Bolzano-Weierstrass theorem

From Conservapedia
This is the current revision of Bolzano-Weierstrass theorem as edited by Aschlafly (Talk | contribs) at 16:00, 17 September 2011. This URL is a permanent link to this version of this page.

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search
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.