Math amateur here, and new to the site. I have to write a technical specification, and am rather unsure about how to express things mathematically properly.
So I have a set of “entities” of some sort. Let's call it A. It shouldn't matter what the entities are for this question.
I also have a notion of equivalence between the entities in A.
But, for any two entities, it may or may not be possible to tell whether they are equivalent. So, the equivalence relationship is not defined for all pairs of entities.
Now, I need to talk a lot about subsets of A where the equivalence relationship is defined for all members of the subset. (For any a and b in the subset, “a equivalent b” is defined.)
What should I call these subsets? Is there a good term for describing exactly that? So I'm looking for a good term for XXX in this sentence: “If a subset B of A is a XXX (that is, “a equivalent b” is defined for any a and b in B), then…”