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Quantity
Quantity or amount is a property that includes numbers and quantifiable phenomena such as mass, time, distance, heat, angle, and information. Quantities can commonly be compared in terms of "more", "less", or "equal", or by assigning a numerical value multiple of a unit of measurement. Quantity is among the basic classes of things along with quality, substance, change, and relation. Some quantities are such by their inner nature (as number), while others function 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.
Under the name of multitude comes what is discontinuous and discrete and divisible ultimately into indivisibles, such as: army, fleet, flock, government, company, party, people, mess (military), chorus, crowd, and number; all which are cases of collective nouns. Under the name of magnitude comes what is continuous and unified and divisible only into smaller divisibles, such as: matter, mass, energy, liquid, material—all cases of non-collective nouns.
Along with analyzing its nature and classification, the issues of quantity involve such closely related topics as 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.
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, Metaphysics, Book V, Ch. 11-14
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.
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Quantity
Quantity or amount is a property that includes numbers and quantifiable phenomena such as mass, time, distance, heat, angle, and information. Quantities can commonly be compared in terms of "more", "less", or "equal", or by assigning a numerical value multiple of a unit of measurement. Quantity is among the basic classes of things along with quality, substance, change, and relation. Some quantities are such by their inner nature (as number), while others function 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.
Under the name of multitude comes what is discontinuous and discrete and divisible ultimately into indivisibles, such as: army, fleet, flock, government, company, party, people, mess (military), chorus, crowd, and number; all which are cases of collective nouns. Under the name of magnitude comes what is continuous and unified and divisible only into smaller divisibles, such as: matter, mass, energy, liquid, material—all cases of non-collective nouns.
Along with analyzing its nature and classification, the issues of quantity involve such closely related topics as 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.
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, Metaphysics, Book V, Ch. 11-14
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.