There are many different numbering schemes for assigning nominal numbers to entities. These generally require an agreed set of rules, or a central coordinator. The schemes can be considered to be examples of a primary key of a database management system

table Table may refer to: * Table (furniture), a piece of furniture with a flat surface and one or more legs * Table (landform), a flat area of land * Table (information), a data arrangement with rows and columns * Table (database), how the table data ...

, whose table definitions require a database design. In computability theory, the simplest

numbering There are many different numbering schemes for assigning nominal numbers to entities. These generally require an agreed set of rules, or a central coordinator. The schemes can be considered to be examples of a primary key of a database management ...

scheme is the assignment of

natural number In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''cardinal ...

s to a

set Set, The Set, SET or SETS may refer to: Science, technology, and mathematics Mathematics *Set (mathematics), a collection of elements *Category of sets, the category whose objects and morphisms are sets and total functions, respectively Electro ...

of objects such as

function Function or functionality may refer to: Computing * Function key, a type of key on computer keyboards * Function model, a structured representation of processes in a system * Function object or functor or functionoid, a concept of object-oriente ...

rational number In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator . For example, is a rational number, as is every integer (e.g. ). The set of all rat ...

graph Graph may refer to: Mathematics *Graph (discrete mathematics), a structure made of vertices and edges **Graph theory, the study of such graphs and their properties *Graph (topology), a topological space resembling a graph in the sense of discre ...

s, or words in some

formal language In logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules. The alphabet of a formal language consists of sy ...

. A numbering can be used to transfer the idea of computability and related concepts, which are originally defined on the natural numbers using

computable function Computable functions are the basic objects of study in computability theory. Computable functions are the formalized analogue of the intuitive notion of algorithms, in the sense that a function is computable if there exists an algorithm that can do ...

s, to these different types of objects. A simple extension is to assign

cardinal number In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality (size) of sets. The cardinality of a finite set is a natural number: the number of elements in the set. T ...

s to physical objects according to the choice of some base of reference and of measurement units for counting or measuring these objects within a given precision. In such case, numbering is a kind of classification, i.e. assigning a numeric property to each object of the set to subdivide this set into related subsets forming a

partition Partition may refer to: Computing Hardware * Disk partitioning, the division of a hard disk drive * Memory partition, a subdivision of a computer's memory, usually for use by a single job Software * Partition (database), the division of a ...

of the initial set, possibly infinite and not enumeratable using a single natural number for each class of the partition. In some cases (such as computing, time-telling, and in some countries the numbering of floors in buildings)

zero-based numbering Zero-based numbering is a way of numbering in which the initial element of a sequence is assigned the index 0, rather than the index 1 as is typical in everyday ''non-mathematical'' or ''non-programming'' circumstances. Under zero-base ...

is used, where the first entity is assigned "zero" instead of "one". Other numbering schemes are listed by field below.

Chemistry

CAS registry number A CAS Registry Number (also referred to as CAS RN or informally CAS Number) is a unique identification number assigned by the Chemical Abstracts Service (CAS), US to every chemical substance described in the open scientific literature. It inclu ...

s for chemical compounds * EC numbers for identifying

enzyme Enzymes () are proteins that act as biological catalysts by accelerating chemical reactions. The molecules upon which enzymes may act are called substrates, and the enzyme converts the substrates into different molecules known as products ...

s *

UN number A UN number (United Nations number) is a four-digit number that identifies hazardous materials, and articles (such as explosives, flammable liquids, oxidizers, toxic, toxic liquids, etc.) in the framework of international trade and transport. Some ...

s for (classes of) hazardous substances * E numbers for food additives

Communications

*The E.164 numbering plan for

telephone A telephone is a telecommunications device that permits two or more users to conduct a conversation when they are too far apart to be easily heard directly. A telephone converts sound, typically and most efficiently the human voice, into e ...

numbers, including: ** Country calling codes **

North American Numbering Plan The North American Numbering Plan (NANP) is a telephone numbering plan for twenty-five regions in twenty countries, primarily in North America and the Caribbean. This group is historically known as World Zone 1 and has the international calling ...

** Numbering plans by country ***Argentina:

Argentine telephone numbering plan In Argentina, area codes are two, three, or four digits long (after the initial zero). Local customer numbers are six to eight figures long. The total number of digits is ten, for example, phone number (11) 1234-5678 for Buenos Aires is made up o ...

