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 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
  - 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)