Solution-Discuss the theorem the archimedean property

Discuss the theorem the archimedean property

Reference no: EM131582610

Question: Prove Theorem II. Use the method of contradiction: If the result is false, then there exists a real number x that is an upper bound of N. Use Theorem I and the definition of supremum to obtain a contradiction.

Theorem I: The supremum property implies the axiom of completeness

Theorem II: The Archimedean property. The set N of the natural numbers is not bounded above (i.e., for any x ∈ R, there exists a natural number n such that n>x).

Reference no: EM131582610

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Discuss the theorem the archimedean property

Reference no: EM131582610

Reference no: EM131582610

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