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There are different sizes of infinity. It turns out that some are larger than others. Mathematician Kelsey Houston-Edwards breaks down what these different sizes are and where they belong in The Hierarchy of Infinities.

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Written and Hosted by Kelsey Houston-Edwards
Produced by Rusty Ward
Graphics by Ray Lux
Made by Kornhaber Brown (www.kornhaberbrown.com)

Sources:

Proof that the real numbers are a bigger infinity than the natural numbers:
http://germain.its.maine.edu/~farlow/...
http://www.people.vcu.edu/~rhammack/B...

Thanks James Barnes and Iian Smythe!