# Definition:Second Principle of Mathematical Induction/Terminology

## Terminology of Second Principle of Mathematical Induction

### Basis for the Induction

The step that shows that the proposition $\map P {n_0}$ is true for the first value $n_0$ is called the basis for the induction.

### Induction Hypothesis

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

### Induction Step

The step which shows that the truth of $\map P {k + 1}$ follows from the assumption of truth of $P$ for all values of $j$ between $n_0$ and $k$ is called the induction step.