Let A be a nonempty set of real numbers. A number m A is a least element of A if x mfor
Chapter 4, Problem 25(choose chapter or problem)
Let A be a nonempty set of real numbers. A number m A is a least element of A if x mfor every x A. For example, every finite nonempty set of real numbers and N have a leastelement, while Z and the open interval (0, 1) of real numbers do not have a least element. Anonempty set S of real numbers is said to be well-ordered if every nonempty subset of S hasa least element.(a) Show that if S is a nonempty set of real numbers and S does not have a least element,then S is not well-ordered.(b) Show that the closed interval [0, 1] of real numbers is not well-ordered (thereby showingthat a set with a least element may not be well-ordered).
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