A numbering scheme is a process of 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".
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: Telephone country codes North American Numbering Plan Numbering plans by country 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)
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 (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#Street layout Montreal Highways in Australia#Route numbering systems
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
See also naming scheme Digital Object Identifier Pagination Stephanus pagination for works of Plato Bekker numbers for the works of Aristotle Persistent identifier Unique identifier UUID
References