***Australia:

Australian telephone numbering plan The Australian telephone numbering plan describes the allocation of phone numbers in Australia. It has changed many times, the most recent major reorganisation by the Australian Communications & Media Authority taking place between 1994 and ...

***China:

China telephone numbering plan Telephone numbers in China are organized according to the Chinese Telephone Code Plan. The numerical formats of landlines and mobile phones are different: landlines have area codes, whereas mobile phones do not. In major cities, landline numbers ...

***France: French telephone numbering plan ***Hong Kong:

Hong Kong telephone numbering plan Telephone numbers in Hong Kong are mostly eight-digit. Fixed land line numbers start with 2 or 3, mobile (cellular) phone numbers with 5, 6, 7 or 9, pager numbers with 7 and forwarding service with 8. Since the end of 1989, there have been no a ...

***India: India telephone numbering plan ***Japan:

Japanese telephone numbering plan Telephone numbers in Japan consist of an area code, an exchange number, and a subscriber number. Dialing prefixes * 001, 00xx, 002xx, 0091xx Carrier selection prefix * 184 Prefix to withhold caller ID * 186 Prefix to provide caller ID Types o ...

***Singapore:

Singapore telephone numbering plan Telephone numbers in Singapore, also known as the National Numbering Plan, are regulated by the Info-communications Media Development Authority (IMDA). Due to the small geographical size of Singapore, there are no area or trunk codes; all numbers ...

***United Kingdom: UK telephone numbering plan ***Germany: German telephone numbering plan *The

IP address An Internet Protocol address (IP address) is a numerical label such as that is connected to a computer network that uses the Internet Protocol for communication.. Updated by . An IP address serves two main functions: network interface ident ...

allocation scheme ( IANA) *The DNIC prefixes of

X.25 X.25 is an ITU-T standard protocol suite for packet-switched data communication in wide area networks (WAN). It was originally defined by the International Telegraph and Telephone Consultative Committee (CCITT, now ITU-T) in a series of drafts ...

NUAs (Network User Address) assigned by the

ITU The International Telecommunication Union is a specialized agency of the United Nations responsible for many matters related to information and communication technologies. It was established on 17 May 1865 as the International Telegraph Unio ...

Object identifier In computing, object identifiers or OIDs are an identifier mechanism standardized by the International Telecommunication Union (ITU) and ISO/IEC for naming any object, concept, or "thing" with a globally unambiguous persistent name. Syntax and le ...

s (OID)

Products

* The GS1 numbering scheme, including **

GTIN The Global Trade Item Number (GTIN) is an identifier for trade items, developed by the international organization GS1. Such identifiers are used to look up product information in a database (often by entering the number through a barcode scanne ...

for products, which includes the UPC and

EAN-13 The International Article Number (also known as European Article Number or EAN) is a standard describing a barcode symbology and numbering system used in global trade to identify a specific retail product type, in a specific packaging configurati ...

barcode A barcode or bar code is a method of representing data in a visual, machine-readable form. Initially, barcodes represented data by varying the widths, spacings and sizes of parallel lines. These barcodes, now commonly referred to as linear or o ...

s **

ISBN The International Standard Book Number (ISBN) is a numeric commercial book identifier that is intended to be unique. Publishers purchase ISBNs from an affiliate of the International ISBN Agency. An ISBN is assigned to each separate edition an ...

codes for books **

ISSN An International Standard Serial Number (ISSN) is an eight-digit serial number used to uniquely identify a serial publication, such as a magazine. The ISSN is especially helpful in distinguishing between serials with the same title. ISSNs ...

codes for periodicals *

Vehicle identification number A vehicle identification number (VIN) (also called a chassis number or frame number) is a unique code, including a serial number, used by the automotive industry to identify individual motor vehicles, towed vehicles, motorcycles, scooters ...

* Stock keeping unit (SKU)

People

Identification numbers

*National identification numbers ** Personal Numeric Code (Romania) **

Personal identification number (Denmark) The Danish Personal Identification number ( da, CPR-nummer or , kl, CPR-normu or ) is a national identification number, which is part of the personal information stored in the Civil Registration System ( da, Det Centrale Personregister, kl, Inu ...

** Social Security number (United States) ** Social Insurance Number (Canada) ** INSEE number (France) **

National Insurance National Insurance (NI) is a fundamental component of the welfare state in the United Kingdom. It acts as a form of social security, since payment of NI contributions establishes entitlement to certain state benefits for workers and their fami ...

number (United Kingdom) **

Aadhaar Aadhaar ( hi, आधार, ādhār, lit=base, foundation, bn, আধার) is a 12-digit unique identity number that can be obtained voluntarily by the citizens of India and resident foreign nationals who have spent over 182 days in twelve ...

