Definition:Principle of Finite Induction/Terminology
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Terminology of 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 made that $n \in S$ for some $n \in \Z$ is the induction hypothesis.
Induction Step
The step which shows that $n \in S \implies n + 1 \in S$ is called the induction step.