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

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.

• This may not be what you want to hear, but the [insert word here] should be "set", and you should be focused instead on the second half of that sentence. If you want the [insert word here] to capture the notion that you're only choosing one element, then why go on to say, ".. we have to select at most one element"? Commented Sep 17, 2020 at 14:39
• If I were reading a mathematical article, I would not blink at all to see something like: "From the set S we select at most one element, and from the set T we select at least one element". Having a different name for those two objects wouldn't necessarily help clarify the issue. Commented Sep 17, 2020 at 14:40
• @BrendanW.Sullivan Thank you for your comment. You are right, in this case that would be a great solution. However, in my text, i refer to the type of set, not just the set itself. This happens many times, so writing it out each time is not a solution. I will change the example. Commented Sep 17, 2020 at 17:42
• You could borrow from user interface terminology and have a “radio selection set”
– Jim
Commented Oct 18, 2020 at 2:06

## 4 Answers

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".

• Multichoose means you can select a single element more than once. Singlechoose works like a deck of cards - it's no longer there after being chosen. Commented Sep 18, 2020 at 0:15
• The question spelled out precisely. Referring to how the set is to be handled, not what properties it possesses (it can even be the empty set). Commented Mar 12, 2022 at 15:52
• "mutually exclusive" is probably the best , although it doesn't clarify whether you must select 1 or can select none. Commented Sep 8, 2022 at 21:10

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.

While not one word, a "singular or empty selection set" would be clear without defining a new term. Avoid creating new vocabulary unless you really must do so.

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

• It's the handler, not the set, that is 'stingy'. Commented Mar 12, 2022 at 15:53