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In mathematics, the absolute
value or modulus |x| of a real numberx is
the non-negative value
of x without regard to its sign.
Namely, |x| = xfor a positivex, |x|
= −x for
a negativex (in
which case −x is positive), 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.
Generalisations 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.
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