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. 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.