A term for a set of which at most one element has to be selected

Question

I'm looking for a term to describe a set of which at most one element can be selected.
Example
We have the set {0,1,2}. As shown earlier, this is a [insert word here], so we have to select at most one element.
The reason for this is that in the same paper, there is also another type of set (of which at least one has to be selected). Therefore, I need to give both these sets a name. For the latter, I'm thinking of something like 'non-empty selection set'. For the former, I don't have a clue.
Thanks in advance!

Anton · Answer

You are asking for terms that may only exist in specialist usage. If new terms are needed and are to be defined by you, I feel that the <=1 set should be given a name with singular overtones, and the >=2 set given a name with plural overtones. Echoes of other mathematical concepts should be avoided, so group/single is not good. For better examples, perhaps item/bunch, stick/bundle, flower/bouquet. Hence you might define your two sets with names such as an item set or a bunch set.
I wish I could think of better names but I can’t. Maybe onemax and onemin would do just as well.

Acccumulation · Answer

The problem is that you're asking for something that is not a property of the set itself, but how the elements of the set interact with some requirement. There's "mutually exclusive", but that refers to the options, not the set. For the other one, maybe "multi-choice". Or "one choice maximum" versus "one choice minimum".

Answered by Acccumulation on August 23, 2021

G. Rem · Answer

How about a stingy set, versus a generous set?  Specifically, a 1-stingy set, versus a 1-generous set.

A term for a set of which at most one element has to be selected

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