iIf is an injection which satisfies then for

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- Jul 16th 2010, 09:21 AM #1

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- Jul 16th 2010, 12:15 PM #2
Proof by contradiction: Suppose that for some x, say where Then , so that .

Now repeat the same argument with in place of x, to see inductively that for n=1,2,3,... . But for n large enough, will be negative (if ), or greater than 1 (if ). In either case that gives a contradiction.