> every real number can be described by some arbitrarily complex symbolic notation
This seems like it would have to be false, because otherwise the reals would be countable (iterate through every possible 1-character string, then every possible 2 character string, then 3 chars, etc and in a finite (but potentially very very large) amount of time you would come across the description of any real number that can be described).
This seems like it would have to be false, because otherwise the reals would be countable (iterate through every possible 1-character string, then every possible 2 character string, then 3 chars, etc and in a finite (but potentially very very large) amount of time you would come across the description of any real number that can be described).