Assuming you do not reject the axiom of choice, every vector space has a basis.

Is the fact that any infinite dimensional vector space has a basis useful in any important result or theorem?

Question

Assuming you do not reject the axiom of choice, every vector space has a basis.

Is the fact that any infinite dimensional vector space has a basis useful in any important result or theorem?

anonymous · Answer

LOL...

..and then u want to prove that a result does NOT depend on a choice of basis.The use of a basis for a vector space should be avoided where possible (IMHO).

I have an idea where to look for an answer to the second question but I don't think that this is a very good way to validate AC.

anonymous · Answer

So you will reject a proof simply because it is nonconstructive?

anonymous · Answer

Not necessarily, depends on what kind of proof it is..

Let's say I prefer constructive proofs because I think u can, in general, learn more from them...

anonymous · Answer

This is really more a question of philosophy than anything else, a strict constructivist would reject...

For myself I have more in common with the constructivists than the ZFCers

anonymous · Answer

Found it finally... http://cs.nyu.edu/pipermail/fom/2003-June/006890.html