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For example, a bit or a boolean can be either 0 or 1 so the number 2 is associated with it. Similarly, for a byte which is 8 bits, the maximum number of different assignments would be 2^8.

Is there a name for this number?

When we pass everything through our system that has ECMAScript, Java and MySQL, then a boolean does not have only two possible assignments. For instance, a false boolean gets saved as a 0 and the boxed value could be null so a boolean suddenly can get true, false, 0, 1, null or even undefined or <missing>.

I think it could get problematic in tests to guarantee that the values are not inconsistent. For instance, a value boolean locked could become null and then when a script or a layout template evaluates it then it will evaluate to false somewhere if the real value was null and similar problems.

So why don't we always assert that a boolean has the same number of possible values (2 values) and similarly for other types?

There is a mathematical term named "arity" that is something similar but not exactly, and statistics and probability theory also has the concept of "event space" that would be almost exactly what I mean. For instance, the event space for a boolean would be the set {0,1} which has cardinality 2 and that cardinality doesn't get preserved throughout the system, especially when data is passed as polyglots and/or serialized (json, jsonp, xml, yaml).

Radiodef
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Niklas Rosencrantz
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2 Answers2

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I would call it cardinality (and indeed I have used it in that sense). It is strictly the cardinality of the set of all values a variable can take.

Edit: for example, a 16-bit integer can take exactly 65536 values. The cardinality of the set of all values that the integer can take is 655536.

Once you start to consider variables that have a range of valid values and also a range of invalid values (like a boolean with a bitwise value of 17), then you have to extend the concept somewhat, but you can still describe those values with set notation and the concept of cardinality still applies.

Edit: Yes, this is the mathematical set, not programming Set. If you were to apply the concept to the C# type short and derive the type short?, this would not have 65537 values, represented by the union of the set of 65536 values mentioned previously and one additional value, null.

david.pfx
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If you subscribe to the "types as a set of values" interpretation of type theory, then cardinality is in fact a good name.

So, the cardinality of bool would be 2, the cardinality of byte would be 256, and the cardinality of String would be &aleph;0.

Jörg W Mittag
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