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Math Help - Bolzano-Weierstrass property

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    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?
    Last edited by jacobn; February 13th 2011 at 08:06 AM. Reason: typo
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    Quote Originally Posted by jacobn View Post
    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?
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