# Definition:Second Principle of Finite Induction/Basis for the Induction

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## Terminology of Second Principle of Finite Induction

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

The step that shows that the integer $n_0$ is an element of $S$ is called the **basis for the induction**.

## Also known as

The **basis for the induction** is often informally referred to as the **base case**.