# Cardinality of Generator of Vector Space

 It has been suggested that this page or section be merged into Cardinality of Generator is not Less than Dimension. (Discuss)

## Theorem

Let $E$ be a vector space of $n$ dimensions.

Let $G$ be a generator for $E$.

Then:

$G$ has at least $n$ elements.

## Proof

From Generator of Vector Space Contains Basis there exists a basis $B$ of $E$ such that $B \subseteq G$.

From Cardinality of Basis of Vector Space, $\card B = n$.

The result follows.

$\blacksquare$