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.