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

It entirely depends on how you count the numbers:

The most common answer to this post is that because you can pair up every number in one set with a number in the other they must be the same size. They’re both continuums.

But there’s another way to count, by measuring (using the Lebesgue measure), which gives us the more intuitive answer that the set of numbers between 0 and 2 is twice the measure of the set of numbers between 0 and 1.

This will probably only lead to more “why” questions.