Nominal number
Encyclopedia
Nominal numbers are numerals
used for identification only. The numerical value is irrelevant, and they do not indicate quantity, rank, or any other measurement.
Mathematically, nominal numbering is a 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 number
s, some driver's license
numbers, and some serial number
s contain letters.
—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 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: 11111 - 12345 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 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 number
s; these latter are thus properly ordinal numbers.
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 retired numbers, where a club "retires" a number that has become associated with a particularly famous player, but reallocate others to new players when they become available.
Numeral system
A numeral system is a writing system for expressing numbers, that is a mathematical notation for representing numbers of a given set, using graphemes or symbols in a consistent manner....
used for identification only. The numerical value is irrelevant, and they do not indicate quantity, rank, or any other measurement.
Definition
The term "nominal number" is quite recent and of limited use. It 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." This usage comes from the sense of nominal as "name".Mathematically, nominal numbering is a one-to-one function
Function (mathematics)
In mathematics, a function associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can...
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
String (computer science)
In formal languages, which are used in mathematical logic and theoretical computer science, a string is a finite sequence of symbols that are chosen from a set or alphabet....
(sequence of symbols), which may not consist entirely of digits—it is often alphanumeric
Alphanumeric
Alphanumeric is a combination of alphabetic and numeric characters, and is used to describe the collection of Latin letters and Arabic digits or a text constructed from this collection. There are either 36 or 62 alphanumeric characters. The alphanumeric character set consists of the numbers 0 to...
. For instance, National Insurance number
National Insurance number
The National Insurance number is a number used in the United Kingdom in the administration of the National Insurance or social security system. It is also used for some purposes in the UK tax system...
s, some driver's license
Driver's license
A driver's license/licence , or driving licence is an official document which states that a person may operate a motorized vehicle, such as a motorcycle, car, truck or a bus, on a public roadway. Most U.S...
numbers, and some serial number
Serial number
A serial number is a unique number assigned for identification which varies from its successor or predecessor by a fixed discrete integer value...
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 integerInteger
The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...
—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
ZIP Code
ZIP codes are a system of postal codes used by the United States Postal Service since 1963. The term ZIP, an acronym for Zone Improvement Plan, is properly written in capital letters and was chosen to suggest that the mail travels more efficiently, and therefore more quickly, when senders use the...
11111 is less than the ZIP code 12345, but that does not 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: 11111 - 12345 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 equal or not (whether they refer to the same object).
Examples
A great variety of numbers meet the broad definition, including:- National identification numberNational identification numberA national identification number, national identity number, or national insurance number is used by the governments of many countries as a means of tracking their citizens, permanent residents, and temporary residents for the purposes of work, taxation, government benefits, health care, and other...
s, such as:- Social Security numberSocial Security numberIn the United States, a Social Security number is a nine-digit number issued to U.S. citizens, permanent residents, and temporary residents under section 205 of the Social Security Act, codified as . The number is issued to an individual by the Social Security Administration, an independent...
s - Driver's licenseDriver's licenseA driver's license/licence , or driving licence is an official document which states that a person may operate a motorized vehicle, such as a motorcycle, car, truck or a bus, on a public roadway. Most U.S...
numbers - National Insurance numberNational Insurance numberThe National Insurance number is a number used in the United Kingdom in the administration of the National Insurance or social security system. It is also used for some purposes in the UK tax system...
- Social Security number
- RoutingRoutingRouting is the process of selecting paths in a network along which to send network traffic. Routing is performed for many kinds of networks, including the telephone network , electronic data networks , and transportation networks...
numbers, such as:- Bank codeBank codeA Bank Code is a code assigned by a central bank, a Bank Supervisory Body or a Bankers Association in a country to all its licensed member banks. The rules vary to a great extent between the countries. Also the name of such a code varies...
s and sort codeSort CodeA sort code is the name given by both the British and Irish banking industry to the bank codes which are used to route money transfers between banks within their respective countries via their respective clearance organisations. In Ireland it is known as the NSC or National Sort Code and is...
s, like IBANInternational Bank Account NumberThe International Bank Account Number is an international standard for identifying bank accounts across national borders with a minimal risk of propagating transcription errors. It was originally adopted by the European Committee for Banking Standards , and was later adopted as an international...
