Number

A Number is a mathematical object used to represent a quantity or measure

• AKA: Numeric Value.
• Context:
  • It can be referenced by a Number Label.
  • It can topically bee a member of a formal number sequence (a number set in an ordering relation with other numbers).
  • It can range from being a Conceptual Number to being a Number Mention.
  • It can range from being a Real Number to being an Imaginary Number.
  • It can range from being a Negative Number, a Non-Positive Number, a Non-Negative Number, or a Positive Number.
  • It can be associated to an Arithmetic System.
  • It can be an Input to: a Scalar-Input Operation, a Scalar-Input Function, a Scalar-Input Relation.
  • It can be an Input to an Arithmetic Operation, e.g. Addition Operation, Multiplication Operation.
  • It can be the Output of a Scalar-Output Function,
  • It can range from being a Small Number to being a Large Number.
  • It can range from being an Observed Number to being a Predicted Number.
  • …
• Example(s):
  • [math]\displaystyle{ 1 }[/math].
  • [math]\displaystyle{ 0 }[/math].
  • [math]\displaystyle{ -0.5 }[/math].
  • [math]\displaystyle{ 1/3 }[/math].
  • [math]\displaystyle{ \pi }[/math].
  • [math]\displaystyle{ \sqrt{-1} }[/math].
  • …
• Counter-Example(s):
  • an Ordinal Value, such as large.
  • a Class Value, such as red, or a telephone number, or a serial number.
  • a Structured Object, such as a parsed sentence.
• See: Scalar Statistic, Vector, Scalar Product, Vector Length Function, Mathematical Object, Counting, Nominal Number, Natural Number, Numeral System.

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References

2016

• (Wikipedia, 2016) ⇒ https://en.wikipedia.org/wiki/number Retrieved:2016-10-1.
  • A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers Template:Num, Template:Num, Template:Num, and so forth. A notational symbol that represents a number is called a numeral. In addition to their use in counting and measuring, numerals are often used for labels (as with telephone numbers), for ordering (as with serial numbers), and for codes (as with ISBNs). In common usage, number may refer to a symbol, a word, or a mathematical abstraction.

    In mathematics, the notion of number has been extended over the centuries to include , negative numbers, rational numbers such as [math]\displaystyle{ \frac{1}{2} }[/math] and [math]\displaystyle{ -\frac{2}{3} }[/math] , real numbers such as [math]\displaystyle{ \sqrt{2} }[/math] and [math]\displaystyle{ \pi }[/math], complex numbers, which extend the real numbers by including [math]\displaystyle{ \sqrt{-1} }[/math], and sometimes additional objects. Calculations with numbers are done with arithmetical operations, the most familiar being addition, subtraction, multiplication, division, and exponentiation. Their study or usage is called arithmetic. The same term may also refer to number theory, the study of the properties of the natural numbers.

    Besides their practical uses, numbers have cultural significance throughout the world. For example, in Western society the number 13 is regarded as unlucky, and "a million” may signify "a lot." Though it is now regarded as pseudoscience, numerology, the belief in a mystical significance of numbers permeated ancient and medieval thought. Numerology heavily influenced the development of Greek mathematics, stimulating the investigation of many problems in number theory which are still of interest today.

    During the 19th century, mathematicians began to develop many different abstractions which share certain properties of numbers and may be seen as extending the concept. Among the first were the hypercomplex numbers, which consist of various extensions or modifications of the complex number system. Today, number systems are considered important special examples of much more general categories such as rings and fields, and the application of the term "number" is a matter of convention, without fundamental significance.

2009

• WordNet.
  • the property possessed by a sum or total or indefinite quantity of units or individuals; "he had a number of chores to do"; "the number of ...
  • a concept of quantity involving zero and units; "every number has a unique position in the sequence"
  • act: a short theatrical performance that is part of a longer program; "he did his act three times every evening"; "she had a catchy little routine"; "it was one of the best numbers he ever did"
  • phone number: the number is used in calling a particular telephone; "he has an unlisted number"
  • numeral: a symbol used to represent a number; "he learned to write the numerals before he went to school"
  • total: add up in number or quantity; "The bills amounted to $2,000"; "The bill came to $2,000"
  • issue: one of a series published periodically; "she found an old issue of the magazine in her dentist's waiting room"
  • give numbers to; "You should number the pages of the thesis"
  • a select company of people; "I hope to become one of their number before I die"
  • enumerate; "We must number the names of the great mathematicians"
  • a numeral or string of numerals that is used for identification; "she refused to give them her Social Security number"
  • count: put into a group; "The academy counts several Nobel Prize winners among its members"
  • a clothing measurement; "a number 13 shoe"
  • count: determine the number or amount of; "Can you count the books on your shelf?"; "Count your change"
  • the grammatical category for the forms of nouns and pronouns and verbs that are used depending on the number of entities involved (singular or dual or plural); "in English the subject and the verb must agree in number"
  • place a limit on the number of
  • an item of merchandise offered for sale; "she preferred the black nylon number"; "this sweater is an all-wool number"
• (WordNet, 2009) ⇒ http://wordnetweb.princeton.edu/perl/webwn?s=scalar
  • S: (n) scalar (a variable quantity that cannot be resolved into components)
  • S: (adj) scalar (of or relating to a musical scale) "he played some basic scalar patterns on his guitar"
  • S: (adj) scalar (of or relating to a directionless magnitude (such as mass or speed etc.) that is completely specified by its magnitude) "scalar quantity"
• http://en.wiktionary.org/wiki/scalar
  • Adjective
    • 1. (mathematics) Having magnitude but not direction
    • 2. Of, or relating to scale
  • Noun
    • 1. (mathematics) A quantity that has magnitude but not direction; compare vector
    • 2. (electronics) An amplifier whose output is a constant multiple of its input
• http://www.math.com/tables/oddsends/vectordefs.htm
  • Definition:A scalar, generally speaking, is another name for "real number."
  • Definition: A vector of dimension n is an ordered collection of n elements, which are called components. … It can represent magnitude and direction simultaneously.

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