In mathematics, the absolute value (or modulus) | a | of a real number a is the non-negative value of a without regard to its sign. Namely, | a | = a for a positive a, | a | = −a for a negative a, and | 0 | = 0. For example, the absolute value of 3 is 3, and the absolute value of −3 is also 3. The absolute value of a number may be thought of as its distance from zero.
Generalizations of the absolute value for real numbers occur in a wide variety of mathematical settings. For example an absolute value is also defined for the complex numbers, the quaternions, ordered rings, fields and vector spaces. The absolute value is closely related to the notions of magnitude, distance, and norm in various mathematical and physical contexts.
Read more about Absolute Value: Terminology and Notation, Absolute Value Function, Distance
Famous quotes containing the words Absolute Value and/or absolute:
“We must not inquire too curiously into the absolute value of literature. Enough that it amuses and exercises us. At least it leaves us where we were. It names things, but does not add things.”
—Ralph Waldo Emerson (1803–1882)
“There is an inner world; and a spiritual faculty of discerning it with absolute clearness, nay, with the most minute and brilliant distinctness. But it is part of our earthly lot that it is the outer world, in which we are encased, which is the lever that brings that spiritual faculty into play.”
—E.T.A.W. (Ernst Theodor Amadeus Wilhelm)