Real Analysis Problem

A set S, a subsequence of the real numbers, is said to have the Bolzano Weierstass property if every sequece {Xi}, a subset of S, has a subsequence Xij converging to a point in S.

1. Let S be unbounded. Show that S does not have the Bolzano Weierstrass property.

2. Let S, a subsequence of the real numbers, not be closed. Show that S does not have the Bolzano Weierstrass property.

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