In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> Absolutely quite. Of course AC is true and every vector space has a > basis. Alas there is nothing uncountable.
The standard definition of a basis for a vector space requires that (1) the vectors of the basis must be linearly independent and (2) every vector in the space must be a linear combination of finitely many basis vectors.
But there are vector spaces, at least outside of Wolkenmuekenheim, which do not have any basis of that form. --