Treating the abusive unsigned syndrome

[Kagamin]

Andrei Alexandrescu Wrote:

> There are several schools of thought (for the lack of a better phrase):
> 
> 1. The Purist Mathematician: We want unsigned to approximate natural 
> numbers, natural numbers aren't closed for subtraction, therefore u1 - 
> u2 should be disallowed.

I thought, mathematics doesn't distinguish between, say, natural 5, integral 5 and real 5. N, Z and R are sets, not types of numbers. There is even notion of equivalence class to deem numbers with different representation as the same (not just equal).