Bolzano-Weierstrass Theorem

According to this theorem, there is at least one point of accumulation (or limit point) in a bounded set having an infinite number of elements. Alternatively, each bounded sequence in the set has a subsequence that converges to a point in the set. 

Not necessarily in a set, its point of accumulation has in its each neighborhood, at least one non-identical point from the set. A closed set contains all of its accumulation points. 

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The Bolzano-Weierstrass Theorem (Section 9.17, p. 277) assures that this sequence contains a subsequence that is convergent on some value, say. Wo- As w approaches Wo, approaches t, thereby implying... 

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