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Prove that if ECR is infinite and bounded, then it has a limit point. [Hint: Bolzano-Weierstrass.] Prove that if ECR is uncountable, then there

Prove that if ECR is infinite and bounded, then it has a limit point. [Hint: Bolzano-Weierstrass.] Prove that if ECR is uncountable, then there is a subset of E that is uncountable and bounded. Deduce that E has a limit point.

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