Recent content by jecharla

Nevermind I figured it out!

Rudin motivates this formula by multiplying two power series and then setting z = 1 and somehow obtaining the cauchy product formula. But I am not following how he does this at all. Can anyone help me understand this?

I have a question about the last inequality Rudin uses in his proof of this theorem. Given that |z| < 1 he gets the inequality |(1-z^(m+1)) / (1-z)| <= 2 / (1-z) I think he is using the fact that |z| = 1, so |(1-z^(m+1)) / (1-z)| <= (1 + |z^(m+1)|) / |1-z| So i am guessing that...

Theorem 3.23 is a very simple one: it says that if a series converges then the limit of the terms of the sequence is zero. However Rudin's way of justifying this fact doesn't seem valid to me. He uses the following logic: A series converges if and only if the sequence of partial sums is...

As of yet I have not been able to get through theorem 3.20. But I am just going to stare at it for longer :) Can't expect them all to be easy.

I have been teaching myself analysis with baby rudin. I have just started chapter three in the past week or so and one thing I am having trouble with is the proofs which use the binomial theorem and various identities derived from it. Rudin pretty much assumes this material as prerequisite and...

Integral, I think you are right that I need to spend more time staring at this proof(which I have been doing for quite a while now). I have no problem understanding this proof in that I can follow the algebra. However I don't understand how one could come up with this proof from scratch...

Part (b) of theorem 3.20 is to prove that the limit as n approaches infinity of the nth root of p equals one(for p>0). The proof given in the text uses some inequality derived from the binomial theorem which seems to me to just come out of nowhere and provide a completely unintuitive proof...

Exercise #17 in Linear Algebra done right is to prove that the dimension of the direct sum of subspaces of V is equal to the sum of the dimensions of the individual subspaces. I have been trying to figure this out for a few days now and I'm really stuck. Here's what I have got so far: Choose...

Thanks guys!

A set S is perfect if S is closed and if every point of S is a limit point of S.

1st part of Exercise #27 is: Define a point p in a metric space X to be a condensation point of a set E in X if every neighborhood of p contains uncountably many points of E. Suppose E is in R^k, E is uncountable and let P be the set of all condensation points of E. Prove P is perfect...

Theorem 2.36 says that given a collection of compact subsets of a metric space X such that the intersection of every finite subcollection is nonempty, then the intersection of the entire collection is nonempty. The proof is very simple and I easily follow the abstract reasoning. However, I think...

so are you agreeing or disagreeing with me that the n is unnecessary and can be dropped?

In Rudin's Principles of Mathematical Analysis, exercise number two is to prove that the set of all algebraic numbers is countable. A complex number z is said to be algebraic if there are integers a_0, ..., a_n, not all zero such that a_0*z^n + a_1*z^(n-1) + ... + a_(n-1)*z + a_n = 0 The...