Well-ordering principle
Statement that all non empty subsets of positive numbers contains a least element / From Wikipedia, the free encyclopedia
Not to be confused with Well-ordering theorem.
In mathematics, the well-ordering principle states that every non-empty subset of positive integers contains a least element.[1] In other words, the set of positive integers is well-ordered by its "natural" or "magnitude" order in which precedes if and only if is either or the sum of and some positive integer (other orderings include the ordering ; and ).
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The phrase "well-ordering principle" is sometimes taken to be synonymous with the "well-ordering theorem". On other occasions it is understood to be the proposition that the set of integers contains a well-ordered subset, called the natural numbers, in which every nonempty subset contains a least element.