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> You could take an item out of both bags until you exhausted the supply of one bag. If the other bag was simultaneously empty, then you’d know they had
by xtrumanx 12y ago
> You could take an item out of both bags until you exhausted the supply of one bag. If the other bag was simultaneously empty, then you’d know they had the same cardinality.
Well, since you can't exhaust the supply of an infinite supply of integers, I don't see how using this method is acceptable when trying to find a one-to-one correspondence.
I feel like I may be missing something so would appreciate if someone could chime in.
- daveFNbuck 12y agoThis is just an analogy to explain why you would want to find a one-to-one correspondence to compare set cardinalities. Pretty much any real-world analogy will break for infinite sets, but it's fairly straightforward to generalize bijections to infinite sets once you realize it's the right thing to do.