Quantity is a kind of property which exists as magnitude or multitude. It is among the basic classes of things along with quality, substance, change, and relation. In the vernacular quality can mean a high degree of excellence (“a quality product” a degree of excellence or the lack of it (“work of average quality” or a property of Quantity was first introduced as quantum, an entity having quantity. An entity is something that has a distinct separate Existence, though it need not be a material existence Being a fundamental term, quantity is used to refer to any type of quantitative properties or attributes of things. Some quantities are such by their inner nature (as number), while others are functioning as states (properties, dimensions, attributes) of things such as heavy and light, long and short, broad and narrow, small and great, or much and little. One form of much, muchly is used to say that something is likely to happen. A small quantity is sometimes referred to as a quantulum.

Two basic divisions of quantity, magnitude and multitude (or number), imply the principal distinction between continuity (continuum) and discontinuity. The magnitude of a mathematical object is its size a property by which it can be larger or smaller than other objects of the same kind in technical terms an Ordering A number is an Abstract object, tokens of which are Symbols used in Counting and measuring.

Under the names of multitude come what is discontinuous and discrete and divisible into indivisibles, all cases of collective nouns: army, fleet, flock, government, company, party, people, chorus, crowd, mess, and number. Under the names of magnitude come what is continuous and unified and divisible into divisibles, all cases of non-collective nouns: the universe, matter, mass, energy, liquid, material, animal, plant, tree.

Along with analyzing its nature and classification, the issues of quantity involve such closely related topics as the relation of magnitudes and multitudes, dimensionality, equality, proportion, the measurements of quantities, the units of measurements, number and numbering systems, the types of numbers and their relations to each other as numerical ratios.

Thus quantity is a property that exists in a range of magnitudes or multitudes. Mass, time, distance, heat, and angular separation are among the familiar examples of quantitative properties. Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object For other uses see Time (disambiguation Time is a component of a measuring system used to sequence events to compare the durations of Distance is a numerical description of how far apart objects are In Physics, heat, symbolized by Q, is Energy transferred from one body or system to another due to a difference in Temperature A quantitative attribute is one that exists in a range of magnitudes and can therefore be measured. Two magnitudes of a continuous quantity stand in relation to one another as a ratio, which is a real number. A ratio is an expression which compares quantities relative to each other In Mathematics, the real numbers may be described informally in several different ways

Contents 1 Background 2 Quantitative structure 3 Quantity in mathematics 4 Quantity in physical science 5 Quantity in logic and semantics 6 Quantity in natural language 7 Further examples 8 References

Background

The concept of quantity is an ancient one which extends back to the time of Aristotle and earlier. Aristotle (Greek Aristotélēs) (384 BC – 322 BC was a Greek philosopher a student of Plato and teacher of Alexander the Great. Aristotle regarded quantity as a fundamental ontological and scientific category. In Aristotle's ontology, quantity or quantum was classified into two different types, which he characterized as follows:

'Quantum' means that which is divisible into two or more constituent parts of which each is by nature a 'one' and a 'this'. In Philosophy, ontology (from the Greek, genitive: of being (part A quantum is a plurality if it is numerable, a magnitude if it is measurable. 'Plurality' means that which is divisible potentially into non-continuous parts, 'magnitude' that which is divisible into continuous parts; of magnitude, that which is continuous in one dimension is length; in two breadth, in three depth. Of these, limited plurality is number, limited length is a line, breadth a surface, depth a solid. (Aristotle, book v, chapters 11-14, Metaphysics).

