I don't know how many people know this, but often it's mindblowing when you learn, that some infinities are bigger than others. [...] The number of c… - Neil deGrasse Tyson

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I don't know how many people know this, but often it's mindblowing when you learn, that some infinities are bigger than others. [...] The number of counting numbers...so 1, 2, 3, up to infinity...the numbers you would use to count things, that's infinite. The number of irrational numbers...so the numbers you cannot represent as a fraction, okay, there are more of those than there are counting numbers, by far. So these are orders of infinity. Then there are more transcendental numbers than there are irrational numbers. So that's a number you'll never find as a solution to an algebraic equation. So pi is a transcendental number. e is a transcendental number. These are magic numbers that show up in mathematics. And it turns out there's an even bigger infinity of those than there is of these other two classes of numbers. And they use the Hebrew letter aleph in ranking. So it's aleph-1, aleph-2, aleph-3, aleph-4. I think there are five levels of infinity.