(India) *

Personal Public Service Number The Personal Public Service Number (PPS Number) ( ga, Uimhir Phearsanta Seirbhíse Poiblí, or ) is an identifier issued by the Client Identity Services section of the Department of Social Protection, on behalf of the Minister for Social Protec ...

(Republic of Ireland) *

Tax file number A tax file number (TFN) is a unique identifier issued by the Australian Taxation Office (ATO) to each taxpaying entity — an individual, company, superannuation fund, partnership, or trust. Not all individuals have a TFN, and a business has both ...

(Australia) *

Unique Master Citizen Number Unique Master Citizen Number ( sh-Latn-Cyrl, Jedinstveni matični broj građana, Јединствени матични број грађана, separator=" / ", JMBG / ЈМБГ, mk, Единствен матичен број на граѓанин� ...

(former Yugoslavia) *

Det Centrale Personregister Det Centrale Personregister (CPR; kl, Inunnik Qitiusumik Nalunaarsuiffik, en, Civil Registration System) is the Realm of Denmark's nationwide civil registry. Established in 1968, the registry contains the name, address, Danish personal identif ...

(Denmark)

Ordinals for names

Regnal number Regnal numbers are ordinal numbers used to distinguish among persons with the same name who held the same office. Most importantly, they are used to distinguish monarchs. An ''ordinal'' is the number placed after a monarch's regnal name to differ ...

s **

Princes of Reuss Reuss (german: Reuß , ) was the name of several historical states located in present-day Thuringia, Germany. Several lordships of the Holy Roman Empire which arose after 1300 and became Imperial Counties from 1673 and Prince of the Holy Roman Em ...

** Popes' ordinals * Generational ordinal suffix to names

Topics

Dewey Decimal Classification The Dewey Decimal Classification (DDC), colloquially known as the Dewey Decimal System, is a proprietary library classification system which allows new books to be added to a library in their appropriate location based on subject. Section 4.1 ...

and

Universal Decimal Classification The Universal Decimal Classification (UDC) is a bibliographic and library classification representing the systematic arrangement of all branches of human knowledge organized as a coherent system in which knowledge fields are related and inter-link ...

for books *

West American Digest System The West American Digest System is a system of identifying points of law from reported cases and organizing them by topic and key number. The system was developed by West Publishing to organize the entire body of American law. This extensive taxon ...

legal topic numbering scheme

Geography and transport

Postal code A postal code (also known locally in various English-speaking countries throughout the world as a postcode, post code, PIN or ZIP Code) is a series of letters or digits or both, sometimes including spaces or punctuation, included in a postal a ...

s ** ZIP codes * Geocodes (used also as ''fine-grained postal codes''): **

Geohash Geohash is a public domain geocode system invented in 2008 by Gustavo NiemeyerEvidences at the Wayback Machine: labix.org in 2008, the G. Niemeyer's blog announcing Geohash *an article about Geohash witnessing and citing G. Niemeyer works, befor ...

Open Location Code The Open Location Code (OLC) is a geocode based in a system of regular grids for identifying an area anywhere on the Earth. It was developed at Google's Zürich engineering office, and released late October 2014. Location codes created by the OL ...

Global Location Number The Global Location Number (GLN) is part of the GS1 systems of standards. It is a simple tool used to identify a location and can identify locations uniquely where required. This identifier is compliant with norm ISO/IEC 6523. The GS1 Identifica ...

s by GS1 *

FIPS place code The Federal Information Processing Standards (FIPS) of the United States are a set of publicly announced standards that the National Institute of Standards and Technology (NIST) has developed for use in computer systems of non-military, American ...

s *

House numbering House numbering is the system of giving a unique number to each building in a street or area, with the intention of making it easier to locate a particular building. The house number is often part of a postal address. The term describes the num ...

schemes *

Floor numbering A storey (British English) or story (American English) is any level part of a building with a floor that could be used by people (for living, work, storage, recreation, etc.). Plurals for the word are ''storeys'' (UK) and ''stories'' (US). T ...

Room number A room number is a number assigned to a room within a building. Its purpose is to identify a particular room, and help building inhabitants locate that room. Room numbers may consist of three digits, but can be any number of digits. The room num ...

Line number In computing, a line number is a method used to specify a particular sequence of characters in a text file. The most common method of assigning numbers to lines is to assign every line a unique number, starting at 1 for the first line, and increme ...