In his Elements, Euclid developed the theory of ratios of magnitudes without studying the nature of magnitudes, as Archimedes, but giving the following significant definitions:

A magnitude is a part of a magnitude, the less of the greater, when it measures the greater; A ratio is a sort of relation in respect of size between two magnitudes of the same kind. Euclid's Elements ( Greek:) is a mathematical and geometric Treatise consisting of 13 books written by the Greek Euclid ( Greek:.) fl 300 BC also known as Euclid of Alexandria, is often referred to as the Father of Geometry

For Aristotle and Euclid, relations were conceived as whole numbers (Michell, 1993). John Wallis later conceived of ratios of magnitudes as real numbers as reflected in the following:

When a comparison in terms of ratio is made, the resultant ratio often [namely with the exception of the 'numerical genus' itself] leaves the genus of quantities compared, and passes into the numerical genus, whatever the genus of quantities compared may have been. John Wallis ( November 23, 1616 - October 28, 1703) was an English mathematician who is given partial credit for the In Mathematics, the real numbers may be described informally in several different ways (John Wallis, Mathesis Universalis)

That is, the ratio of magnitudes of any quantity, whether volume, mass, heat and so on, is a number. Following this, Newton then defined number, and the relationship between quantity and number, in the following terms: "By number we understand not so much a multitude of unities, as the abstracted ratio of any quantity to another quantity of the same kind, which we take for unity" (Newton, 1728). Sir Isaac Newton, FRS (ˈnjuːtən 4 January 1643 31 March 1727) Biography Early years See also Isaac Newton's early life and achievements

Quantitative structure

Continuous quantities possess a particular structure which was first explicitly characterized by Hölder (1901) as a set of axioms which define such features as identities and relations between magnitudes. Otto Ludwig Hölder ( December 22, 1859 - August 29, 1937) was a German Mathematician born in Stuttgart. In science, quantitative structure is the subject of empirical investigation and cannot be assumed to exist a priori for any given property. "A priori" redirects here For other uses see A priori. The linear continuum represents the prototype of continuous quantitative structure as characterized by Hölder (1901) (translated in Michell & Ernst, 1996). In Mathematics, the word continuum has at least two distinct meanings outlined in the sections below A fundamental feature of any type of quantity is that the relationships of equality or inequality can in principle be stated in comparisons between particular magnitudes, unlike quality which is marked by likeness, similarity and difference, diversity. Another fundamental feature is additivity. Additivity may involve concatenation, such as adding two lengths A and B to obtain a third A + B. Additivity is not, however, restricted to extensive quantities but may also entail relations between magnitudes that can be established through experiments which permit tests of hypothesized observable manifestations of the additive relations of magnitudes. Another feature is continuity, on which Michell (1999, p. 51) says of length, as a type of quantitative attribute, "what continuity means is that if any arbitrary length, a, is selected as a unit, then for every positive real number, r, there is a length b such that b = ra".

Quantity in mathematics

Being of two types, magnitude and multitude (or number), quantities are further divided as mathematical and physical. Formally, quantities (numbers and magnitudes), their ratios, proportions, order and formal relationships of equality and inequality, are studied by mathematics. The essential part of mathematical quantities is made up with a collection variables each assuming a set of values and coming as scalar, vectors, or tensors, and functioning as infinitesimal, arguments, independent or dependent variables, or random and stochastic quantities. In Linear algebra, Real numbers are called Scalars and relate to vectors in a Vector space through the operation of Scalar multiplication History The word tensor was introduced in 1846 by William Rowan Hamilton to describe the norm operation in a certain type of algebraic system (eventually Stochastic (from the Greek "Στόχος" for "aim" or "guess" means Random. In mathematics, magnitudes and multitudes are not only two kinds of quantity but they are also commensurable with each other. The topics of the discrete quantities as numbers, number systems, with their kinds and relations, fall into the number theory. Geometry studies the issues of spatial magnitudes: straight lines (their length, and relationships as parallels, perpendiculars, angles) and curved lines (kinds and number and degree) with their relationships (tangents, secants, and asymptotes). Also it encompasses surfaces and solids, their transformations, measurements and relationships.

Quantity in physical science

Establishing quantitative structure and relationships between different quantities is the cornerstone of modern physical sciences. Physics is fundamentally a quantitative science. Its progress is chiefly achieved due to rendering the abstract qualities of material entities into Physical quantities, by postulating that all material bodies marked by quantitative properties or physical dimensions, which are subject to some measurements and observations. A physical Quantity is a physical property that can be quantified Setting the units of measurement, physics covers such fundamental quantities as space (length, breadth, and depth) and time, mass and force, temperature, energy and quantum.

