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![[parent]](http://images.planetmath.org:8080/images/uparrow.png) Viewing Correction to 'principle of finite induction proven from the well-ordering principle for natural numbers'
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not the "well-ordering principle" by smw
Correction id: 7574
Filed on: 2006-02-20 14:35:54
Status: Accepted on 2006-03-06 14:44:08
Type: Meta/Minor
Correction text:
"The well-ordering principle" is the wrong phrase here. What you're actually using is the fact that every nonempty subset of the natural numbers has a smallest element. The well-ordering principle, on the other hand, states that every set can be well-ordered (and this is equivalent to the axiom of choice).
Suggestion: Use the notion of "well-foundedness," that is every subset has a smallest element. Replace the phrase "the well-ordering principle says..." with "since < is a well-founded relation on the positive integers..." or something to that effect. |
Comment from object owner smw:
| Just changed "The Well-Ordering Principle says..." to "The Well-Ordering Principle for the positive integers says..." Will probably make more revisions later. Note that, at least right now, we are using the terminology "Well-ordering principle for the positive integers" to name the property that every nonempty subset of the positive integers has a smallest element. |
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