prin'ciple of mathemat'ical induc'tion
a law in set theory which states that if a set is a subset of the set of all positive integers and contains 1, and if for each number in the given set the succeeding natural number is in the set, then the given set is identical to the set of all positive integers. Cf. induction (def. 5).
Random House Unabridged Dictionary, Copyright © 1997, by Random House, Inc., on Infoplease.