# Definition:Principle of Mathematical Induction/Terminology

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## Terminology of 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 made that $\map P k$ is true for some $k \in \Z$ is the **induction hypothesis**.

### Induction Step

The step which shows that $\map P k \implies \map P {k + 1}$ is called the **induction step**.