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  3. prove corollary 4.22: a set of real numbers e is c

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

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Advance Math

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

Use Theorem 4.21: [Bolzano-Weierstrass Property] A set of realnumbers is closed and bounded if and only if every sequence ofpoints chosen from the set has a subsequence that converges to apoint that belongs to E.

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

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

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