[−][src]Trait maths_traits::analysis::ordered::AddOrdered
A marker trait signifying that for x > y, x+z > x+z and z+x > z+x for all z
Note that for monoids with some negative or positive element x this
automatically means that the magma is infinite, as otherwise, there would be a
maximum element M and minimum m, contradicting M + x > M + 0 = M (if x > 0)
or m + x < m + 0 = m (if x < 0). (Of course, the bitwise representations of these
structures size limited by size, but in practice, we treat them as infinite anyway.)
Futhermore, for monoids and groups, this provides a way to embed the Naturals and Integers into the structure respectively, and if the structure also is an ordered semiring with one, then there is even a canonical embedding following both addition and multiplication rules