In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 12 Dez., 18:51, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote: > > > > > A bad translation; it's not the domain that is real, but the numbers: > > You agree that the numbers are real? But you do not agree that these > numbers are real numbers? Remarkable. > > > "The first number-class (I) is the set of finite integers > > 1,2,3, ...,nu,..., > > And you have already forgotten that finite integers are real numbers?
The non-negative integers may well be only cardinalities, which will not be simultaneously real numbers in any context where most real numbers are nonsensical, such as in counting. One cannot have pi people or any other non-natural number of people, other than 0 if your notion of N excludes 0.
So in counting contexts, the results of a count will always be counting numbers, i.e., 0's or naturals, and will not be= integers, nor rationals, nor reals or complexes, nor quaternions, nor anything else. --