I'm not trying to argue for R being more a set than C.
In my head a one dimensional thing like R is fundamentally different from a multidimensional thing like C.
In my head a one dimensional thing like R is fundamentally different from a multidimensional thing like C.
Edit: FWIW, I consider the terminology of 'real' vs 'imaginary' completely stupid and misleading. This terminology didn't really make it to other languages, e.g. in Russian it's 'material' vs 'complex' numbers, but they don't use the term 'imaginary'.