Traditionally, a distinction has also been made between intensive quantity and extensive quantity as two types of quantitative property, state or relation. In the Physical sciences an intensive property (also called a bulk property) is a Physical property of a system that does not depend on the In the Physical sciences an intensive property (also called a bulk property) is a Physical property of a system that does not depend on the The magnitude of an intensive quantity does not depend on the size, or extent, of the object or system of which the quantity is a property whereas magnitudes of an extensive quantity are additive for parts of an entity or subsystems. Thus, magnitude does depend on the extent of the entity or system in the case of extensive quantity. Examples of intensive quantities are density and pressure, while examples of extensive quantities are energy, volume and mass. The density of a material is defined as its Mass per unit Volume: \rho = \frac{m}{V} Different materials usually have different Pressure (symbol 'p' is the force per unit Area applied to an object in a direction perpendicular to the surface In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός The volume of any solid plasma vacuum or theoretical object is how much three- Dimensional space it occupies often quantified numerically Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object

Quantity in logic and semantics

In respect to quantity, propositions are grouped as universal and particular, applying to the whole subject or a part of the subject to be predicated. Accordingly, there are existential and universal quantifiers. In relation to the meaning of a construct, quantity involves two semantic dimensions: 1. extension or extent (determining the specific classes or individual instances indicated by the construct) 2. intension (content or comprehension or definition) measuring all the implications (relationships and associations involved in a construct, its intrinsic, inherent, internal, built-in, and constitutional implicit meanings and relations).

Quantity in natural language

In human languages, including English, number is a syntactic category, along with person and gender. English is a West Germanic language originating in England and is the First language for most people in the United Kingdom, the United States In linguistics grammatical number is a Grammatical category of nouns pronouns and adjective and verb agreement that expresses count distinctions (such as "one" The term person is used in Common sense to mean an individual Human being. Gender comprises a range of differences between men and women extending from the biological to the social The quantity is expressed by identifiers, definite and indefinite, and quantifiers, definite and indefinite, as well as by three types of nouns: 1. count unit nouns or countables; 2. mass nouns, uncountables, referring to the indefinite, unidentified amounts; 3. nouns of multitude (collective nouns). In Linguistics, a collective noun is a word used to define a group of objects where "objects" can be People, Animals Inanimate things The word ‘number’ belongs to a noun of multitude standing either for a single entity or for the individuals making the whole. An amount in general is expressed by a special class of words called identifiers, indefinite and definite and quantifiers, definite and indefinite. The amount may be expressed by: singular form and plural from, ordinal numbers before a count noun singular (first, second, third…), the demonstratives; definite and indefinite numbers and measurements (hundred/hundreds, million/millions), or cardinal numbers before count nouns. The set of language quantifiers covers "a few, a great number, many, several (for count names); a bit of, a little, less, a great deal (amount) of, much (for mass names); all, plenty of, a lot of, enough, more, most, some, any, both, each, either, neither, every, no". For the complex case of unidentified amounts, the parts and examples of a mass are indicated with respect to the following: a measure of a mass (two kilos of rice and twenty bottles of milk or ten pieces of paper); a piece or part of a mass (part, element, atom, item, article, drop); or a shape of a container (a basket, box, case, cup, bottle, vessel, jar).

Further examples

Some further examples of quantities are:

• 1. 76 litres (liters) of milk, a continuous quantity
• 2πr metres, where r is the length of a radius of a circle expressed in metres (or meters), also a continuous quantity
• one apple, two apples, three apples, where the number is an integer representing the count of a denumerable collection of objects (apples)
• 500 people (also a count)
• a couple conventionally refers to two objects

References

© 2009 citizendia.org; parts available under the terms of GNU Free Documentation License, from http://en.wikipedia.org
Dapyx Software network: MP3 Explorer | Ebook Manager | Zenithic