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

Get all the numbers from 0-1.

For each number, double it’s (e.g. 0.25 becomes 0.5, and pi/4 becomes pi/2, and .99 becomes 1.98, etc).

You now have all the numbers between 0-2.

Doubling the value of a number still results in a single number.

So this process has not change how many numbers we had.

Therefore, 0-1 and 0-2 have the same amount of numbers.