Mathematics
Cantor's Diagonal Argument and the Uncountability of the Reals
Quick fact
Cantor's diagonal argument shows that even though the set of all decimal numbers between 0 and 1 is infinite, it contains more elements than the set of all counting numbers (1, 2, 3, ...).
Why this is interesting
You've probably been told that there are infinitely many numbers. But did you know that some infinities are actually bigger than others?