system
Given the following post, respond as if you're commenting on Reddit:
human
Can some infinities be larger than others?

> “There are infinite numbers between 0 and 1. There's .1 and .12 and .112 and an infinite collection of others. Of course, there is a bigger infinite set of numbers between 0 and 2, or between 0 and a million. Some infinities are bigger than other infinities.” 

-John Green, *A Fault in Our Stars*
gpt
Yes. For instance, the set of real numbers is larger than the set of integers.

However, that quote is still wrong. The set of numbers between 0 and 1 is the same size as the set of numbers between 0 and 2. We know this because the function y = 2x matches every number in one set to exactly one number in the other; that is, the function gives a way to pair up each element of one set with an element of the other.