# Definition:Principle of Mathematical Induction/Induction Step

## Terminology of Principle of Mathematical Induction

Consider a **Proof by Mathematical Induction**.

The step which shows that $\map P k \implies \map P {k + 1}$ is called the **induction step**.

## Also known as

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

## 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 $1.29$