Mathematical induction and reduction to absurdity are both deductive proofs. In fact, mathematics only recognizes the results of deductive proof.

Mathematical induction is an inference of the axiomatic system of natural numbers (that is, the application of the nature of natural numbers).

Reduction to absurdity is actually a theorem of logic.

In addition, similar to mathematical induction, there is transfinite induction, which is a kind of axiom of choice's inference.