mathematical induction

Formal method of proof in which the proposition P(n + 1) is proved true on the hypothesis that the proposition P(n) is true. The proposition is then shown to be true for a particular value of n, say k, and therefore by induction the proposition must be true for n = k + 1, k + 2, k + 3, ... . In many cases k = 1, so then the proposition is true for all positive integers.