Recent content by Guffel

If you haven't done so, take a look at this page. Among other things that might interest you, a generating function is provided there. EDIT: Considering the thread title is an exact copy of the title of the series in the link, I guess you have seen it. Dig deeper and you'll find a g.f. :)

A set whose sum of the reciprocals diverges is said to be a large set. Similarly, if the sum of the reciprocals converges, the set is said to be a small set. The natural numbers thus make up a large set, while the set of squares is a small set. There is a famous conjecture which is still...

Check out this post.

Ah, thanks micromass!

But doesn't the equivalence to the identity theorem on real functions hold?

A quick question, which I think is related enough not to be off topic: On the wikipedia page on the identity theorem, it is stated that "Thus a holomorphic function is completely determined by its values on a (possibly quite small) neighborhood in D. This is not true for real-differentiable...

http://en.wikipedia.org/wiki/Percolation_theory"

Since no one has answered yet, I'll give it a go. Starting from the triangle inequality, we get |a+b| <= |a| + |b| => |a+b|^2 <= (|a| + |b|)^2 = |a|^2 + |b|^2 + 2|a||b| => |(a+b)/2|^2 <= |a|^2 / 4 + |b|^2 / 4 + |a||b| / 2If we can prove that |a|^2 + |b|^2 >= |a|^2 / 4 + |b|^2 / 4 +...

I think you are right if you are considering a hollow cone. I was assuming the OP asked about a solid cone, but of course I might be wrong. For me, it is not very intuitive that the cross-sectional triangle trick will work if a hollow cone is considered. How did you come to that conclusion?

phinds, could you elaborate on your method of using only the Pythagorean theorem? I'm not getting it.

Not really answering your question, but a generating function should not be very hard to find. Also, check out http://www.btinternet.com/~se16/js/partitionstest.htm if you haven't done that already.

Thanks guys (Dodo in particular) for the very nice introductions to abstract algebraic structures! I think many books on the subject would be significantly improved by including any or all of the above texts.

First, the Dirac pulse is the derivative of the Heaviside step function, which is not exactly the same as the standard definition of the sign function. The Dirac delta function actually IS infinity at x = 0 and not 1. However, the integral of the Dirac delta function on an interval containing...

The Lambert function needs to be used to express the non-trivial solutions. http://www.wolframalpha.com/input/?i=solve+T+%3D+Q+%2B+2%5E%28Q-2%29+for+Q

I think he's investigating the n for which 2n+1 (or 2n-1, this is unclear to me) is prime. It's not very clear, but he seems to suggest that he's found a pattern in the behaviour of n. From what I'm able to decode, he hasn't presented any results yet.