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Mathematical induction is a case of deductive reasoning.

It uses some kind of inductive principle, and the justifications for why that holds are a different matter. But its use is a case of rigorous, deductive reasoning.

Finding the matter to be proved deductively is often a creative process that involves induction. This is also true for mathematical induction; finding the rule to be established might be a process of induction, which is then verified by deduction.