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    Well-Ordering Axiom - Strong Induction

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    Prove the well-ordering Axiom by strong induction.

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    Strong induction:

    Assume there is a proposition that is a function of a single natural number, that is P(x).

    If P(1) is true
    P(1) and P(2) and so on through P(n) imply P(n+1)
    P(i) is true for all natural numbers.

    Proof of Well-ordering axiom by strong induction:

    We will do induction based on the size of the subset.

    That is, the property P(i) in strong induction will ...

    Solution Summary

    The well-ordering axiom is proven by strong induction is examined.