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Yeah, this is a pretty significant difference between a set and an element.

The fix is simple: Put the type of the variable in the type name. Then "UnitInterval proportion" tells you everything you need to know.

That's three words though, and the SO OP asked for a single word.

I like this idea of using the type name to define the domain, and variable name to define the purpose.

Names of types usually refer to individual members thereof: number, integer, vector, string, list… A variable of a UnitInterval type would one that holds unit intervals. This is no fix.

"Belongs to the unit interval" is correct, but I like to think most of us have gotten enough exposure to cognitive science to know that the brain prefers to have a word or adjective for everything, and that's the problem here.

Also, Unit Interval is only an answer to this exact question, not a class of questions to which this one belongs. If the range was [0,5] then you couldn't even shorten it with Unit Interval.

I guess this is like "mammal" vs "mammalia".