## induction

<*logic*>

IF for all t in S, t < s => 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 "<" to be a well-founded partial order on S, not necessarily a well-ordering of S.)

Last updated: 1999-12-09

### Nearby terms:

indirect jump ♦ **induction** ♦ inductive inference ♦ inductive relation

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