Suppose you have infinitely many bowling balls and two huge barrels. You take th

Question

Suppose you have infinitely many bowling balls and two huge barrels. You take the bowling balls and put each ball in one of the two barrels. What can you conclude about the cardinality of at least one of the barrels? Prove your answer.
Suppose you have infinitely many bowling balls and two huge barrels. You take the bowling balls and put each ball in one of the two barrels. What can you conclude about the cardinality of at least one of the barrels? Prove your answer.
Suppose you have infinitely many bowling balls and two huge barrels. You take the bowling balls and put each ball in one of the two barrels. What can you conclude about the cardinality of at least one of the barrels? Prove your answer.

Explanation / Answer

Let A and b to denote each barrel

assume that |A| >or= |B| (or vice versa). Just by the rules you can put each of the balls in one of the two barrels, I'm assuming then that you can put bowling balls in each barrel how ever you please. Because of this then you have an injective function wherein the bowling balls in A are distinct from the balls in B (if there are any in B). This one depends really on how you divide your bowling balls, and whether you're making proper assumptions. I think I

If both barrels ended up finite, say with A and B ball respectively, then the original set had only A+B balls, a contradiction.

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