Dimension of Free Vector Space on Set

Theorem
Let $k$ be a division ring.

Let $X$ be a set.

Let $k^{\paren X}$ be the free vector space on $X$.

The vector space $k^{\paren X}$ has dimension the cardinality of $X$.

Proof
Follows from:
 * Canonical Basis of Free Module on Set is Basis
 * Cardinality of Canonical Basis of Free Module on Set