I see. It still does not make sense to me that there are necessarily undefinable numbers. That is, for any given number x there is not an English sentence y that defines the number. That sentence may need to be arbitrarily long, but so what? English has more flexibility than math in defining things, maybe that is the disconnect. It seems to me that insofar English can define any number, it can define all of them.

It feels to me like this is trying to draw an equivalence between language and mathematics yet disallowing the inherent ambiguity of language. At that point, the comparison is just silly.