"Unnameable" and "unnamed" are two different things, in my opinion. Are there real numbers that are unnameable or are those just unnamed?
There are some that unnameable with my mathematical understanding, but that's not saying much.
There are some that unnameable with my mathematical understanding, but that's not saying much.
On the other hand, given any real number, I can name it. I'll run out of unique names, since no injective function exists from real numbers to names.
So, some unnamed real numbers will always remain (non-constructively), I can make real numbers that escape a naming scheme (constructively), and no unnameable real numbers exist.
Assigning a symbol? But who said that the set of symbols must be countable?