Nominal number

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For the economics term, see real vs. nominal in economics.

Nominal numbers are numbers used for identification only. They do not indicate quantity, rank, or any other measurement. The properties of nominal numbers are the minimum required to refer to an entity as a number.

The term "nominal number" is quite recent, and appears to have originated as a usage in school textbooks derived from the statistical term "nominal data", defined as data indicating "...[m]erely statements of qualitative category of membership."

Mathematicians would typically describe this concept simply as a mapping between objects, or sets of objects, to the ordinal numbers.

Nontrivial numerical identifiers that are truly nominal numbers in the sense defined above are actually quite rare. For example, telephone numbers, zip codes, and transportation route numbers, although they may appear to be arbitrary, all actually either have internal structure or correlate with external quantities. Similarly, serial numbers are not nominal numbers in this sense, since they at the very least encode their allocation order. Sport jersey numbers may be a true example of nominal numbers, but it is difficult to tell whether they truly are, since it is in general unclear what policies are used by clubs to allocate them. For example, a club may "retire" a number that has become associated with a particularly famous player, but reallocate others to new players when they become available.