> [!NOTE] Definition > Let $S\subset \mathbb{R}^{n}$ be a [[Subsets|subset]] of a [[Real n-Space|real n-space]]. Then $S$ is a basis of $\mathbb{R}^{n}$ iff $S$ is [[Linearly Independent Subset of Real n-Space|linearly independent]] and is a [[Spanning Set of Real n-Space|spanning set]] of $\mathbb{R}^{n}.$ # Properties By [[Basis of Real n-Space has n Elements]], $S$ is finite with $|S|=n.$