# Definition:Mathematical Induction/Terminology

## Terminology of Mathematical Induction

### Basis for the Induction

The step that establishes the truth of $Q$ for $w_0$ is called the basis for the induction.

### Induction Hypothesis

The assumption that $Q$ is true for $w_p$ is called the induction hypothesis.

### Induction Step

The proof that the truth of $Q$ for $w_p$ implies the truth of $Q$ for $w_{p^+}$is called the induction step.