Cardinality of Generator of Vector Space

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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.

$\blacksquare$


Sources