# Definition:Second Principle of Finite Induction/Terminology

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## Terminology of Second 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 that $\forall k: n_0 \le k \le n: k \in S$ for some $n \in \Z$ is the **induction hypothesis**.

### Induction Step

The step which shows that $n + 1 \in S$ follows from the assumption that $k \in S$ for all values of $k$ between $n_0$ and $n$ is called the **induction step**.