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In: Advanced Math

Prove Corollary 4.22: A set of real numbers E is closed and bounded if and only...

Prove Corollary 4.22: A set of real numbers E is closed and bounded if and only if every infinite subset of E has a point of accumulation that belongs to E.

Use Theorem 4.21: [Bolzano-Weierstrass Property] A set of real numbers 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.

Must use Theorem 4.21 to prove Corollary 4.22 and there should be no mention of closed and bounded in the proof. The proof should start with,

[E closed and bounded] iff [E has the BW Property]

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Colby Messinger answered 2 years ago
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