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
- 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): complete induction
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): induction: 1. (in mathematics)