Analogue of the term 'summand' for unions and intersections.

If we have a sum $\sum\limits_{i=1}^na_i$, we call the terms $a_i$ summands. In fact, in the cases of addition, subtraction, multiplication, and division, we have a large vocabulary to describe the various components; see here.

Is there an analogue of the term 'summand' for unions and intersections?

That is, for $\bigcup\limits_{i=1}^n A_i$ and $\bigcap\limits_{i=1}^nA_i$, is there a term which refers to the sets $A_i$?

Solution 1:

I've just decided to call them "uniands", but I came here hoping there was something standard.

I believe you could get away with calling them "summands" and "factors" by analogy of $\cup$ with $+$ and $\cap$ with $\times$ (the first being the sum and product of the Boolean ring of subsets of a set, and the second being the generic terms for sum and product in a ring of any sort).

Solution 2:

I would go to the etymology of summand and re-engineer the word you want. For union: etymology: https://www.google.com/search?q=summand+etymology

latin for union (merge): "conjugo"

So my guess is "conjugand" or something like that.

For intersection a similar guess would be: "disjungand"

Aside: I would be comfortable using "conjugand" for the parts of any commutative, associative, operator, including intersection, logical conjunction and disjunction, max, min, etc.