# Definition:Principle of Mathematical Induction/Basis for the Induction

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## Terminology of Principle of Mathematical Induction

Consider a **Proof by Mathematical 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**.

## Also known as

The **basis for the induction** is often informally referred to as the **base case**.

## Sources

- 1979: John E. Hopcroft and Jeffrey D. Ullman:
*Introduction to Automata Theory, Languages, and Computation*... (previous) ... (next): Chapter $1$: Preliminaries: $1.3$ Inductive Proofs - 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 $1.29$