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

## Second Principle of Finite Induction: Also known as

Some sources refer to the **Second Principle of Finite Induction** as the **Second Principle of Mathematical Induction**, and gloss over the differences between the two proof techniques if they discuss them both at all.

Hence the word **finite** may well not appear in the various published expositions of this technique.

The **Second Principle of Finite Induction** is also known as the **Principle of Complete (Finite) Induction**.

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

The abbreviations **PCI** or **PCFI** can sometimes be seen.

Some sources call it the **Principle of Strong (Finite) Induction**.

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

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

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