# Definition:Second Principle of Mathematical Induction/Also known as

Jump to navigation
Jump to search

## Second Principle of Mathematical Induction: Also known as

The **Second Principle of Mathematical Induction** is also known as the **Principle of Complete Induction**.

Both terms are used on $\mathsf{Pr} \infty \mathsf{fWiki}$.

The abbreviation **PCI** is also used.

Some sources call it the **Principle of Strong Induction**.

Such sources may similarly refer to the **(First) Principle of Mathematical Induction** as the **Principle of Weak Induction**.

These names are misleading, as both principles are equivalent, and so neither is weaker or stronger than the other.

Some sources prefer to call it **course-of-values induction**, but this is possibly idiosyncratic.

The process of demonstrating a proof by means of the **Second Principle of Mathematical Induction** is often referred to as **Proof by Complete Induction**.

## Sources

- 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**complete induction** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**complete induction**