Definition:Principle of Finite Induction/Also known as
Principle of Finite Induction: Also known as
Some sources refer to the Principle of Finite Induction as the Principle of Mathematical Induction, and gloss over the differences between the two proof techniques if they discuss them both at all.
Some sources refer to it as just the Principle of Induction.
Hence the word finite may well not appear in the various published expositions of this technique.
Some sources refer to the Principle of Finite Induction as the First Principle of (Finite) Induction, to distinguish it from the Second Principle of Finite Induction.
Some call it the induction principle.
The abbreviation PFI is often seen.
Some sources call it the Principle of Weak (Finite) Induction.
Such sources may similarly refer to the Second Principle of Finite Induction as the Principle of Strong (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 Principle of Finite Induction is often referred to as Proof by (Finite) Induction.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): induction: 1. (in mathematics)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): induction: 1. (in mathematics)