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, 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".

Other numbering schemes are listed by field below.

## Contents

* 1 Chemistry
* 2 Communications
* 3 Products
* 4 People
* 4.1 Identification numbers
* 4.2 Ordinals for names
* 5 Topics
* 6 Geography and transport
* 6.1 Vehicles
* 6.2 Roads
* 7 Others/general
* 8 See also
* 9 References

## 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)

## 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
* Line 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

1. ↑ "Computability Theory - an overview | ScienceDirect Topics". https://www.sciencedirect.com/topics/mathematics/computability-theory.

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