Well-Ordering Axiom - Strong Induction
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Prove the well-ordering Axiom by strong induction.
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Solution Summary
The well-ordering axiom is proven by strong induction is examined.
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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
and
P(1) and P(2) and so on through P(n) imply P(n+1)
then
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 ...
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