# Definition:Principle of Mathematical Induction/Induction Hypothesis

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## Terminology of Principle of Mathematical Induction

Consider a **Proof by Mathematical Induction**.

The assumption made that $\map P k$ is true for some $k \in \Z$ is the **induction hypothesis**.

## Also known as

The **induction hypothesis** can also be referred to as the **inductive hypothesis**.

## Sources

- 1966: Richard A. Dean:
*Elements of Abstract Algebra*... (previous) ... (next): $\S 0.1$ - 2000: Michael R.A. Huth and Mark D. Ryan:
*Logic in Computer Science: Modelling and reasoning about systems*... (previous) ... (next): $\S 1.4.2$: Mathematical induction: Definition $1.29$ - 2008: David Joyner:
*Adventures in Group Theory*(2nd ed.) ... (previous) ... (next): Chapter $2$: 'And you do addition?': $\S 2.4$: Counting and mathematical induction: Definition $2.4.1$