I saw this problem on AOPS and, at the end of pi$37$'s proof, he mentioned something about the infinite pigeonhole principle. Can someone explain what he means by this?
2026-03-29 11:02:38.1774782158
What is the Infinite Pigeonhole Principle?
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If you have infinitely many pigeons and put them in finitely many pigeonholes, then some pigeonhole must contain infinitely many pigeons.