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In this problem we prove that the Strong Induction Principle and Induction Principle are essentially equiv- alent...

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Advance Math

In this problem we prove that the Strong Induction Principle andInduction Principle are essentially equiv-
alent via Well-Ordering Principle.
(a) Assume that (i) there is no positive integer less than 1, (ii)if n is a positive integer, there is no
positive integer between n and n+1, and (iii) the Principle ofMathematical Induction is true. Prove
the Well-Ordering Principle: If X is a nonempty set of positiveintegers, X contains a least element.
(b) Assume the Well-Ordering Principle and prove the StrongMathematical Induction Principle.

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