### Counting all the Numbers between Zero and One

One of my favorite songs of late is &Run by Sir Sly. I discovered it around the time I started running, and it has a little gem buried in the chorus:

♫ I’m counting all the numbers between zero and one ♫

Sounds simple, right? 0… 1. That’s it.

^{1}However, this assumes that “numbers” only refers to whole numbers. What if we include fractions, decimals, and weird numbers like π? How many of those exist between zero and one?

It turns out the answer is a lot. Think: infinity, but more.