Definition:Mathematical Induction/Terminology

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Terminology of Mathematical Induction

Basis for the Induction

The step that establishes the truth of $Q$ for $w_0$ is called the basis for the induction.

Induction Hypothesis

The assumption that $Q$ is true for $w_p$ is called the induction hypothesis.

Induction Step

The proof that the truth of $Q$ for $w_p$ implies the truth of $Q$ for $w_{p^+}$is called the induction step.