# 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)

## 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