I finally have a favorite number. Well, actually, I have one favorite number for every well-ordering of the real numbers. If you don’t believe in the axiom of choice, I don’t have any favorite numbers.
Let (< ) be a well-ordering of the real numbers. There are aleph-0 many sequences of characters, and 2^aleph-0 (which is strictly larger than aleph-0) many real numbers. Therefore, there must be a real number which is not describable in words. My favorite number is the least such number according to the well-ordering.
Uh oh… I think I just described it in words.