Recent content by AnthonyAcc

Let B={s|s is a function mapping the set of natural numbers to {0,1}}. Is B a countable set-that is, is it possible to find a function \Phi() mapping the set of natural numbers onto B-? I know that it has to do with infinite binary sequences, but the countability part confuses me. Can...

A more fundamental question I have, I guess, is if I know that \sum^{\infty}_{\nu=0} (^{n}_{\nu}) a^{\nu} b^{n-\nu} = (a+b)^{n} then do I know that \sum^{n}_{\nu=0} (^{n}_{n-\nu}) a^{\nu} b^{n-\nu} = (a+b)^{n}? How does the changing of infinity to n and the \nu to n - \nu impact the series?

Does this \sum^{\infty}_{\nu=0} (^{n}_{\nu}) imply \sum^{n}_{\nu=0} (^{n}_{\nu}) because it's for every n choose \nu so there can only be n many \nus?

Show that (^{n}_{n}) - (^{n}_{n-1}) + (^{n}_{n-2}) - (^{n}_{n-3}) + ...(^{n}_{0}) = 0 (a+b)^{n} = \sum^{\infty}_{\nu=0} (^{n}_{\nu})a^{\nu}b^{n-\nu}a=1 b=-1 0 = (1+(-1))^{n} = \sum^{\infty}_{\nu=0}(^{n}_{\nu}) 1^{\nu}(-1)^{n-\nu} = \sum^{\infty}_{\nu=0}(^{n}_{\nu})(-1)^{n-\nu} = ...I don't...

I'm taking an introductory class on analysis right now and I'm trying to get through the book that we are reading. I'm having difficulty understanding a park of it and was hoping someone could help me out. The part I'm reading about now is on null sequences: Here's an excerpt. I'm having...