Solution
= Solution
The <Chebyshev alternation theorem> says that a <polynomial> $p$ of degree at most $n$ is a <best uniform approximation> to a real <continuous function> $f$ on a <compact> interval if and only if there are $n+2$ ordered points at which $f-p$ attains its <uniform norm> with alternating signs. For nonzero error these are equal-magnitude alternating extrema; the zero-error case is understood separately. The best approximating <polynomial> is unique.