## Problem 4. Prove using the completeness property that √2 is a real number by considering the set {x∈(0,2)|x^2<2}.

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# Calculus

## 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

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