Definition:Second Principle of Mathematical Induction/Terminology
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Terminology of Second 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 that $\forall j: n_0 \le j \le k: \map P j$ is true for some $k \in \Z$ is the induction hypothesis.
Induction Step
The step which shows that the truth of $\map P {k + 1}$ follows from the assumption of truth of $P$ for all values of $j$ between $n_0$ and $k$ is called the induction step.