Nominal number
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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[
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
Use of nominal numbers
"Nominal" refers to the use of numbers: any nominal number can be used by its
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).
Examples
A great variety of numbers meet the broad definition, including:
- National identification numbers, such as:
- Routing numbers, such as:
- Bank codes and sort codes, such as International Bank Account Numbers or ABA routing transit numbers.
- ZIP codes(These are generally numeric in the United States, but other nations often use alphanumeric systems.)
- Telephone numbers, assigned by various telephone numbering plans, such as the ITU-T E.164 and the North American Numbering Plan (NANPA).
- Numbers of train or bus routes or the individual vehicles in public transport
- Car model names from some car manufacturers, such as BMW or Peugeot, are plain numbers.
These are usually assigned either in some hierarchical way, such as how telephone numbers are assigned (in NANPA) as
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
See also
- Numbering scheme
- Serial number
- Symbol (programming)
- Unique key
- Universally Unique Identifier
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. ISBN 978-1-4833-3399-1.