Blumenthal, Leonard M. Formerly, Department of Mathematics, University of Missouri, Columbia, Missouri.
Last reviewed:January 2021
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A term that became part of mathematical language during the development of analytic geometry (no equivalent word is found in the writings of Archimedes and other Greek mathematicians), and which is frequently not defined in modern works, apparently in the belief that the meaning ordinarily attached to the word is sufficiently precise. When a definition is given, it is usually to the effect that a symbol x is a variable if it may denote any member of a set S of objects. A variable is discrete or continuous according as its range (the set S) is discrete (for example, a subset of the natural numbers) or continuous (for example, all real numbers between two real numbers), respectively. Such a working definition usually suffices for the needs of mathematics. See also: Analytic geometry; Number theory; Parametric equation
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