Alright, so in fact my proposed solution was correct, except for the fact that I wrote down the pythagoras theorem as C² = sqrt(A² + B²) for some reason. That sqrt shouldn't be there!
> Ribenboim says "The method of proof is interesting, in that the inequality is shown first under the assumption that the Riemann hypothesis is true, secondly under the contrary assumption
Do any of you veterans here know of a question on the main site about programs that work out nonlinear differential equations numerically (or perhaps know yourselves)? I wouldn't want to clog the site with a duplicate question.
No I don't, but I'd be happy to learn. I happen to have mathematica (from a friend); is that better than 'traditional' programming platforms like C++ for differential equations' modelling (I'm as inept in all fields of programming at the moment, so could learn either)?
@Alyosha I also use Mathematica and I have never been able to get mathematica to efficiently produce numerical solutions to nonlinear PDE's. If you are talking about ODE's then Mathematica is actually a fairly good solver.
I don't really know any programming either, but I found that FreeFem++/C++ was remarkably easy to learn and implement.
"It is also typical to use Cauchy's Theorem to prove the first of Sylow's Theorems, though this is not required."
"Cauchy's theorem is a theorem in the mathematics of group theory, named after Augustin Louis Cauchy. It states that if G is a finite group and p is a prime number dividing the order of G (the number of elements in G), then G contains an element of order p."
@Theorem H/N doesn't make sense if N is not fully contained in H
@PeterTamaroff There is in fact a proof of Sylow I using only group actions and arithmetic information (ie a finite group's order). I like it much more than something based upon induction.
@anon If two Dirichlet series' $f(s)$ and $g(s)$ converge conditionally for s>1, and $$f(s)/g(s)$$ can be bounded between two constants , can I conclude that $$\lim_{s\to 1}\frac{f(s)}{g(s)}$$ exists?
