Recent content by A-ManESL

Hello all... I have a problem which I have been grappling with for some time. Let b be a positive integer and consider the equation z = x + y + b where x,y,z are variables. Suppose the integers {1,2,...4b+5} are partitioned in two classes. I wish to show that at least one of the classes contains...

I am having trouble establishing the divergence. Can you be more explicit? Thanks.

I want an example of a complex sequence (x_n) which converges to 0 but is not in ℓ^p, for p\ge 1 i.e. the series \sum |x_n|^p is never convergent for any p\ge 1. Can someone provide an example please?

Where can I get a very basic introduction to the current research directions in functional analysis? I have done a basic course in it. Also I am interested in knowing about applications of Ramsey theory to functional analysis. Thanks.

Can you please me more explicit? All I can think of is that for large x, f(x) will be close to 1.

Yes I meant f:[0,\infty)\rightarrow \mathbb{R}. Sorry for the mistake. Obviously [0,\infty) is not compact and so the above stated result doesn't apply.

Suppose f:[0,\infty]\rightarrow \mathbb{R} is a continuous function such that \lim_{x\rightarrow \infty} f(x)=1. I want to show that f is uniformly continuous. Thanks.

Hello PF members This is my first post. It is rather complicated to understand but I request you to bear with me. The Problem: I have a theorem in my book, the proof of which I do not understand fully. The theorem may be viewed...