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Calculus

Infimum version of the Axiom of Completeness. Assuming the Axiom of Completeness, prove that any nonempty set of real numbers A which is bounded below has a greatest lower bound. Hint. Consider the set {−a : a ∈ A}.

Leave a Comment / Calculus, Mathematics / By wegoki

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Problem 5. Show that the assertion of the Heine-Borel theorem is equivalent to the completeness Axiom for the real numbers.

Leave a Comment / Calculus, Mathematics / By wegoki

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Question. Open exercise 2.18 let (a_n) be an increasing bounded sequence.by the completeness Axiom the sequence converges to some real numbers a. show that its range {a_n| n∈N} has a supremum and that the supremum equals a

Leave a Comment / Calculus, Mathematics / By wegoki

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Give five consequences of the completeness axioms of real numbers.

Leave a Comment / Calculus, Mathematics, Uncategorized / By wegoki

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

Leave a Comment / Calculus, Mathematics / By wegoki

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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