Mathematical, nominal numbering is an one-to-one function from a set of objects being named to the set of numerals: it is a function because each object is assigned a numeral, and it is one-to-one because different objects are assigned different numerals.
"Nominal number" can be broadly defined as "any numeral used for identification, however it was assigned", or narrowly as "a numeral with no information other than identification".
For the purposes of naming, the term "number" is often used loosely to refer to any string (sequence of symbols), which may not consist entirely of digits—it is often alphanumeric. For instance, National Insurance numbers, some driver's license numbers, and some serial numbers contain letters.
In general, the only meaningful operation with nominal numbers is to compare two nominal numbers to see whether they are equal or not (whether they refer to the same object).
These are usually assigned either in some hierarchical way, such as how telephone numbers are assigned (in NANPA) as Country Code + Area Code + Prefix + Suffix, where the first 3 are geographically based, or sequentially, as in serial numbers; these latter are thus properly ordinal numbers.
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