11.6 Prove by induction on n that if A is a set of positive integers without a least element then Nn Szt - A for every n

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11 6 Prove By Induction On N That If A Is A Set Of Positive Integers Without A Least Element Then Nn Szt A For Every N 1 (97.93 KiB) Viewed 62 times

11.6 Prove by induction on n that if A is a set of positive integers without a least element then Nn Szt - A for every n so that A is the empty set. Deduce the well-ordering principle: every non-empty set of positive integers has a least element. † The reader should be aware (and beware) of the way in which some notation is used in a variety of ways. Here we are using (a, b) for the greatest common divisor of two integers, but we have previously used this notation to devote an element of the Cartesian product Z Z and to denote the open interval {XER|a<x<b}. It is usually clear from the context which of these meanings is intended. The reader just has to get used to this sort of ambiguity.