In p. 30 of Baby Rudin, I find a reference to the fact that the binary representation of a real number implies the uncountablity of the set of real numbers. But I have two questions:
- Does every real number have a binary representation? If yes, how do I prove it?
- How can I generate the binary representation of a given real number $a$?
I'm aware of the binary representation of integers, but had never thought of a binary representation of real numbers earlier.