From Internet Encyclopedia of Philosophy

The mathematical proof technique called “mathematical induction” is deductive and not inductive. Proofs that make use of mathematical induction typically take the following form:

Property P is true of the natural number 0.

For all natural numbers *n*, if P holds of *n* then P also holds of *n* + 1.

Therefore, P is true of *all* natural numbers.

When such a proof is given by a mathematician, and when all the premises are true, then the conclusion follows necessarily. Therefore, such an inductive argument is deductive. It is deductively sound, too.