Sorry, it's been a few years since I've looked into this stuff so my terminology may be off. Please bear with me.
When a set is ordered, the < operator is defined for that set. I can't think of an example, but my gut says that just because < is defined, that does not mean that - is defined.
Assuming what I said is true, what is it called when a set implements "distance" or "subtraction" or whatever you want to call it?
A set "closed over addition/subtraction" doesn't seem right to me. I'm thinking (again with my gut) that the function result does not have to be an element of the set.
