Numbering scheme

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, whose table definitions require a database design.

In computability theory, the simplest numbering scheme is the assignment of natural numbers to a set of objects such as functions, rational numbers, graphs, or words in some formal language. 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 numbers 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 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 enzymes
 * UN numbers for (classes of) hazardous substances
 * E numbers for food additives

Communications

 * The E.164 numbering plan for telephone numbers, including:
 * Country calling codes
 * North American Numbering Plan
 * 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 allocation scheme (IANA)
 * The DNIC prefixes of X.25 NUAs (Network User Address) assigned by the ITU
 * Object identifiers (OID)

Computing

 * Line number

Products

 * The GS1 numbering scheme, including
 * GTIN for products, which includes the UPC and EAN-13 barcodes
 * ISBN codes for books
 * ISSN codes for periodicals
 * Vehicle identification number
 * Stock keeping unit (SKU)

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 (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 codes
 * ZIP codes
 * Geocodes (used also as fine-grained postal codes):
 * Geohash
 * Open Location Code
 * Global Location Numbers by GS1
 * FIPS place codes
 * House numbering schemes
 * Floor numbering
 * Room number
 * See also: Country code; Address (geography).

Vehicles

 * Vehicle registration plates
 * British Carriage and Wagon Numbering and Classification
 * British Rail locomotive and multiple unit numbering and classification
 * 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
 * Numbered highways in the United States
 * Edmonton, Alberta
 * Montreal
 * Highways in Australia

Others/general

 * API well numbers for numbering oil and gas wells in the United States
 * Bank card number
 * International Bank Account Number
 * International Geo Sample Number (IGSN)
 * International Statistical Classification of Diseases and Related Health Problems for diseases
 * 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