Let α be a Dedekind Cut. w a positive rational.How to prove that there exists a integer n such that nw is a member of α and (n+1)w is not a member of α, using Archemedian propoerty of Q.(adsbygoogle = window.adsbygoogle || []).push({});

Suppose p is a member of α. we can find n such that nw < p < (n+1)w. So nw is

a member of α. Further I am not able to proceed.

Please help me.

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# Dedekind Cut and Archemedean Q

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