A real quantity having a value less than zero () is said to be negative. Negative numbers are denoted with a minus sign preceding the corresponding positive number, i.e., .

The concept of negative numbers is one that took millennia to become firmly embedded in mathematics. For example, the Greek geometer Diophantus (first or third century AD) rejected negative solutions to equations, and the Indian mathematician Bhaskara (1114-ca. 1185) comments on the negative root of the quadratic equation, "The second value is in this case not to be taken, for it is inadequate; people do not approve of negative roots" (Wells 1986, p. 20). The acceptance of the square roots of negative numbers (i.e., so-called complex numbers) as useful abstract quantities took longer still.

Cajori, F. A History of Mathematical Notations, Vols. 1-2. New York: Dover, 1993.

Wells, D. The Penguin Dictionary of Curious and Interesting Numbers. Middlesex, England: Penguin Books, pp. 20-21, 1986.

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Weisstein, Eric W. "Negative." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Negative.html