4 . The Bolzano-Weierstrass theorem for R states that every bounded sequence {n} in R has a convergent subsequence. As observed in the course, this result is an easy consequence of a much stronger result which says that {xn} has a subsequence whose limit is lim sup In. There are alternative well-known proofs of the Bolzano-Weierstrass theorem. For example, one can start by showing that every sequence in R has a monotone subsequence and then deduce the Bolzano-Weierstrass theorem. There is also another proof that uses the Squeeze Lemma. Give one such proof of the Bolzano-Weierstrass theorem for R