This 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

This 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.