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.

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

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).

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