Answer
Showing that we can prove the well-ordering property when we take strong induction as an axiom instead of taking
the well-ordering property as an axiom.
Work Step by Step
--Strong induction:
implies the principle of mathematical induction,
for
-if one has shown that P(k) → P(k + 1) is true,
then
- one has also shown that [P(1)∧· · ·∧P(k)]→P(k+1) is
true.
-the principle of mathematical induction implies the well-ordering property.
-- Therefore by assuming strong induction as an axiom, we can prove the well-ordering property.
