@N3buchadnezzar Inverse trigonometric functions always trip me up. I looked for a solution to sin x = 1/2 in the first quadrant (so x is between 0 and pi/2) and got x = pi/6 (a 30-60-90 triangle)

And going to the left you find x = -7pi/6.

Now you just shift that around by 2pi.

Indeed

(I drew the graph. For shame.)

Probably one should be able to look at arcsin, find pi/6, then use the symmetries of sin x.

@AsafKaragila Congratulations too, on your Magidor win. I deleted the comment. Now going to read your new answer.

I noticed that rooms get frozen and can no longer be used if left unused for more than 14 days. A bit inconvenient as otherwise one could collect same topic questions in same rooms.

@Matt See you in an hour when you're done ;-)

@AsafKaragila Don't be too optimistic. : )

@AsafKaragila How's your gf btw, I heard she fainted?

@Matt She's okay now.

@AsafKaragila I'll feel free to correct typos, ok?

Sure.

Writing such a long answer there are bound to be infinitely many of them :-)

@Ilya Congratulations for your presentation! Hope you can have some rest now.

@tb Thanks!

@AsafKaragila Point 2 is a complicated way of saying that aleph zero is the number of elements in a countably infinite set?

@Matt Not just that, but also that it is "the smallest infinity" while $\infty$ can be reached via several ways.

Yes. Hm...

@tb Well... As you write it is just... well uh. Trivial?

I wouldn't say it's a trivial result, but after someone wrote this I'm not particularly inclined to elaborate.

Yes, but if you can understand that previous question and have seen the answer, one should be able to solve this one?

Agreed. That's why I voted to close as a duplicate....

Finished it :-).

Okay, the guy that wrote me an e-mail about my estimate has now given me the full argument. My advisor and I couldn't see it and it is very simple :').

He is 32 and I think that he is way better than all the other analysts I have ever met irl. Quite... frustrating if you try to solve something for a week and someone solves it in a few minutes 8-).

Don't give up. You've still got us.

Give up.

@Matt Did you finish reading? ;-)

@JonasTeuwen Don't feel bad. "Even" your supervisor didn't see it.

@AsafKaragila Your answer, yes. Now I'm reading the things you linked to. : )

@Matt Cool. Let me know what you were thinking about it when you're done.

@Matt Yes :-).

I am tired.

Man who runs infront of car gets tired.

Man who run behind car gets exhausted.

@AsafKaragila I particularly liked that you linked to other "Reading material".

Well, I felt that this question was answered in parts on other links, and I also referred to the construction of alephs and whatnot...

@AsafKaragila I meant with "don't give up" his life. Surely he can give up the exam.

@JonasTeuwen I meant with "give up" that he should embrace extreme fatalism laced with nihilism. Simply let go and give up all hope.

That will work.

I sure hope so.

Can I confirm this with you: if I want to compute the dual of a vector space, I can't always do the same trick of taking an element in the space and defining an isomorphism (from the space into its dual) in the form of an inner product?

I'm not sure this is useful anyway because to do this I already need to know what the dual is isomorphic to.

This works for inner product spaces by the Riesz representation theorem. However, you don't have a natural map from $X$ to $X^\ast$ in general.

Inner product space = Hilbert space?

Yes. A bit more generally, you can do this with a non-degenerate bilinear form on $X$.

I guess does the inner product space need to be complete

Yes, of course.

I'm not quite sure what category we're talking about here.

@Matt Duals can be quite hard to find :(.

@tb What do you mean by category?

@JonasTeuwen I was actually hoping to get some intuition for it.

@Matt Down to earth answer: What kind of vector spaces? Highbrow answer: Categories (Mathematics)

But I assume you're thinking of functional analysis, no?

Yes.

@tb Are you sometimes giving a course in FA there? :-)

where?

ETH

Well, I gave one on harmonic analysis about a year and a half ago.

When you say harmonic analysis...

