Definition:Second Principle of Mathematical Induction/Induction Hypothesis

Terminology of Principle of Complete Induction
Consider a proof by complete induction.

The assumption made that $\forall j: n_0 \le j \le k: \map P j$ is true for some $k \in \N$ is the induction hypothesis.

Also known as
The induction hypothesis can also be referred to as the inductive hypothesis.