Nominal number

Source: Wikipedia, the free encyclopedia.

Nominal numbers are numerals used as labels to identify items uniquely. Importantly, the actual values of the numbers which these numerals represent are less relevant, as they do not indicate quantity, rank, or any other measurement.

Labelling referees Smith and Kumar as referees "1" and "2" is a use of nominal numbers. Any set of numbers (a subset of the natural numbers) will be consistent labels as long as a distinct number is uniquely used for each distinct term which needs to be labelled. Nonetheless, sequences of integers may naturally be used as the simplest way to begin labelling; for example, 1, 2, 3, and so on.

Definition

The term "nominal number" may be quite recent and of limited use. It appears[

nominal data", defined as data indicating "...merely statements of qualitative category of membership." This usage comes from the sense of nominal
as "name".

Mathematically, nominal numbering is a one-to-one and onto function from a set of objects being named to a set of numerals, which may change (typically growing) over time: it is a function because each object is assigned a single numeral, it is one-to-one because different objects are assigned different numerals, and it is onto because every numeral in the set at a given time has associated with it a single named object.

"Nominal number" can be broadly defined as "any numeral used for identification, however it was assigned", or narrowly as "a numeral with no information other than identification".

For the purposes of naming, the term "number" is often used loosely to refer to any

driver's licence numbers, and some serial numbers
contain letters.

Use of nominal numbers

"Nominal" refers to the use of numbers: any nominal number can be used by its

ZIP code
11111 is less than the ZIP code 12345, but that does not necessarily mean that 11111 was issued before 12345 or that the region denoted by 11111 is further south than 12345, though it might be. Similarly, one can add or subtract ZIP codes, but this is meaningless: 12345 − 11111 does not have any meaning as a ZIP code.

In general, the only meaningful operation with nominal numbers is to compare two nominal numbers to see whether they are identical or not (whether they refer to the same object).

Numbers 102 and 400: bus route 102 in London, run by an Alexander Dennis Enviro400 double-decker bus.
Number 107: the car Peugeot 107.

Examples

A great variety of numbers meet the broad definition, including:

These are usually assigned either in some hierarchical way, such as how telephone numbers are assigned (in NANPA) as

Area Code + Prefix + Suffix, where the first three are geographically based, or sequentially, as in serial numbers
; these latter are thus properly ordinal numbers.

Narrowly defined

Numerical identifiers that are nominal numbers narrowly defined, viz, convey no information other than identity, are quite rare. These must be defined either arbitrarily or randomly, and most commonly arise in computer applications, such as dynamic

"retired numbers"
, where a club no longer issues a number that has become associated with a particularly famous player, but reallocate others to new players when they become available.

See also

External links

  • Cardinal, Ordinal and Nominal Numbers
  • Cardinal, Ordinal, and Nominal Numbers
  • Posamentier, Alfred S.; Farber, William; Germain-Williams, Terri L.; Paris, Elaine; Thaller, Bernd; Lehmann, Ingmar (2013). "Nominal Numbers". 100 Commonly Asked Questions in Math Class. p. 60. .