628:). 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).
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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 that permit tests of hypothesized
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340:
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entities into physical quantities, by postulating that all material bodies marked by quantitative properties or physical dimensions are subject to some measurements and observations. Setting the units of measurement, physics covers such fundamental quantities as space (length, breadth, and depth) and time, mass and force, temperature, energy, and
162:
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
393:
Magnitude (how much) and multitude (how many), the two principal types of quantities, are further divided as mathematical and physical. In formal terms, quantities—their ratios, proportions, order and formal relationships of equality and inequality—are studied by mathematics. The essential part of
481:
different quantities is the cornerstone of modern science, especially but not restricted to physical sciences. Physics is fundamentally a quantitative science; chemistry, biology and others are increasingly so. Their progress is chiefly achieved due to rendering the abstract qualities of material
296:
represents the prototype of continuous quantitative structure as characterized by Hölder (1901) (translated in
Michell & Ernst, 1996). 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
301:
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,
127:, 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.
101:, 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.
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and remaining popular until the eighteenth century, held that mathematics is the "science of quantity". Quantity was considered to be divided into the discrete (studied by arithmetic) and the continuous (studied by geometry and later
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230:
When a comparison in terms of ratio is made, the resultant ratio often leaves the genus of quantities compared, and passes into the numerical genus, whatever the genus of quantities compared may have been.
1354:
Michell, J. & Ernst, C. (1996). The axioms of quantity and the theory of measurement: translated from Part I of Otto Hölder's German text "Die Axiome der
Quantität und die Lehre vom Mass".
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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
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922:
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463:). The theory fits reasonably well elementary or school mathematics but less well the abstract topological and algebraic structures of modern mathematics.
189:
developed the theory of ratios of magnitudes without studying the nature of magnitudes, as
Archimedes, but giving the following significant definitions:
255:
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.
447:
studies the issues of spatial magnitudes: straight lines, curved lines, surfaces and solids, all with their respective measurements and relationships.
1295:
Aristotle, Physical
Treatises: Physics, in Great Books of the Western World, V.1, ed. by Adler, M.J., Encyclopædia Britannica, Inc., Chicago (1990)
800:, the use of dimensionless parameters is evident in geometric relationships and transformations. Physics relies on dimensionless numbers like the
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quantities. In mathematics, magnitudes and multitudes are also not only two distinct kinds of quantity but furthermore relatable to each other.
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one apple, two apples, three apples, where the number is an integer representing the count of a denumerable collection of objects (apples)
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380:
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Aristotle, Metaphysics, in Great Books of the
Western World, V.1, ed. by Adler, M.J., Encyclopædia Britannica, Inc., Chicago (1990)
1361:
Newton, I. (1728/1967). Universal
Arithmetic: Or, a Treatise of Arithmetical Composition and Resolution. In D.T. Whiteside (Ed.),
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124:
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does not depend on the size, or extent, of the object or system of which the quantity is a property, whereas magnitudes of an
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The mathematical usage of a quantity can then be varied and so is situationally dependent. Quantities can be used as being
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Under the name of multitude comes what is discontinuous and discrete and divisible ultimately into indivisibles, such as:
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116:. Under the name of magnitude comes what is continuous and unified and divisible only into smaller divisibles, such as:
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55:
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That is, the ratio of magnitudes of any quantity, whether volume, mass, heat and so on, is a number. Following this,
62:. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value multiple of a
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Michell, J. (1993). The origins of the representational theory of measurement: Helmholtz, Hölder, and
Russell.
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and earlier. Aristotle regarded quantity as a fundamental ontological and scientific category. In
Aristotle's
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Webb, J. K.; King, J. A.; Murphy, M. T.; Flambaum, V. V.; Carswell, R. F.; Bainbridge, M. B. (2011-10-31).
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Aristotle, Logic (Organon): Categories, in Great Books of the
Western World, V.1. ed. by Adler, M.J.,
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Berichte über die Verhandlungen der Königlich Sachsischen Gesellschaft der Wissenschaften zu Leipzig
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143:, quantity or quantum was classified into two different types, which he characterized as follows:
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Continuous quantities possess a particular structure that was first explicitly characterized by
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refers to an indefinite, but usually small, number – usually indefinitely greater than "a few".
