Both mathematical induction and proof by contradiction are deductive proofs. In fact, mathematics only recognizes the results of deductive proofs.
Mathematical induction is a corollary of the axiom system of natural numbers (that is, the application of the properties of natural numbers).
Argument by contradiction is actually a theorem of logic.
In addition, similar to mathematical induction, there is transfinite induction, which is a corollary of the axiom of choice.