# Weierstrass Approximation Theorem

## 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.

## 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.