Weierstrass theorem

For any continuous real-valued function $f( x)$ on the interval $[ a, b]$ there exists a sequence of algebraic polynomials $P _ {0} ( x), P _ {1} ( x), \dots$ which converges uniformly on $[ a, b]$ to the function $f( x)$; established by K. Weierstrass . For generalizations, see Stone–Weierstrass theorem.

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Author of the notes: Antonio J. Pan-Collantes

antonio.pan@uca.es