well-ordering principle for natural numbers
Every nonempty set of natural numbers contains a least element; that is, there is some number in such that for all belonging to .
Beware that there is another statement (which is equivalent to the axiom of choice) called the well-ordering principle. It asserts that every set can be well-ordered.
Note that the well-ordering principle for natural numbers is equivalent to the principle of mathematical induction (or, the principle of finite induction).
Title | well-ordering principle for natural numbers |
---|---|
Canonical name | WellorderingPrincipleForNaturalNumbers |
Date of creation | 2013-03-22 11:46:38 |
Last modified on | 2013-03-22 11:46:38 |
Owner | CWoo (3771) |
Last modified by | CWoo (3771) |
Numerical id | 18 |
Author | CWoo (3771) |
Entry type | Axiom |
Classification | msc 06F25 |
Classification | msc 65A05 |
Classification | msc 11Y70 |
Related topic | MaximalityPrinciple |
Related topic | WellOrderedSet |
Related topic | ExistenceAndUniquenessOfTheGcdOfTwoIntegers |