Editing Numbering scheme

{{Short description|System of rules for assigning mathematical values to database items}}
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 (database)|table]], whose table definitions require a [[database design]].

In [[computability theory]], the simplest [[Numbering (computability theory)|numbering]] scheme is the assignment of [[natural number]]s to a [[Set (mathematics)|set]] of objects such as [[function (mathematics)|function]]s, [[rational number]]s, [[Graph (discrete mathematics)|graph]]s, or words in some [[formal language]]. A numbering can be used to transfer the idea of computability<ref>{{Cite web|title=Computability Theory - an overview {{!}} ScienceDirect Topics|url=https://www.sciencedirect.com/topics/mathematics/computability-theory|access-date=2021-01-19|website=www.sciencedirect.com}}</ref> and related concepts, which are originally defined on the natural numbers using [[computable function]]s, to these different types of objects.

A simple extension is to assign [[cardinal number]]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 of a set|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 Number]]s for chemical compounds
*[[Enzyme Commission number|EC numbers]] for identifying [[enzyme]]s
*[[UN number]]s for (classes of) hazardous substances 
*[[E number]]s for [[food additive]]s

==Communications==
*The [[E.164]] numbering plan for [[telephone]] numbers, including:
**[[Country calling code]]s
**[[North American Numbering Plan]]
**[[Telephone 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: [[Telephone numbers in India|India telephone numbering plan]]
***Japan: [[Japanese telephone numbering plan]]
***Singapore: [[Singapore telephone numbering plan]]
***United Kingdom: [[Telephone numbers in the United Kingdom|UK telephone numbering plan]]
***Germany: [[Telephone numbers in Germany|German telephone numbering plan]]
*The [[IP address]] allocation scheme ([[Internet Assigned Numbers Authority|IANA]])
*The [[Data Network Identification Code|DNIC]] prefixes of [[X.25]] NUAs (Network User Address) assigned by the [[International Telecommunication Union|ITU]]
*[[Object identifier]]s (OID)

==Computing==

*[[Line number]]

==Products==

* The [[GS1]] numbering scheme, including
** [[GTIN]] for products, which includes the [[Universal Product Code|UPC]] and [[EAN-13]] [[barcode]]s
** [[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 number]]s
**[[Princes of Reuss]]
**[[List of popes#Numbering of popes|Popes' ordinals]]
* [[Suffix (name)#Generational titles|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]]s
**[[ZIP code]]s
* Geocodes (used also as ''fine-grained postal codes''):
** [[Geohash]]
** [[Open Location Code]]
*[[Global Location Number]]s by [[GS1]]
*[[FIPS place code]]s
*[[House numbering]] schemes
*[[Floor numbering]]
*[[Room number]]
* See also: [[Country code]]; [[Address (geography)]].

===Vehicles===
* [[Vehicle registration plate]]s
* [[British Carriage and Wagon Numbering and Classification]]
* [[British Rail locomotive and multiple unit numbering and classification]]
* [[UIC classification of goods wagons]]

===Roads===

[[Road numbering scheme]]s
*[[Arlington County, Virginia, street-naming system]]
*[[China road numbering]]
*[[Great Britain road numbering scheme]]
*[[European route]] by [[United Nations Economic Commission for Europe|UNECE]]
*[[Numbered highways in the United States]]
*[[Edmonton, Alberta#Street layout]]
*[[Montreal#Street grid system|Montreal]]
*[[Highways in Australia#Route numbering systems]]

==Others/general==
*[[API well numbers]] for numbering [[Natural gas|oil and gas]] [[Oil well|wells]] in the [[United States]]
*[[Bank card number]]
*[[International Bank Account Number]]
*[[International Geo Sample Number]] (IGSN)
*[[ICD|International Statistical Classification of Diseases and Related Health Problems]] for [[disease]]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#Numbering of boxes|Post office box]]
*[[Production code number]]
*[[Stamp numbering system]]
*[[Help:Wiki markup#Lists|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}}

{{Authority control}}

[[Category:Identifiers|*]]