Weierstrass Approximation Theorem

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Theorem

Let $f$ be a real function which is continuous on the closed interval $\Bbb I$.

Then $f$ can be uniformly approximated on $\Bbb I$ by a polynomial function to any given degree of accuracy.


Proof


Also known as

This result is also seen referred to as Weierstrass's theorem, but as there are a number of results bearing Karl Weierstrass's name, it makes sense to be more specific.


Source of Name

This entry was named for Karl Weierstrass.


Historical Note

The Weierstrass Approximation Theorem has been demonstrated to have far-reaching and important effects in every aspect of the field of analysis.

It has also been given a significant generalisation by Marshall Harvey Stone.


Sources