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then defined number, and the relationship between quantity and number, in the following terms:
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means that which is divisible into two or more constituent parts, of which each is by nature a
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International vocabulary of metrology — Basic and general concepts and associated terms (VIM)
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also refers to an indefinite, but surprisingly (in relation to the context) large number.
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In mathematics, the concept of quantity is an ancient one extending back to the time of
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that align with another system, these quantities do not necessitate explicitly defined
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army, fleet, flock, government, company, party, people, mess (military), chorus, crowd
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is a sort of relation in respect of size between two magnitudes of the same kind.
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158:. A quantum is a plurality if it is numerable, a magnitude if it is measurable.
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as two types of quantitative property, state or relation. The magnitude of an
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usually refers to an indefinite, but usually small number, greater than one.
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1182:"Dimensionless Equation of State to Predict Microemulsion Phase Behavior"
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A History of the Circle: Mathematical Reasoning and the Physical Universe
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612:. The quantity is expressed by identifiers, definite and indefinite, and
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between magnitudes. In science, quantitative structure is the subject of
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of a magnitude, the less of the greater, when it measures the greater; A
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of values. These can be a set of a single quantity, referred to as a
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Laycock, H. (2006). Words without Objects: Oxford, Clarendon Press.
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Hölder, O. (1901). Die Axiome der Quantität und die Lehre vom Mass.
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when represented by real numbers, or have multiple quantities as do
1094:"Indications of a Spatial Variation of the Fine Structure Constant"
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1151:"Zur Elektrodynamik bewegter Körper [AdP 17, 891 (1905)]"
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Greek Mathematical Thought and the Origin of Algebra. Cambridge
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EBOOK: Fluid Mechanics Fundamentals and Applications (SI units)
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429:(independent or dependent), or probabilistic as in random and
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1309:, ed. D.D. Novotny and L. Novak, New York: Routledge, 221–44.
944:"SI Brochure: The International System of Units, 9th Edition"
915:"1.8 (1.6) quantity of dimension one dimensionless quantity"
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are among the familiar examples of quantitative properties.
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expressed in metres (or meters), also a continuous quantity
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as numbers: number systems with their kinds and relations.
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mathematical quantities consists of having a collection of
1365:, Vol. 2 (pp. 3–134). New York: Johnson Reprint Corp.
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Dimensionless quantities play a crucial role serving as
616:, definite and indefinite, as well as by three types of
274:(1901) as a set of axioms that define such features as
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Establishing quantitative structure and relationships
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For Aristotle and Euclid, relations were conceived as
318:(1960) and by the American mathematical psychologist
1180:Ghosh, Soumyadeep; Johns, Russell T. (2016-09-06).
770:, derived from the universal ratio of 2π times the
893:. Basingstoke: Palgrave Macmillan. p. 31-2.
890:An Aristotelian Realist Philosophy of Mathematics
723:in a manner that prevents their aggregation into
719:, or quantities of dimension one, are quantities
743:; its value remains independent of the specific
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228:
191:
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774:of a circle being equal to its circumference.
452:Aristotelian realist philosophy of mathematics
314:, independently developed by French economist
513:, while examples of extensive quantities are
310:a". A further generalization is given by the
8:
1338:Studies in History and Philosophy of Science
1307:Neo-Aristotelian Perspectives in Metaphysics
560:. There might be a discussion about this on
361:. There might be a discussion about this on
1065:Cengel, Yunus; Cimbala, John (2013-10-16).
796:often involve dimensionless quantities. In
222:later conceived of ratios of magnitudes as
1316:, Mathematische-Physicke Klasse, 53, 1–64.
1274:Learn how and when to remove this message
1109:
636:Some further examples of quantities are:
580:Learn how and when to remove this message
489:A distinction has also been made between
381:Learn how and when to remove this message
1237:This article includes a list of general
620:: 1. count unit nouns or countables; 2.
