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

There are not more numbers between 0 and 2 than between 0 and 1. At least when you accept the way mathematicians compare relative sizes (even for infinite amounts).

Mathematicians say for each number (x) between 0 and 1 there is a number between 0 and 2 (2x) and vice Vera’s: for each number between 0 and 2 (y) there is a number (y/2) between 0 and 1.

As long as you can find every number being co-paired in some way, like you do when counting, the amount is the same.