Three forms of mathematical induction: Difference between revisions

Revision as of 02:40, 6 March 2006

Revision as of 02:41, 6 March 2006

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Proofs that a subset of { 1, 2, 3, ... } is in fact the whole set { 1, 2, 3, ... } by [[mathematical induction]] usually have one of the following three forms. They are collectcollected here in order to show the contrast between them, and its coexistence with the commonality between them.

# The basis for induction is trivial; the substantial part of the proof goes from case ''n'' to case ''n'' + 1.