I watched "The Fault in Our Stars" last night, and at some point a character states, "[t]here 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." While the last statement is quite true, the initial reasoning is, in fact, false. There are the same number of numbers between 0 and 1 as there are between 0 and 2. The problem is that this ruined the sentiment the character was trying to potray to me. The author (or editor) should have fact checked. Maybe they did and didn't really understand what was being said. Anyway, here is a blog post on the subject.

http://blogs.scientificamerican.com/roots-of-unity/2014/07/10/the-fault-in-our-stars-infinities/