# Definition:Principle of Finite Induction/Terminology

## Terminology of Principle of Finite Induction

### Basis for the Induction

The step that shows that the integer $n_0$ is an element of $S$ is called the basis for the induction.

### Induction Hypothesis

The assumption made that $n \in S$ for some $n \in \Z$ is the induction hypothesis.

### Induction Step

The step which shows that $n \in S \implies n + 1 \in S$ is called the induction step.