{{Short description|System of rules for assigning mathematical values to database items}}{{Onesource|article|date=September 2025}} 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<ref>{{cite book |title=Computability Theory |chapter=Foreword |date=2011 |pages=ix |doi=10.1016/B978-0-12-384958-8.00016-8 |isbn=978-0-12-384958-8 |first1=Herbert B. |last1=Enderton }}</ref> 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==
==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=== {{main|:Category:National 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== {{Reflist}}
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