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For example; I am constructing a web page that asks two questions. The first question is titled Marital status: from a list of choices; there can be only one. The other is a multiple-checkbox asking Devices owned, here there could be none, some, or all choices selected.

I'm seeking a word which differentiates the two types with respect to how one allows multiple selections, and the other does not. Words that are close, but don't cut it are things like "multiplicity", "factor" or "deviation".

In computer programming we use such interesting words like singleton, scalar, and idempotent. Is there a discriminating word for "multiple choice / single choice"?

It's difficult to put into a sentence without getting too technical, I'm building an application that has different strategies for validating answers based on if they are multiple choice or not. There are two strategies: one for answers that can only have one choice selected at a time, and one that can have N choices. The "strategy" is used to determine which [insert word] validation strategy to employ.

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    If you were to put an example sentence into which the word sought would be used you'd get better answers. – P. O. Jun 23 '16 at 14:14
  • Actually, the first is not a single choice -- it's what we usually call a Y/N question -- a "binary" -- and the other is an "n-ary". In any case, this rather academic terminology may not be useful in your context. User interfaces always explain at greater length -- "Hold Ctrl key to select multiple options from the list" and so on. HTH. – Kris Jun 23 '16 at 14:17
  • Even, "Marital status: Married - Single - Divorced - Other" – Kris Jun 23 '16 at 14:19
  • Something like cardinality? – Damkerng T. Jun 23 '16 at 14:22
  • Cardinality is pretty good, actually. I've expanded my question, a little bit. – Lunster Jun 23 '16 at 14:27
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I believe you are referring to quantifiers. In natural language, quantifiers are words or phrases like each, any, all, one, some, several, many, a few of, lots of, and more. These words indicate the number or amount of something.

Since you mention computer programming, you may also already be aware of two other uses of quantifier in our field. One of these is REGEX, where the quantifier symbols +, ?, *, and {n} specify one or more, zero or one, zero or more, and exactly n matches respectively. Also in SQL, "select distinct" or "where exists" clauses within queries are called quantifiers.

Your title mentions mathematics. This field also uses the word quantifier, specifically in logic. When a theorem is phrased "For all natural numbers, blah..." or "There exists a set which blah..." the portions "for all" and "there exists" are quantifiers. Note the words are similar to those used in natural language, but are more precisely defined here. The methods used to prove such theorems may vary depending on the quantifiers.

The difference between a radio button group and a check box group is what kind of quantifier dictates its behavior.

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