* See also:

Country code Country codes are short alphabetic or numeric geographical codes (geocodes) developed to represent countries and dependent areas, for use in data processing and communications. Several different systems have been developed to do this. The term ...

;

Address (geography) An address is a collection of information, presented in a mostly fixed format, used to give the location of a building, apartment, or other structure or a plot of land, generally using border, political boundaries and street names as references, ...

Vehicles

Vehicle registration plate A vehicle registration plate, also known as a number plate (British English), license plate (American English), or licence plate ( Canadian English), is a metal or plastic plate attached to a motor vehicle or trailer for official identific ...

s *

British Carriage and Wagon Numbering and Classification A number of different numbering and classification schemes have been used for carriages and wagons on Britain's railways, and this page explains the principal systems. Carriages and wagons (either not self-propelled, or part of a multiple unit wh ...

British Rail locomotive and multiple unit numbering and classification A number of different numbering and classification schemes were used for locomotives and multiple units operated by British Railways (BR), and this page explains the principal systems. This section also covers the post-privatisation period, as th ...

* UIC classification of goods wagons

Roads

Road numbering schemes *

Arlington County, Virginia, street-naming system This article details the street-naming system of Arlington County, Virginia in the United States. Although the streets of Arlington County are not laid out on a grid plan, its local streets follow sequential numbered or alphabetic patterns tha ...

* China road numbering *

Great Britain road numbering scheme The Great Britain road numbering scheme is a numbering scheme used to classify and identify all roads in Great Britain. Each road is given a single letter (which represents the road's category) and a subsequent number (between 1 and 4 digits). ...

European route The international E-road network is a numbering system for roads in Europe developed by the United Nations Economic Commission for Europe (UNECE). The network is numbered from E1 up and its roads cross national borders. It also reaches Centr ...

UNECE The United Nations Economic Commission for Europe (ECE or UNECE) is one of the five regional commissions under the jurisdiction of the United Nations Economic and Social Council. It was established in order to promote economic cooperation and ...

Numbered highways in the United States Highways in the United States are split into at least four different types of systems: Interstate Highways, U.S. Highways, state highways, and county highways. Highways are generally organized by a route number or letter. These designations are ge ...

* Edmonton, Alberta#Street layout *

Montreal Montreal ( ; officially Montréal, ) is the second-most populous city in Canada and most populous city in the Canadian province of Quebec. Founded in 1642 as '' Ville-Marie'', or "City of Mary", it is named after Mount Royal, the triple ...

* Highways in Australia#Route numbering systems

Others/general

API well numbers An API well number or API number is a "unique, permanent, numeric identifier" assigned to each oil well, well drilled for oil and gas in the United States.American Petroleum Institute, 1979, The API well number and standard state and county numeric ...

for numbering

oil and gas A fossil fuel is a hydrocarbon-containing material formed naturally in the Earth's crust from the remains of dead plants and animals that is extracted and combustion, burned as a fuel. The main fossil fuels are coal, petroleum, oil, and natura ...

wells in the

United States The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territori ...

Bank card number A payment card number, primary account number (PAN), or simply a card number, is the card identifier found on payment cards, such as credit cards and debit cards, as well as stored-value cards, gift cards and other similar cards. In some situat ...

International Bank Account Number The International Bank Account Number (IBAN) is an internationally agreed system of identifying bank accounts across national borders to facilitate the communication and processing of cross border transactions with a reduced risk of transcription ...

International Geo Sample Number The International Generic Sample Number or IGSN is a persistent identifier for sample. As an active persistent identifier it can be resolved through the Handle System. The system is used in production by the System for Earth Sample Registration (S ...

(IGSN) * International Statistical Classification of Diseases and Related Health Problems for

disease A disease is a particular abnormal condition that negatively affects the structure or function of all or part of an organism, and that is not immediately due to any external injury. Diseases are often known to be medical conditions that a ...

s *The

MAC address A media access control address (MAC address) is a unique identifier assigned to a network interface controller (NIC) for use as a network address in communications within a network segment. This use is common in most IEEE 802 networking tec ...

allocation scheme for hardware addresses of certain networking products *

National Animal Identification System The National Animal Identification System, (naisG) is a government-run program in the United States intended to extend government animal health surveillance by identifying and tracking specific animals. Administered at the federal level by the Anim ...

* National Pokédex *The NSAP allocation scheme * Post office box * Production code number * Stamp numbering system * Wikipedia markup syntax for numbered lists

References

{{Authority control *