By this point you're probably used to the idea that most of the real numbers are irrational numbers. That is, even though there are countably many rational numb

By this point you're probably used to the idea that most of the real numbers are irrational numbers. That is, even though there are countably many rational numbers, there are uncountably many real numbers. Numbers like pi and e, even though they are irrational, can still be described. There is still an algorithm that computes their digits. The same goes for 0.112358132134... or Apery's constant. But the vast majority of real numbers can never even be described. Proof: Any description of a number (any algorithm that computes its digits) is a finite string of symbols. There are countably many finite strings of symbols, but uncountably many reals. Math goblins.