
especially the blog posts
8:33 PM
Up until a few weeks ago, I didn't even drink coffee. It would give me a rush for 20 minutes, then headaches the rest of the day, muddy thinking, and so on. My wife bought some fresh stuff, and I had some: it made me sharp for around 8 hours afterward. I had such clarity. I even began studying again. This last week, I've been studying around 8 or 10 hours a day.
what fresh stuff?
So, we ran out of coffee a few days ago. We bought some, the same brand. Nothing. No effect. I'm so sleepy, my thinking is muddy again. It's terrible. I can't concentrate. I can't hold shapes and numbers in my head.
Fresh stuff I mean..another can :)
this is the reason I don't want to rely on chemicals - you become resistant to them
We all rely on chemicals.
what is the term for this thing I have in mind..
like artificial tablets, synthetic or extract etc.
8:37 PM
But I understand your point. However, last week was fantastic. I haven't had that clarity for years probably. If a cup of coffee is all I need to get that, then where's the harm?
But anyway, my point wasn't to talk about coffee. I wanted to find out if anyone has had a similar experience with anything other than caffeine.
I wanted to know if there was any credibility in the claims of other foods, and so on.
@qed yes, I'm reading it and switching back and forth to here.
@QED this is a good link, thanks.
it seems like grasping at straws to me though
What do you mean?
just this whole western idea of natural genius and stuff
people just want everything to fall into place magically and I don't think that's realistic
8:48 PM
I think it depends on how you look at it. If you're looking for cure-all, you're not going to find it. If you're looking for a drug to make everything easy with no drawbacks, that's not going to happen.
yeah, exactly
But then there's caffeine. You may be capable of more, but most days you're running at 70%. Caffeine just stimulates you enough to allow you to perform as well as you are naturally able.
It's not making you any smarter than that.
And sometimes, that can be very valuable.
How did you get on with your analysis stuff
You asked some very good fundamental questions
thanks :) (couldn't have asked them without caffeine :P)
haha
8:53 PM
You know, I'm so grateful this site exists. I don't know of anywhere else I can go and ask, what seem to me to be sensible, common sense questions.
So yes, it went very well. I filled in some important holes in my understanding.
Though I still have a long way to go.
That question I asked about functions being equal and yet not was the hottest question on the whole of stackexchange O_O
@Martin Any progress?
I was surprised.
@AsafKaragila With regard to $C(X)$? I did not have a look at it at all :-(
It would be nice to spent my life hanging around MSE (and few other sites I frequent). Unfortunately, there are things I have to do in real life, too.
But I guess instead of chatting here today I could have had look at that problem.
8:58 PM
I hope wont waste too much time with that "real life" thing
Real life is overrated.
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