Try this link: http://ocw.mit.edu/OcwWeb/Mathematics/18-06Spring-2005/CourseHome/index.htm
#3
neiraj
2
0
thanks
thanks dude but do u know any other than this
#4
Siress
7
0
That's great! Thank you.
I'm in the course now but it's incredibly boring and doesn't deal with the theory, dimensional process, of what we're doing. This is an eye opener from what we've been doing the past two weeks.
Seeing that this video is nearly a decade out of date and that some of the terminology is different from what I'm learning.
It is well known that a vector space always admits an algebraic (Hamel) basis. This is a theorem that follows from Zorn's lemma based on the Axiom of Choice (AC).
Now consider any specific instance of vector space. Since the AC axiom may or may not be included in the underlying set theory, might there be examples of vector spaces in which an Hamel basis actually doesn't exist ?