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 In computing, a database is an organized collection of data or a type of data store based on the use of a database management system (DBMS), the software that interacts with end users, applications, and the database itself to capture and an ...

table, whose table definitions require a database design. In

computability theory Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. The field has since ex ...

, the simplest numbering scheme is the assignment of

natural number In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...

s to a set of objects such as functions,

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 (for example, The set of all ...

s, graphs, or words in some

formal language In logic, mathematics, computer science, and linguistics, a formal language is a set of strings whose symbols are taken from a set called "alphabet". The alphabet of a formal language consists of symbols that concatenate into strings (also c ...

. A numbering can be used to transfer the idea of computability and related concepts, which are originally defined on the natural numbers using computable functions, to these different types of objects. A simple extension is to assign

cardinal number In mathematics, a cardinal number, or cardinal for short, is what is commonly called the number of elements of a set. In the case of a finite set, its cardinal number, or cardinality is therefore a natural number. For dealing with the cas ...

s to physical objects according to the choice of some base of reference and of

measurement Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement is a process of determining how large or small a physical quantity is as compared to ...

units for counting or measuring these objects within a given precision. In such case, numbering is a kind of

classification Classification is the activity of assigning objects to some pre-existing classes or categories. This is distinct from the task of establishing the classes themselves (for example through cluster analysis). Examples include diagnostic tests, identif ...

, i.e. assigning a numeric property to each object of the set to subdivide this set into related subsets forming a partition 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 is used, where the first entity is assigned "zero" instead of "one". Other numbering schemes are listed by field below.

Chemistry

* CAS Registry Numbers for chemical compounds * EC numbers for identifying

enzyme An enzyme () is a protein that acts as a biological catalyst by accelerating chemical reactions. The molecules upon which enzymes may act are called substrate (chemistry), substrates, and the enzyme converts the substrates into different mol ...

s * UN numbers for (classes of) hazardous substances *

E number E numbers, short for Europe numbers, are codes for substances used as food additives, including those found naturally in many foods, such as vitamin C, for use within the European Union (EU) and European Free Trade Association (EFTA). Commonly ...

s for

food additive Food additives are substances added to food to preserve flavor or enhance taste, appearance, or other sensory qualities. Some additives, such as vinegar ( pickling), salt ( salting), smoke ( smoking) and sugar ( crystallization), have been used f ...

Communications

*The E.164 numbering plan for

telephone A telephone, colloquially referred to as a phone, is a telecommunications device that enables 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 ...

numbers, including: ** Country calling codes **

North American Numbering Plan The North American Numbering Plan (NANP) is an integrated 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, World Numbering Zone ...

** Numbering plans by country ***Argentina: Argentine telephone numbering plan ***Australia: Australian telephone numbering plan ***China: China telephone numbering plan ***France: French telephone numbering plan ***Hong Kong: Hong Kong telephone numbering plan ***India: India telephone numbering plan ***Japan: Japanese telephone numbering plan ***Singapore: Singapore telephone numbering plan ***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 assigned to a device connected to a computer network that uses the Internet Protocol for communication. IP addresses serve two main functions: network interface i ...

allocation scheme ( IANA) *The DNIC prefixes of

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

NUAs (Network User Address) assigned by the ITU * Object identifiers (OID)

Computing

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 increm ...

Products

* The GS1 numbering scheme, including ** GTIN for products, which includes the UPC and EAN-13 barcodes **

ISBN The International Standard Book Number (ISBN) is a numeric commercial book identifier that is intended to be unique. Publishers purchase or receive ISBNs from an affiliate of the International ISBN Agency. A different ISBN is assigned to e ...

codes for books **

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

codes for periodicals * Vehicle identification number *

Stock keeping unit In inventory management, a stock keeping unit (abbreviated as SKU, pronounced or ) is the unit of measure in which the stocks of a material are managed. It is a distinct type of item for sale, purchase, or tracking in inventory, such as a produ ...

(SKU)

People

Identification numbers

*National identification numbers ** Personal Numeric Code (Romania) ** Personal identification number (Denmark) ** Social Security number (United States) ** Social insurance number (Canada) ** INSEE number (France) ** National Insurance number (United Kingdom) **

Aadhaar Aadhaar (Hindi: आधार, ) is a twelve-digit unique identity number that can be obtained voluntarily by all residents of India, based on their biometrics and demography, demographic data. The data is collected by the Unique Identification ...

(India) * Personal Public Service Number (Republic of Ireland) * Tax file number (Australia) * Unique Master Citizen Number (former Yugoslavia) * Det Centrale Personregister (Denmark)

Ordinals for names

* Regnal numbers ** Princes of Reuss ** Popes' ordinals * Generational ordinal suffix to names

Topics

* Dewey Decimal Classification and Universal Decimal Classification for books * West American Digest System 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 numerical digit, digits or both, sometimes including spaces or punctuation, inclu ...

s ** ZIP codes * Geocodes (used also as ''fine-grained postal codes''): ** Geohash ** Open Location Code * Global Location Numbers by GS1 * FIPS place codes *

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 Address (geography), postal address. The ter ...

schemes * Floor numbering * Room number * See also:

Country code A country code is a short alphanumeric identification code for countries and dependent areas. Its primary use is in data processing and communications. Several identification systems have been developed. The term ''country code'' frequently re ...

;

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 political boundaries and street names as references, along ...

Vehicles

* Vehicle registration plates * British Carriage and Wagon Numbering and Classification *

British Rail locomotive and multiple unit numbering and classification #REDIRECT British Rail locomotive and multiple unit numbering and classification {{R from other capitalisation ...

* UIC classification of goods wagons

Roads

Road numbering schemes * Arlington County, Virginia, street-naming system * China road numbering * Great Britain road numbering scheme * European route by

UNECE The United Nations Economic Commission for Europe (ECE or UNECE) is an intergovernmental organization or a specialized body of the United Nations. The UNECE is one of five regional commissions under the jurisdiction of the United Nations Econ ...

* Numbered highways in the United States * Edmonton, Alberta#Street layout *

Montreal Montreal is the List of towns in Quebec, largest city in the Provinces and territories of Canada, province of Quebec, the List of the largest municipalities in Canada by population, second-largest in Canada, and the List of North American cit ...

* Highways in Australia#Route numbering systems

Others/general

* API well numbers for numbering oil and gas wells in the

United States The United States of America (USA), also known as the United States (U.S.) or America, is a country primarily located in North America. It is a federal republic of 50 U.S. state, states and a federal capital district, Washington, D.C. The 48 ...

* Bank card number * International Bank Account Number * International Geo Sample Number (IGSN) * International Statistical Classification of Diseases and Related Health Problems for

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

s *The MAC address allocation scheme for hardware addresses of certain networking products * National Animal Identification System * National Pokédex *The NSAP allocation scheme * Post office box * Production code number * Stamp numbering system * Wikipedia markup syntax for numbered lists

References

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