Bolzano–Weierstrass theorem
Bounded sequence in finite-dimensional Euclidean space has a convergent subsequence / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Bolzano%E2%80%93Weierstrass theorem?
Summarize this article for a 10 year old
SHOW ALL QUESTIONS
In mathematics, specifically in real analysis, the Bolzano–Weierstrass theorem, named after Bernard Bolzano and Karl Weierstrass, is a fundamental result about convergence in a finite-dimensional Euclidean space . The theorem states that each infinite bounded sequence in has a convergent subsequence.[1] An equivalent formulation is that a subset of is sequentially compact if and only if it is closed and bounded.[2] The theorem is sometimes called the sequential compactness theorem.[3]