principle of mathematical induction

noun

, Mathematics.

1. 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. Compare induction ( def 5 ).

Example Sentences

As far as investigating AA/NA, I know by the the principle of mathematical induction that if you can show you can get to the first step and for all arbitrary values, k, by the rule of implication if you can get to step k and you prove you can get to step k+1 with the inductive hypothesis, then you can reach all the steps in the program.

From New York Times

Therefore, the program is sound by the principle of mathematical induction.

From New York Times