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^[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[edit]

CAS Registry Numbers for chemical compounds
EC numbers for identifying enzymes
UN numbers for (classes of) hazardous substances
E numbers for food additives

Communications[edit]

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[edit]

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)