# Bolzano-Weierstrass theorem

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 $\frac{d}{dx} \sin x=?\,$ This article/section deals with mathematical concepts appropriate for a student in late high school or early university.

The Bolzano-Weierstrass theorem is an extremely important theorem of real analysis in mathematics. It states that any infinite, bounded set of real numbers has an accumulation point. Equivalently, it states that any bounded infinite sequence of real numbers has a subsequence that converges.

The theorem has useful applications to economics. It asserts the existence of an equilibrium in certain economic problems.