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Quantity is a property that can exist as a magnitude or multitude. Quantities can be compared in terms of "more," "less," or "equal," or by assigning a numerical value in terms of a unit of measurement. Quantity is among the basic classes of things along with quality, substance, change, and relation. 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. A small quantity is sometimes referred to as a quantulum. Two basic divisions of quantity, magnitude and multitude, imply the principal distinction between continuity (continuum) and discontinuity. 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. Two magnitudes of a continuous quantity stand in relation to one another as a ratio which is a real number. ==Background== In mathematics the concept of quantity is an ancient one extending back to the time of Aristotle and earlier. 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'. 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. 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 (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, ''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). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「quantity」の詳細全文を読む スポンサード リンク
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