> Since R is a subset of C, you can write C as R with additional axioms. That's not even remotely how it works. You may want to read up on logical theories and

> Since R is a subset of C, you can write C as R with additional axioms. That's not even remotely how it works. You may want to read up on logical theories and models[1]. > Well in language, in which I am corresponding with you, there is such a thing as 'makes no sense'. Yes, and for the same reason we can have such a thing as "undefined" (that means more than merely 'not specified') in informal mathematics -- because both English and informal math are informal. But we are talking about formal languages[2], which do not have such a thing. [1]: https://en.wikipedia.org/wiki/Theory_(mathematical_logic) https://en.wikipedia.org/wiki/Theory_(mathematical_logic), https://en.wikipedia.org/wiki/Structure_(mathematical_logic) https://en.wikipedia.org/wiki/Structure_(mathematical_logic) [2]: https://en.wikipedia.org/wiki/Formal_system https://en.wikipedia.org/wiki/Formal_system