Meaning of INDUCTION in English


< logic > A method of proving statements about well-ordered sets . If S is a well-ordered set with ordering " IF for all t in S, t P(t) THEN P(s)

I.e. if P holds for anything less than s then it holds for s. In this case we say P is proved by induction.

The most common instance of proof by induction is induction over the natural numbers where we prove that some property holds for n=0 and that if it holds for n, it holds for n+1.

(In fact it is sufficient for " well-founded partial order on S, not necessarily a well-ordering of S.)


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