# Definition:Second Principle of Finite Induction/Induction Step

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## Terminology of Second Principle of Finite Induction

Consider a **Proof by Complete Finite Induction**.

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**.

## Also known as

The **induction step** can also be referred to as the **inductive step**.