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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^[1] 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

References

^ Enderton, Herbert B. (2011). "Foreword". Computability Theory. pp. ix. doi:10.1016/B978-0-12-384958-8.00016-8. ISBN 978-0-12-384958-8.

[1] Enderton, Herbert B. (2011). "Foreword". Computability Theory. pp. ix. doi:10.1016/B978-0-12-384958-8.00016-8. ISBN 978-0-12-384958-8.