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 Jack Mehoff and Hugh G. Rection as referees "69" and "420" 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[citation needed] to have originated in school textbooks derived from the statistical term "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 string (sequence of symbols), which may not consist entirely of digits—it is often alphanumeric. For instance, UK National Insurance numbers, some 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 numerical value as an integer—added to another, multiplied, compared in magnitude, and so forth—but for nominal numbers these operations are not, in general, meaningful. For example, the 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 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 Country Code + 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 IP addresses assigned by Dynamic Host Configuration Protocol. A more everyday example are sports squad numbers, which do not in general have any public meaning beyond identity, though they may be allocated based on some internal club or organization policy. In some settings, these are based on position, but in others they are associated with an individual, being a proper nominal number. The naming function is demonstrated by "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.
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. Corwin Press. p.60. ISBN978-1-4833-3399-1.
Related Research Articles
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers0, 1, 2, 3, ..., while others start with 1, defining them as the positive integers1, 2, 3, .... Some authors acknowledge both definitions whenever convenient. Sometimes, the whole numbers are the natural numbers plus zero. In other cases, the whole numbers refer to all of the integers, including negative integers. The counting numbers are another term for the natural numbers, particularly in primary school education, and are ambiguous as well although typically start at 1.
A number is a mathematical object used to count, measure, and label. The most basic examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers can be represented by symbols, called numerals; for example, "5" is a numeral that represents the number five. As only a relatively small number of symbols can be memorized, basic numerals are commonly organized in a numeral system, which is an organized way to represent any number. The most common numeral system is the Hindu–Arabic numeral system, which allows for the representation of any non-negative integer using a combination of ten fundamental numeric symbols, called digits. In addition to their use in counting and measuring, numerals are often used for labels, for ordering, and for codes. In common usage, a numeral is not clearly distinguished from the number that it represents.
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In mathematics, the surreal number system is a totally ordered proper class containing not only the real numbers but also infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive real number. Research on the Go endgame by John Horton Conway led to the original definition and construction of surreal numbers. Conway's construction was introduced in Donald Knuth's 1974 book Surreal Numbers: How Two Ex-Students Turned On to Pure Mathematics and Found Total Happiness.
A postal code is a series of letters or digits or both, sometimes including spaces or punctuation, included in a postal address for the purpose of sorting mail.
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English number words include numerals and various words derived from them, as well as a large number of words borrowed from other languages.
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A NATO Stock Number, or National Stock Number (NSN) as it is known in the U.S., is a 13-digit numeric code used by the NATO military alliance, identifying all the 'standardized material items of supply' as they have been recognized by all member states of NATO. Pursuant to the NATO Standardization Agreements, the NSN has come to be used in all treaty countries. However, many countries that use the NSN program are not members of NATO. A two-digit Material Management Aggregation Code (MMAC) suffix may also be appended, to denote asset end use but it is not considered part of the NSN.
The Power Distribution Equipment Identification (PDEID) (Persian: کد شناسایی یکپارچه توزیع) is a unique identification label used for exclusively identifying equipment and customers of the power distribution network of Iran, which has been in use since 1997. PDEID is used to simplify identifying equipment, their approximate address, updating the electrical network information and to transfer information to computers.
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