Full Idea
The number of English expressions is denumerably infinite. But Cantor's theorem can be used to show that there are nondenumerably many real numbers. So not every real number has a (simple or complex name in English).
Gist of Idea
English expressions are denumerably infinite, but reals are nondenumerable, so many are unnameable
Source
Leon Horsten (The Tarskian Turn [2011], 06.3)
Book Reference
Horsten,Leon: 'The Tarskian Turn' [MIT 2011], p.73
A Reaction
This really bothers me. Are we supposed to be committed to the existence of entities which are beyond our powers of naming? How precise must naming be? If I say 'pick a random real number', might that potentially name all of them?