## Blog posts from 2012

## The Axiom of Choice and Self-Dual Vector Spaces

Oct 28 2012, 01:28

I have uploaded a note titled The Axiom of Choice and Self-Duality of Vector Spaces. Here is a short summary and background.

It is a well known fact (in \(\ZFC\) at least) that if \(V\) is a vector space, and \(V^\ast\) is the algebraic dual of \(V\) then \(V\cong V^{\ast\ast}\) if and only if \(\dim V<\infty\).

Continue reading...## First Post

Oct 19 2012, 05:46

Well... This is my first post on this blog, and I have absolutely no idea how to start it.

Should I make it about myself? about my life? about my academic status? How I about I tell cool stories from my life, perhaps inebriated adventures? army experiences? Maybe I should write about mathematics. Perhaps some nice proof or some nice theorem?

Continue reading...