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The Info List - Nominal Number


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Nominal numbers or categorical numbers are numeric codes, meaning numerals used for labelling or identification only. The values of the numerals are irrelevant, and they do not indicate quantity, rank, or any other measurement.

Contents

1 Definition

1.1 Use of nominal numbers

2 Examples

2.1 Narrowly defined

3 See also 4 External links

Definition[edit] The term "nominal number" is quite recent and of limited use. It appears[citation needed] to have originated as a usage 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, National Insurance numbers, some driver's license numbers, and some serial numbers contain letters. Use of nominal numbers[edit] "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
ZIP code
12345, but that does not 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
Peugeot
107.

Examples[edit] A great variety of numbers meet the broad definition, including:

National identification numbers, such as:

Social Security numbers Driver's license
Driver's license
numbers National Insurance number

Routing
Routing
numbers, such as:

Bank codes and sort codes, such as International Bank Account Numbers or ABA routing transit numbers. Postal codes, such as 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
North American Numbering Plan
(NANPA). Numbers of train or bus routes in public transport

Car model
Car model
names from some car manufacturers, such as BMW
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
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[edit] 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 See also[edit]

Serial number Symbol (programming) Unique key Universally Unique Identifier

External links[edit]

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-

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The Info List - Nominal Number


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Nominal numbers or categorical numbers are numeric codes, meaning numerals used for labelling or identification only. The values of the numerals are irrelevant, and they do not indicate quantity, rank, or any other measurement.

Contents

1 Definition

1.1 Use of nominal numbers

2 Examples

2.1 Narrowly defined

3 See also 4 External links

Definition[edit] The term "nominal number" is quite recent and of limited use. It appears[citation needed] to have originated as a usage 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, National Insurance numbers, some driver's license numbers, and some serial numbers contain letters. Use of nominal numbers[edit] "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
ZIP code
12345, but that does not 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
Peugeot
107.

Examples[edit] A great variety of numbers meet the broad definition, including:

National identification numbers, such as:

Social Security numbers Driver's license
Driver's license
numbers National Insurance number

Routing
Routing
numbers, such as:

Bank codes and sort codes, such as International Bank Account Numbers or ABA routing transit numbers. Postal codes, such as 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
North American Numbering Plan
(NANPA). Numbers of train or bus routes in public transport

Car model
Car model
names from some car manufacturers, such as BMW
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
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[edit] 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 See also[edit]

Serial number Symbol (programming) Unique key Universally Unique Identifier

External links[edit]

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-

.

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