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For example, the arity property of a function might be unary or binary. The (???) property of a variable might be discrete or continuous?

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  • Depending on what you're talking about (discrete ~ continuous is a cline that covers a lot of semantic territory), one could speak of dimensionality (points are discrete, lines are continuous), granularity (stones ~ stone; beans ~ rice), subcategorization (weigh X ~ count X), etc. See Frawley's Linguistic Semantics for available categories, like the ones for Entities, i.e, "nouns".
    – John Lawler
    May 27, 2014 at 20:15
  • Have you tried asking on Mathematics ? I think it's OT here.
    – Kris
    May 28, 2014 at 9:29

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Since I didn't recognize the word arity, I looked it up. OED defines it as

The number of elements by virtue of which something is unary, binary, etc.
First citation (emphasis mine):
1968 ...the order of enlargeability and the arity or the order of reducibility of abstract algebras

In light of that I'm inclined to favour an -ability type of word. The first one that came to mind was quantisability - which you probably won't find in any dictionaries (yet! :), but which I would naturally understand as...

quantisability - an attribute defining whether/to what extent something can be quantized
...from...
quantize - to approximate (a signal varying continuously in amplitude) by one whose amplitude is restricted to a prescribed set of discrete values. (Again, emphasis mine)

It's my understanding that if a variable can be quantized, it's digital/discrete. If not, it's continuous.

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A variable can only take on one value at a time. Therefore it is neither discrete nor continuous. It just has a value.

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