Difference between revisions of "Bolzano-Weierstrass theorem"
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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 '''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. | ||
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The theorem has useful applications to [[economics]]. It asserts the existence of an equilibrium in certain economic problems. | The theorem has useful applications to [[economics]]. It asserts the existence of an equilibrium in certain economic problems. | ||
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Revision as of 20:00, September 17, 2011
| <math>\frac{d}{dx} \sin x=?\,</math> | This article/section deals with mathematical concepts appropriate for late high school or early college. |
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.