Definition:Principle of Mathematical Induction/Terminology
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Terminology of Principle of Mathematical Induction
Basis for the Induction
The step that shows that the proposition $\map P {n_0}$ is true for the first value $n_0$ is called the basis for the induction.
Induction Hypothesis
The assumption made that $\map P k$ is true for some $k \in \Z$ is the induction hypothesis.
Induction Step
The step which shows that $\map P k \implies \map P {k + 1}$ is called the induction step.