All the ways of encoding Reals that you mention in your comment are limited to Rationals. It seems like you just didn't know that one can encode Reals too, which puffoflogic assumed readers to know.

Yes, they could have made their comment more accessible and mentioned the encoding (but I think then the problem may have sounded less "natural", since you'd have Turing machines mentioned). But you also could have noticed you're building a strawman argument, and instead just asked how does one encode Reals. Heuristics: if other person's argument sounds too absurd, there's a chance you're misunderstanding something.