Re: Base of a vector space

On Jun 20, 9:39 am, A N Niel <ann...@xxxxxxxxxxxxxxxxxxxxx> wrote:
In article <485baa64$0$7989$426a3...@xxxxxxxxxxxx>, Fatal





<fa...@xxxxxxxx> wrote:
Saysero a écrit :
On 2008-06-20, José Carlos Santos <jcsan...@xxxxxxxx> wrote:
On 20-06-2008 12:25, Saysero Shyoph wrote:

How to prove that every vector space has a base?
In general or just for finitely generated ones?

In general.

Use Axiom of Choice, e.g. via Zorn's lemma:
the set of free families of a (non-zero) vector space, ordered by the
relation "is a sub-family of", is an inductive set (every totally
rodered subset has a majorant) so, by Zorn's lemma, there exists à
maximal free family. It is then easy to verify that such a family is a
basis.

"free" also called "linearly independent"- Hide quoted text -

A useful comment, IMHO.

Is this word undergoing a vogue? I see many more "free" this and
"free" that than I remember from, say, a decade ago.

.