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Line 1: − The Bolzano-Weierstrass theorem is a statement about the convergence of sequences, and is a basic theorem of [[real analysis]] in [[mathematics]]. + − + + +
Bolzano-Weierstrass theorem (view source)
Revision as of 03:08, November 7, 2009
, 03:08, November 7, 2009Put in stuff about accumulation points. I hope I haven't messed up the economics stuff, but it doesn't seem very clear, either before or after. Can someone tell us just what the theorem says about e
{{Template:Math-h}}
The Bolzano-Weierstrass theorem holds that if a sequence of real numbers is finite with endpoints, then it must have a subsequence that converges. The theorem holds that an equilibrium exists in the form of a convergent subsequence. The proof of the existence of such an equilibrium has become useful to [[economics]].
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.
[[Category:mathematics]]
[[Category:mathematics]]
[[Category:economics]]
[[Category:economics]]