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· 7 min read

Rational numbers are easy. They include the integers, with which you can count up and down the number line, as well as fractions - written as the division of two integers or as a finitely-long decimal expansion.

But there aren't that many rational numbers on the real number line, as there are irrationals. These beasts of infinitely-long decimal expansions take the vast majority of the infinity of real numbers. They can't be written as a fraction, and they can't be written exactly as a decimal expansion (it would be infinitely long).