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Complete Induction




In Mathematics , complete induction, also known as '''strong induction''', is a variant on the principle of Mathematical Induction . The induction hypothesis, instead of being simply

:P(n-1)\,\! ,

is

: orall i \in \left\{1,\ldots, n-1 ight\} P(i).\,

This is clearly a ''stronger'' hypothesis, hence the name ''strong induction''. It is obvious that anything provable with Mathematical Induction is provable with strong induction.

On the other hand it requires only the introduction of a new proposition ''Q''(''n'') which is the Logical Conjunction of the ''P''(''m'') for 0 ≤ ''m'' ≤ ''n'' to write a strong induction argument as a conventional induction. This is sometimes done implicitly, as in Minimal Counterexample arguments by Contradiction .