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There are many differentnumbering 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 aprimary key of adatabase management systemtable, whose table definitions require adatabase design.
Incomputability theory, the simplestnumbering scheme is the assignment ofnatural numbers to aset of objects such asfunctions,rational numbers,graphs, or words in someformal language. A numbering can be used to transfer the idea of computability[1] and related concepts, which are originally defined on the natural numbers usingcomputable functions, to these different types of objects.
A simple extension is to assigncardinal numbers to physical objects according to the choice of some base of reference and ofmeasurement units for counting or measuring these objects within a given precision. In such case, numbering is a kind ofclassification, i.e. assigning a numeric property to each object of the set to subdivide this set into related subsets forming apartition 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.
