Definition:Principle of Mathematical Induction/Also known as

Principle of Mathematical Induction: Also known as
Some sources refer to the principle of mathematical induction as the first principle of mathematical induction, to distinguish it from the second principle of mathematical induction.

Some call it the induction principle.

The abbreviation  is often seen.

Some sources call it the principle of weak induction.

Such sources may similarly refer to the second principle of mathematical induction as the principle of strong induction.

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

When applied to the subset of the natural numbers, it is often referred to as the principle of finite induction.

The process of demonstrating a proof by means of the principle of mathematical induction is often referred to as proof by (mathematical) induction.