# Definition:Principle of General Induction/Minimally Closed Class/Induction Hypothesis

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## Terminology of Principle of General Induction for Minimally Closed Class

Consider a **Proof by General Induction for a minimally closed class under $g$ with respect to $b$**.

The assumption made that $\map P x$ is true for some $x \in M$ is called the **induction hypothesis**.

## Also known as

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