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![[parent]](http://images.planetmath.org:8080/images/uparrow.png) Viewing Correction to 'proof of pigeonhole principle'
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Unconvincing proof. by ratboy
Correction id: 7755
Filed on: 2006-03-24 23:45:33
Status: Rejected on 2006-05-02 14:40:24
Type: Erratum
Correction text:
The fact that the sets in question are finite plays no role in the proof. The validity of the proof is not affected if all occurrences of "finite" are deleted. If the first PM definition of cardinality is intended, then the result is equilalent to:
For finite sets S and T, if |S| = |T|, then |S| = |T|.
Otherwise, I cannot think of a principle to justify the inference from "f is injective" to "|S|=|ran f|" that would not immediately justify the conclusion "|S| = |T|".
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No comment from object owner Wkbj79.
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