3 ms·
The "something resembling the pigeonhole principle" is the fact that if the union of finitely many sets is infinite, then at least one of the sets must be infin
by CurtMonash 13y ago
The "something resembling the pigeonhole principle" is the fact that if the union of finitely many sets is infinite, then at least one of the sets must be infinite as well.
I don't know whether it has a name.
- jb17 13y agoI think it's usually just called the pigeonhole principle. It's a special case of the Infinite Ramsey Theorem.
- CurtMonash 13y agoPerhaps. But it's simpler than all that. Assume that 70 million disjoint sets all have finite cardinality. Then the cardinality of the union is the sum of the cardinalities, and is finite by construction. Contradiction; QED.