Editing Numbering scheme (section)

{{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 (database)|table]], whose table definitions require a [[database design]].

In [[computability theory]], the simplest [[Numbering (computability theory)|numbering]] scheme is the assignment of [[natural number]]s to a [[Set (mathematics)|set]] of objects such as [[function (mathematics)|function]]s, [[rational number]]s, [[Graph (discrete mathematics)|graph]]s, or words in some [[formal language]]. A numbering can be used to transfer the idea of computability<ref>{{Cite web|title=Computability Theory - an overview {{!}} ScienceDirect Topics|url=https://www.sciencedirect.com/topics/mathematics/computability-theory|access-date=2021-01-19|website=www.sciencedirect.com}}</ref> and related concepts, which are originally defined on the natural numbers using [[computable function]]s, to these different types of objects.

A simple extension is to assign [[cardinal number]]s 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 a set|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.