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High Quality Content by WIKIPEDIA articles! In mathematical analysis, the Weierstrass approximation theorem states that every continuous function defined on an interval can be uniformly approximated as closely as desired by a polynomial function. Because polynomials are the simplest functions, and computers can directly evaluate polynomials, this theorem has both practical and theoretical relevance, especially in polynomial interpolation. The original version of this result was established by Karl Weierstrass in 1885.