Definition
Bounded Sequence
A sequence is called bounded or limited if it is bounded above or bounded below.
Bolzano–Weierstrass Theorem
Definition
Link to originalBolzano–Weierstrass Theorem
The Bolzano–Weierstrass theorem states that every bounded sequence in has at least one limit point.
Equivalently, every bounded sequence in contains a convergent subsequence.
The theorem is named after Bernard Bolzano and Karl Weierstrass. It is a fundamental result in analysis that characterises compactness in Euclidean space.