If you actually look at how real numbers are constructed. They are quite bizarre. The simple concept of the number line becomes a quite complicated set of sets that follow certain conditions.
(Sqrt(2) as a real number, is actually encoded as the set of all rationals less than sqrt(2) on the number line).
(Sqrt(2) as a real number, is actually encoded as the set of all rationals less than sqrt(2) on the number line).