Recent content by Treadstone 71

Both can be done easily by contradiction.

Thanks for the suggestions. I've discovered a book called "Prime Numbers: The Most Mysterious Figures in Math" which I really like. It may sound like a popularized math book, but it's actually like "Unsolved Problems in Number Theory" by Guy, though it lists topics that are solved and unsolved...

I'm looking for a book that will do a thorough exposition of everything we know about the distribution of primes. Can anyone recommend one?

If a,...,d are functions and a~b, c~d, can I conclude that a-c~b-d?

Any jobs at NASA for mathematicians?

How do you know metaphysics exists?

Sorry about digging up an old thread, but I've never encountered such notation before. Is this an older notation? I'm not in physics so I don't understand the explanation given above.

There's a copy at my university, so I picked it up and read parts of it. It is a horrible, horrible mess.

I was just about to post that I got it. T(0) is not used it my proof. Thanks anyway.

Here's a simple question that I can't seem to get: "Suppose for some v T^{m-1}v\neq 0 and T^mv=0. Prove that (v,Tv,...,T^{m-1}v) is linearly independent." I know that m\leq \dim V and v,Tv,...,T^{m-1}v are all nonzero.

Differentiation and intergration is pretty much the whole of calculus.

Yes, I did the first question. I've got an idea about the second one that doesn't involve Jordan forms, but I'm still working on it.

How do I show that R is commutative <=> the minimal and characteristic polynomials of T are the same? (T might not be diagonalizable)

If e is an eigenvalue of T, then e-k is an eigenvalue of T+kI.

Well I gave what I have here. I think it would work out if we replaced d with d_i = \dim null (T-\lambda_i I)^{dim V}.