876:
788:, concepts like the unitless ratios in
1363:The mathematical Works of Isaac Newton
118:matter, mass, energy, liquid, material
784:in various technical disciplines. In
680:conventionally refers to two objects.
7:
306:, there is a length b such that b =
123:Along with analyzing its nature and
120:—all cases of non-collective nouns.
292:for any given property. The linear
1356:Journal of Mathematical Psychology
1243:it lacks sufficient corresponding
414:, two kinds of geometric objects.
46:is a property that can exist as a
27:Property of magnitude or multitude
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766:serve as dimensionless units for
758:is recognized as a dimensionless
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708:This section is an excerpt from
644:) of milk, a continuous quantity
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968:"Dimensionless units in the SI"
286:and cannot be assumed to exist
30:For the term in phonetics, see
1128:10.1103/PhysRevLett.107.191101
592:In human languages, including
312:theory of conjoint measurement
1:
1198:10.1021/acs.langmuir.6b02666
1044:. Rutgers University Press.
89:Quantity is among the basic
1372:(as quoted in Klein, 1968).
1149:Einstein, A. (2005-02-23).
669:500 people (also a type of
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1349:Cambridge University Press
1038:Zebrowski, Ernest (1999).
1017:10.1088/0026-1394/31/6/013
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1345:Measurement in Psychology
991:Mills, I. M. (May 1995).
727:. Typically expressed as
439:covers the topics of the
112:; all which are cases of
964:Phillips, William Daniel
865:Numerical value equation
855:Quantification (science)
751:per milliliter (mL/mL).
717:Dimensionless quantities
1397:Metaphysical properties
1290:Encyclopædia Britannica
1258:more precise citations.
1098:Physical Review Letters
952:ISBN 978-92-822-2272-0.
810:fine-structure constant
423:arguments of a function
284:empirical investigation
163:surface, depth a solid.
1292:, Inc., Chicago (1990)
1167:10.1002/andp.200590006
782:differential equations
710:Dimensionless quantity
703:Dimensionless quantity
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1332:Oxfordscholarship.com
1301:Franklin, J. (2014).
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93:of things along with
1370:Mathesis universalis
1343:Michell, J. (1999).
837:concentration ratios
768:angular measurements
725:units of measurement
550:confusing or unclear
351:confusing or unclear
237:Mathesis Universalis
1303:Quantity and number
1120:2011PhRvL.107s1101W
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860:Observable quantity
832:and ratios such as
739:(ABV) represents a
655:is the length of a
558:clarify the section
529:In natural language
441:discrete quantities
359:clarify the section
174:, Book V, Ch. 11-14
64:unit of measurement
54:, which illustrate
1319:Klein, J. (1968).
1155:Annalen der Physik
839:are dimensionless.
721:implicitly defined
602:syntactic category
503:extensive quantity
499:intensive quantity
495:extensive quantity
491:intensive quantity
473:Quantity (science)
425:, variables in an
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32:length (phonetics)
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1192:(35): 8969–8979.
1078:978-0-07-717359-3
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993:"Unity as a Unit"
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814:quantum mechanics
747:used, such as in
737:alcohol by volume
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690:quite a few
614:quantifiers
220:John Wallis
171:Metaphysics
168:Aristotle,
1386:Categories
1239:references
997:Metrologia
973:Metrologia
929:2011-03-22
871:References
822:relativity
816:, and the
778:parameters
756:number one
671:count data
622:mass nouns
552:to readers
467:In science
431:stochastic
427:expression
371:March 2012
353:to readers
324:John Tukey
299:observable
276:identities
131:Background
60:continuity
1325:MIT Press
1264:July 2010
1206:0743-7463
1111:1008.3907
1025:0026-1394
826:chemistry
456:Aristotle
396:variables
294:continuum
280:relations
266:Structure
160:Plurality
137:Aristotle
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1407:Ontology
1392:Quantity
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844:See also
786:calculus
570:May 2021
511:pressure
461:calculus
445:Geometry
326:(1964).
289:a priori
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208:Elements
206:Euclid,
204:—
182:Elements
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141:ontology
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1252:improve
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764:Radians
696:several
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684:a few
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