Then we mean different things by define. I am saying the set R (with all its elements) is an uncontroversial, well-defined construction within ZFC.
I am leaving out any linguistic or Turing-computability aspects out of this, and people try to bring it back in, mixing computability with definability.
I am leaving out any linguistic or Turing-computability aspects out of this, and people try to bring it back in, mixing computability with definability.
For instance, Chaitin's constant is a perfectly well-defined number, albeit uncomputable by construction: https://en.wikipedia.org/wiki/Chaitin%27s_constant