> [!NOTE] Definiton (Finite Dimensional Real Vector Space) > Let $V$ be a [[Real Vector Space|real vector space]]. Then $V$ is finite dimensional iff and only there exists $S$ [[Finite Set|finite]] [[Subsets|subset]] of $V$ such that $S$ is a [[Spanning Set of Real Vector Space|spanning set]] of $V$: that is, its [[Span of Subset of Real Vector Space|span]] is given $\langle S\rangle=V.$