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.