I have a very elementary terminology question:
When you say "$x$ and $y$ commute under some operation", can you only say that if the operation is generally commutative, or is it also used to mean that it just happens to be commutative for $x$ and $y$?
For example, is it correct usage to say, "1 and 1 commute under subtraction"?
What about, "$x$ and $y$ commute under subtraction when $x=y$"?
Edit: Additionally, is it incorrect usage to say a non-commutative operation is commutative under a set of circumstances, e.g. "subtraction is commutative when both operands are equal"?