Question

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State and Prove Archimedean property of real number ? DUG
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Answer 1

Definition An ordered field F has the Archimedean Property if, given any positive x and y in F there is an integer n > 0 so that nx > y. Theorem The set of real numbers (an ordered field with the Least Upper Bound property) has the Archimedean Property. ... Thus n ≤ α for all n ∈ N and is the smallest such real number.