Representation theory of locally compact groups, e.g. Fourier theory and Pontryagin duality.

@tb You'd rather not have the link to the VVZ posted here, right?

@tb Gelfand transform and stuff?

@Matt It doesn't say much about the contents anyway, as far as I remember.

@AsafKaragila Yes, I mentioned that, of course.

VVZ? Vuvuzela?

@AsafKaragila Yes, exactly.

@tb I see. I learned all that in the course about representation theory two years ago. It was interesting.

All that? :)

And more.

The first third of the course was about finite dimensional representations and finite groups and whatnot.

chuckpalahniuk.net/features/shorts/guts

Thanks, @tb

@Matt As Jonas said, duals are often hard to identify explicitly. Try to understand the Riesz representation theorem thoroughly first, then turn to the duality between $L^p$ and $L^q$. Then you have the Riesz-Markov theorem identifying the dual space of $C(K)$, for example.

Two threads awaiting closure here and here

Thank you.

@tb That is not what I call harmonic analysis :-).

Can one usually pay with Mastercard in the US?

Why not? It's called a **master**card for a reason.

Because I've checked out a hotel and they say one can pay with Visa and American Express.

Find a better hotel.

Sleep on the street/take so much speed that you don't need a hotel.

This already has **** :(.

Yeah, but the streets of NYC at night... How are those?

Is there not a big park in NYC?

Problem solved

boom!

@JonasTeuwen If they don't mention master card then they probably don't accept it but you could send them an email and check. Only costs you a minute.

True, but I want to know if this is common in the US otherwise I need a Visa card.

True. Because if you change your Euros into dollars they might not be worth anything anymore by the time your plane lands.

:D.

Blue Stilton is one fine cheese.

My girlfriend complains about the smell of that cheese (and my breath after I ate it) :(.

I have a cool reputation now. 19191

@JonasTeuwen No wonder : D

Let me ruin that.

Beat me to it : D

Oh well. I guess it would have happen sooner or later ;-)

We had a question about that group representation on the final today.

@tb Now that was quite a surprise.

@TheChaz No, that's not what I meant.

This is the equivalent of asking a question about a multiset of statistical data and tag it under descriptive-set-theory ;-)

Woot. I broke the 200 already today! I can take 2-3 more upvotes and I will really cap out.

First Blue Stilton, then Laphroaigh Quarter Cask. Ahh, life is good 8-).

Jerk.

Earlier this evening I had the wine @Matt recommended. I was not really impressed but it was okay. I drank it together with some nice pasta.

@JonasTeuwen Sorry to hear that! I quite like it. But then again you should've known better: I told you I knew nothing about wine : P

Well, it was okay. I'm not disappointed that I bought it 8-).

phew

I was going to read something but it looks as if that's not going to happen today. So I guess that means it's bed time.

You're a quiet bunch today, anyway.

@Matt Well now is too late to start reading me thinks 8-).

I am trying to prove that there is always a dense chain in $P(X)$

@JonasTeuwen And in the morning it's too early...

Exactly.

So you're like me? Idle time most of the day?

Idling most of the day is what gets the job done!

Time to go to bed I think. Good night folks, sleep well!

How do you guys figure out how much time to spend doing mathematics?

@Matt Yes I am.

@Matt Good night.

@N3buchadnezzar I don't I just do it when I feel like it 8-).

Luckily I often feel like it.

What if you awlays feel like doing it 8-)

But you know you will not accomplish much by doingso much math, because you are far from being a genious.

@N3buchadnezzar I never really stop.

Wooo, one more vote and I'm capping out for the day! :-)

What is a genious?

a misspelling =)

Good night guys.

Goodnight jerk.

Thanks.

@JonasTeuwen Hello

I understand analysis is your field of speciality

do you have a copy of baby rudin with you?

maybe you understand probabilities too? :D

I am also going to sleep. I was tired 3 hours ago.