The study of quantity starts with numbers, first the familiar natural numbers and integers ("whole numbers") and arithmetical operations on them, which are characterized in arithmetic. The deeper properties of integers are studied in number theory, from which come such popular results as Fermat's Last Theorem. The twin prime conjecture and Goldbach's conjecture are two unsolved problems in number theory.
As the number system is further developed, the integers are recognized as a subset of the rational numbers ("fractions"). These, in turn, are contained within the real numbers, which are used to represent continuous quantities. Real numbers are generalized to complex numbers. These are the first steps of a hierarchy of numbers that goes on to include quarternions and octonions. Consideration of the natural numbers also leads to the transfinite numbers, which formalize the concept of "infinity". Another area of study is size, which leads to the cardinal numbers and then to another conception of infinity: the aleph numbers, which allow meaningful comparison of the size of infinitely large sets.
Natural numbers Integers Rational numbers Real numbers Complex numbers
Other articles related to "quantity":
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Famous quotes containing the word quantity:
“... nothing is more human than substituting the quantity of words and actions for their character. But using imprecise words is very similar to using lots of words, for the more imprecise a word is, the greater the area it covers.”
—Robert Musil (18801942)
“The Great Society is a place where every child can find knowledge to enrich his mind and to enlarge his talents.... It is a place where the city of man serves not only the needs of the body and the demands of commerce but the desire for beauty and the hunger for community.... It is a place where men are more concerned with the quality of their goals than the quantity of their goods.”
—Lyndon Baines Johnson (19081973)
“A bureaucracy is sure to think that its duty is to augment official power, official business, or official members, rather than to leave free the energies of mankind; it overdoes the quantity of government, as well as impairs its quality. The truth is, that a skilled bureaucracy ... is, though it boasts of an appearance of science, quite inconsistent with the true principles of the art of business.”
—Walter Bagehot (18261877)