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If $B$ is a finite set of orthonormal vectors, then every vector in the span of $B$ can be written as a linear combination of vectors in $B$. |
Suppose $f$ is a continuous function defined on a compact set $S$. For every $\epsilon > 0$, there exists a polynomial p such that for all $x \in S$, we have $|f(x) - p(x)| < \epsilon$. |