Show that the assertion of the Heine-Borel Theorem is equivalent to the completeness axiom for the real numbers. Show that the assertion of the Nested set theorem is equivalent to the completeness axiom for the real numbers

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Show that the assertion of the Heine-Borel Theorem is equivalent to the completeness axiom for  the real numbers. Show that the assertion of the Nested set theorem is equivalent to the completeness axiom for the real numbers

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