Three forms of mathematical induction: Difference between revisions

Revision as of 21:20, 12 March 2006

Revision as of 01:26, 14 April 2006

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===Second form===

* The case ''n'' = 1 is [[vacuous truth|vacuously true]];

* the step that proves the case ''n'' = ''k'' + 1 is trivial, but relies on '''two''' previous cases: the case ''n'' = ''k'' and the case ''n'' = 2. This step cannot be used to prove the the case ''n'' = 2 as to do so would be a [[circular argument]] (since the case ''n'' = 2 had not yet been proved).

* the substantial part of the proof is to give a (different) proof of the case ''n'' = 2.

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===Second form===

====Product rule====