Proof of mathematical induction: Difference between revisions

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Suppose ''m′'' > 0.
 
From the definition of ''m′'', ''P''(''m′'' - 1), hence by (2) ''P''(''m′''). This also gives a contradiction, ''P''(''m′'') & '''not''' ''P''(''m′'').
 
It thus follows that (1) and (2) together imply '''not''' (4), which we have already established is just (3).