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![[parent]](http://images.planetmath.org:8080/images/uparrow.png) Viewing Correction to 'pigeonhole principle'
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perhaps $n$ should "set with cardinality $n$"? by saforres
Correction id: 883
Filed on: 2002-07-06 17:39:56
Status: Rejected on 2002-07-21 00:24:54
Type: Erratum
Correction text:
Perhaps it would be better to say "bijection between a set with cardinality $n$..." rather than "bijection between $n$..."
Of course, using the construction from your "natural number" entry, every natural number _is_ a set with cardinality equal to itself. This is probably not intuitive however, especially to those unfamiliar with foundations. |
Comment from object owner djao:
I am really wavering on whether I should accept your suggestion. In the end I have decided to reject it, even though in another situation (for "simplicial complex") I did accept the same suggestion.
The reason I would keep it the way it is now is that, although the statement of the pigeonhole principle is relatively accessible without a formal definition of finiteness, cardinality, and natural number, the _proof_ of the pigeonhole principle is I think by no means accessible without having gone through a formal statement of what a natural number is, and what finiteness means.
In other words, I am saying that, unlike a typical entry, a good understanding of this particular entry does require a good grasp of the relevant foundational material. So if my abstruse wording keeps some people away from it, and induces others to explore the foundational material more deeply, then that is a feature, not a bug.
It is undeniably true that the entry is rather threadbare at this time and could use some additional explanation even if that is not directed toward a formal proof of the theorem. I would be happy to receive some addenda to this effect.
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