, and the ABAAmerican Bankers AssociationThe American Bankers Association is an industry trade group and professional association representing the United States' banking industry...
Routing transit numberRouting transit numberA routing transit number is a nine digit bank code, used in the United States, which appears on the bottom of negotiable instruments such as checks identifying the financial institution on which it was drawn...
. - Postal codePostal codeA postal code is a series of letters and/or digits appended to a postal address for the purpose of sorting mail. Once postal codes were introduced, other applications became possible.In February 2005, 117 of the 190 member countries of the Universal Postal Union had postal code systems...
s, such as ZIP codeZIP CodeZIP codes are a system of postal codes used by the United States Postal Service since 1963. The term ZIP, an acronym for Zone Improvement Plan, is properly written in capital letters and was chosen to suggest that the mail travels more efficiently, and therefore more quickly, when senders use the...
s (These are generally numeric in the United States, but other nations often use alphanumeric systems.) - Telephone numberTelephone numberA telephone number or phone number is a sequence of digits used to call from one telephone line to another in a public switched telephone network. When telephone numbers were invented, they were short — as few as one, two or three digits — and were given orally to a switchboard operator...
s, assigned by various telephone numbering planTelephone numbering planA telephone numbering plan is a type of numbering scheme used in telecommunications to allocate telephone numbers to subscribers and to route telephone calls in a telephone network. A closed numbering plan, such as found in North America, imposes a fixed total length to numbers...
s, such as the ITU-TITU-TThe ITU Telecommunication Standardization Sector is one of the three sectors of the International Telecommunication Union ; it coordinates standards for telecommunications....
E.164E.164E.164 is an ITU-T recommendation that defines the international public telecommunication numbering plan used in the PSTN and some other data networks. It also defines the format of telephone numbers. E.164 numbers can have a maximum of fifteen digits and are usually written with a + prefix...
and the North American Numbering PlanNorth American Numbering PlanThe North American Numbering Plan is an integrated telephone numbering plan administered by Neustar which encompasses 24 countries and territories, including the United States and its territories, Canada, Bermuda, and 16 nations of the Caribbean...
(NANPA). - Numbers of city-bus routes
- Bank code
- Magic numbersMagic number (programming)In computer programming, the term magic number has multiple meanings. It could refer to one or more of the following:* A constant numerical or text value used to identify a file format or protocol; for files, see List of file signatures...
These are usually assigned either in some hierarchical way, such as how telephone numbers are assigned (in NANPA) as Country Code
Country code
Country codes are short alphabetic or numeric geographical codes developed to represent countries and dependent areas, for use in data processing and communications. Several different systems have been developed to do this. The best known of these is ISO 3166-1...
+ Area Code + Prefix + Suffix, where the first 3 are geographically based, or sequentially, as in serial number
Serial number
A serial number is a unique number assigned for identification which varies from its successor or predecessor by a fixed discrete integer value...
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 addressIP address
An Internet Protocol address is a numerical label assigned to each device participating in a computer network that uses the Internet Protocol for communication. An IP address serves two principal functions: host or network interface identification and location addressing...
es assigned by Dynamic Host Configuration Protocol
Dynamic Host Configuration Protocol
The Dynamic Host Configuration Protocol is a network configuration protocol for hosts on Internet Protocol networks. Computers that are connected to IP networks must be configured before they can communicate with other hosts. The most essential information needed is an IP address, and a default...
. A more everyday example are sports squad number
Squad number
In team sports, the squad number, shirt number, jersey number, sweater number, uniform number or simply a number is the number worn on a player's uniform, to identify and distinguish each player from others wearing the same or similar uniforms...
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 retired numbers, where a club "retires" a number that has become associated with a particularly famous player, but reallocate others to new players when they become available.