Question

A. Let S be an ordered set such that for any two elements p <r in S, there is an element q ES withP<q<r. Suppose a and 6 are elements of S such that for every xE S with r > a, one has x> B.Show that 6<a. B. Show by example that this does not remain true if we drop the assumption that whenever p <r there is a q with p <q<r.

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