Editing Nominal number (section)

==Definition==
The term "nominal number" may be quite recent and of limited use. It appears{{citation needed|date=October 2012}} to have originated in school textbooks derived from the statistical term "[[nominal data]]", defined as data indicating "...merely statements of qualitative category of membership." This usage comes from the sense of [[wikt:nominal|nominal]] as "name".

Mathematically, nominal numbering is a [[Bijection|one-to-one and onto function]] from a set of objects being named to a set of numerals, which may change (typically growing) over time: it is a [[function (mathematics)|function]] because each object is assigned a single numeral, it is [[Injective function|one-to-one]] because different objects are assigned different numerals, and it is [[Injective function|onto]] because every numeral in the set at a given time has associated with it a single named object.

"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 (computer science)|string]] (sequence of symbols), which may not consist entirely of digits—it is often [[alphanumeric]]. For instance, UK [[National Insurance number]]s, some [[driver's licence]] numbers, and some [[serial number]]s contain letters.

===Use of nominal numbers===
"Nominal" refers to the ''use'' of numbers: any nominal number can be used by its [[numerical value]] as an [[integer]]—added to another, multiplied, compared in magnitude, and so forth—but for nominal numbers these operations are not, in general, meaningful. For example, the [[ZIP code]] 11111 is less than the ZIP code 12345, but that does not necessarily mean that 11111 was issued before 12345 or that the region denoted by 11111 is further south than 12345, though it might be. Similarly, one can add or subtract ZIP codes, but this is meaningless: {{nowrap|12345 − 11111}} does not have any meaning as a ZIP code.

In general, the only meaningful operation with nominal numbers is to compare two nominal numbers to see whether they are identical or not (whether they refer to the same object).

[[File:Arriva T6 nearside.JPG|thumb|right|Numbers 102 and 400: bus route 102 in [[London Buses|London]], run by an [[Alexander Dennis Enviro400]] [[double-decker bus]].]]
[[File:Peugeot 107 Dreitürer Scarletrot.JPG|thumb|Number 107: the car [[Peugeot 107]].]]