# Math Help - Bolzano-Weierstrass property

1. ## Bolzano-Weierstrass property

Why would the interval [0, infinity) not have the Bolzano-Weierstrass property, which states that A set of real numbers E is closed and bounded if and only if every sequence of points chosen from the set has a subsequence that converges to a point that belongs to E?

2. Originally Posted by jacobn
Why would the interval [0, infinity) not have the Bolzano-Weierstrass property, which states that A set of real numbers E is closed and bounded if and only if every sequence of points chosen from the set has a subsequence that converges to a point that belongs to E?
Is the set $[0,\infty)$ bounded?

Let $\{x_n=n:n\in\mathbb{Z}^+\}$.
Does that sequence have a convergent subsequence?