Question: Use the Heine-Borel Theorem to prove the following version of the Bolzano-Weierstrass Theorem: Every bounded infinite subset of R has a cluster point in R.

Use the Heine-Borel Theorem to prove the following version of the Bolzano-Weierstrass Theorem: Every bounded infinite subset of R has a cluster point in R. (If a set has no cluster points, then it is closed by Theorem 11.1.8.)

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