It's probably easier to give an example of a number that I can't represent symbolically. However, I can't give you a specific example, since if I uniquely defin

It's probably easier to give an example of a number that I can't represent symbolically. However, I can't give you a specific example, since if I uniquely define a number then that definition is itself a symbolic representation of that number. But here is an example: a uniformly random real number on [0, 1]. Or, computationally speaking, uniformly sample an infinite number of Bernoulli random variables, and write down the binary representation. Of course, this process takes infinite time, which suggests that they are not representable. For a proof, consider the fact that every representable number, by definition (I know I haven't given a formal definition), is represented by some finite string. But the number of finite strings is countable. So it must be a measure zero subset of [0, 1], so a random sample is representable with probability zero.