Editing Nominal number

{{short description|Numeric or alphanumeric code (without independent meaning) used for labelling or identification}}
{{For|the [[economics]] term|Real vs. nominal in economics}}
{{More citations needed|date=March 2008}}
'''Nominal numbers''' are numerals used as labels to [[Unique identifier|identify items uniquely]]. Importantly, the actual values of the numbers which these numerals represent are less relevant, as they do not indicate quantity, rank, or any other measurement.

Labelling referees Smith and Kumar as referees "1" and "2" is a use of nominal numbers. Any set of numbers (a subset of the natural numbers) will be consistent labels as long as a ''distinct'' number is uniquely used for each distinct term which needs to be labelled. Nonetheless, sequences of integers may naturally be used as the simplest way to begin labelling; for example, 1, 2, 3, and so on.

==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]].]]

==Examples==
A great variety of numbers meet the broad definition, including:
* [[National identification number]]s, such as:
** [[Social Security number]]s
** [[Driver's license]] numbers
** [[National Insurance number]]
* [[Routing]] numbers, such as:
** [[Bank code]]s and [[sort code]]s, such as [[International Bank Account Number]]s or [[ABA routing transit number]]s.
** [[Postal code]]s, such as [[ZIP code]]s (These are generally numeric in the United States, but other nations often use alphanumeric systems.)
** [[Telephone number]]s, assigned by various [[telephone numbering plan]]s, such as the [[ITU-T]] [[E.164]] and the [[North American Numbering Plan]] (NANPA).
** Numbers of train or bus routes or the individual vehicles in public transport
* [[Car model]] names from some car manufacturers, such as [[BMW]] or [[Peugeot]], are plain numbers.

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 three are geographically based, or sequentially, as in [[serial number]]s; these latter are thus properly ''ordinal'' numbers.

===Narrowly defined===
Numerical identifiers that are nominal numbers narrowly defined, viz, convey no information other than identity, are quite rare. These must be defined either arbitrarily or randomly, and most commonly arise in computer applications, such as dynamic [[IP address]]es assigned by [[Dynamic Host Configuration Protocol]]. A more everyday example are sports [[squad number]]s, which do not in general have any public meaning beyond identity, though they may be allocated based on some internal club or organization policy. In some settings, these are based on position, but in others they are associated with an individual, being a proper nominal number. The naming function is demonstrated by [[Squad number#Retired numbers|"retired numbers"]], where a club no longer issues a number that has become associated with a particularly famous player, but reallocate others to new players when they become available.

== See also ==
* [[Numbering scheme]]
* [[Serial number]]
* [[Symbol (programming)]]
* [[Unique key]]
* [[Universally Unique Identifier]]

==External links==
*[http://www.mathsisfun.com/numbers/cardinal-ordinal-nominal.html Cardinal, Ordinal and Nominal Numbers]
*[http://www.factmonster.com/ipka/A0875618.html Cardinal, Ordinal, and Nominal Numbers]
*{{cite book |first1=Alfred S. |last1=Posamentier |first2=William |last2=Farber |first3=Terri L. |last3=Germain-Williams |first4=Elaine |last4=Paris |first5=Bernd |last5=Thaller |first6=Ingmar |last6=Lehmann |year=2013 |chapter=Nominal Numbers |chapter-url=https://books.google.com/books?id=WQ51AQAAQBAJ&pg=PA60 |page=60 |title=100 Commonly Asked Questions in Math Class |publisher=Corwin Press |isbn=978-1-4833-3399-1}}

[[Category:Identifiers]]
[[Category:Numerals]]