Well-ordering principle

Sometimes the phrase well-ordering principle is taken to be synonymous with "well-ordering theorem". On other occasions the phrase is taken to mean the proposition that the set of integers  contains a well-ordered subset, called the natural numbers, of which any nonempty subset always contains a least element.

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Sometimes the phrase well-ordering principle is taken to be synonymous with "well-ordering theorem".
On other occasions the phrase is taken to mean the proposition that the set of integers  contains a well-ordered subset, called the natural numbers, of which any nonempty subset always contains a least element.
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