Recent content by Robert1986

Well, I can list some topics, but other people will have more to say (the following is in roughly order of importance with the most important at the top; but lots of people will probably disagree and I might agree with their disagreements once I see them): complex analysis more analysis an...

Not knowing anything about you personally, I would assume this would be very difficult. I would imagine most grad complex analysis classed already assume you know a lot of stuff (like what is an analytic function, Cauchy's theorems, maximum modulus stuff, etc) and these topics are quickly...

We all know the the epsilon delta definition of a limit of a sequence. But, if I give you a sequence, to use this definition to determine if the sequence converges, you have to know (or have a good guess) about what the limit is converging to. If this is a sequene of numbers, it might not be so...

If you want a series that converges to c, take a series that converges to b, and add this term: (c-b) to the front.

Are you sure the matrix is real? Usually if the matrix is real, people say "Orthogonal" instead of "Unitary" and instead of using a star, they use either a T or a dagger (T is to denote transpose.) Does the paper explicitly say that the matrix is real?

I don't understand why you would want to publish your problem so that other people can solve it? You came up with the problem; don't let someone else solve your problem for you. Publishing a conjecture in some kind of journal might be nice, but working hard to solve it and then publishing the...

Well, you could define a group that way, but at some point, you'll have to show that this definition of group and the "normal" definition are the same. And then there's all the stuff that Office_Shredder said. I'm not very experienced with category theory, but it seems that one of the best uses...

Well, I was just pointing out that uniform convergence is still important when it comes to lebesgue integral, even though you are certainly correct that uniform convergence doesn't play nearly the same role in lebesgue integration as in riemann.

I don't think this is quite true. For example, Egorov's Theorem is a theorem about uniform convergence. Most of the time, though, this is used on a compact set, and as long as the functions are also riemann integrable, we can just use riemann integrals, but this isn't always the case and can be...

I'm not sure this is correct. For example, functions can converge in L2-norm without converging uniformly. Indeed, functions can converge in L2-norm without even converging ae. True, but so what? This is not relevant in this case. This is true, but you don't need hypotheses this strong...

As a side question, what the heck is a "frontier" of a set? This looks equivalent to the definition of boundary. Is this just another word for boundary? If so, why? That is, why have a new word?

It means that p divides the numerator of the fraction but not the denominator. So, p divides the fraction.

I am assuming p is prime. Do you agree that p divides p! and that p does not divide k! and that p does not divide (p-k)! ? If so, then p must divide p choose k since there are no factors of p in the denominator that would "cancel" the p in the numerator. As a side note, I would suggest not...

Yes, m and n must both be integers. Otherwise, as you pointed out, the two functions are not orthogonal. So, not only must m and n but integer differences of each other, they must both be integers.

If I understand correctly, the pumping lemma gives you a number, p, such that a bunch of stuff happens. Can you reference the exact pumping lemma you are talking about?