There are infinitely many real numbers between 0 and 1. Are there twice as many between 0 and 2, or are the two amounts equal?

Question

I know the actual technical answer. I’m looking for a witty parallel that has a low chance of triggering an infinite “why?” procedure in a child.

In: 1335

Answer 1

Take every real number between 0 and 1, and pair it up with a number between 0 and 2, according to the rule: numbers from [0,1] are paired with themselves-times-two.

See how every number in the set [0,1] has exactly one partner in [0,2]? And, though it takes a couple extra steps to think about, every number in [0,2] has exactly one partner, too?

Well, if there weren’t the same ~~number~~ quantity of numbers in the two sets, that wouldn’t be possible, would it? Whichever set was bigger would have to have elements who didn’t get paired up, right? Isn’t that *what it means* for one set to be bigger than the other?