What is the relationship between span and dimension?

[safi]

Homework Statement

Hi, I have to prove that there's no exist a generating set for "x" with less of "n" vectors when "n" is the dimension of the basis of "x"

Homework Equations

is there a span(x) whith dimension m? when m<n and n is the dimension of the basis

The Attempt at a Solution

I know that all the basis of a vectorial space must have the same dimension, and the basis have linearly independient vectors, so I can't remove any of them, but I don't know how sow that its not possible that existence of that span

 

[BruceW]

to start this proof, I think you need to start with a mathematical definition of what a basis actually is.