# Definition:Second Principle of Mathematical Induction/Terminology

Jump to navigation
Jump to search

## Contents

## 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**.