absolute value
absolute value
English Definitions:
absolute value, numerical value (noun)
a real number regardless of its sign
absolute value (Noun)
For a real number, its numerical value without regard to its sign; formally, -1 times the number if the number is negative, and the number unmodified if it is zero or positive.
absolute value (Noun)
For a complex number, the square root of the sum of the squares of its real and imaginary parts.
Absolute value
In mathematics, the absolute value | x | of a real number x is the non-negative value of x without regard to its sign. Namely, | x | = x for a positive x, | x | = −x for a negative x, 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.
Absolute value
In mathematics, the absolute value or modulus of a real number x {\displaystyle x} , denoted | x | {\displaystyle |x|} , is the non-negative value of x {\displaystyle x} without regard to its sign. Namely, | x | = x {\displaystyle |x|=x} if x {\displaystyle x} is a positive number, and | x | = − x {\displaystyle |x|=-x} if x {\displaystyle x} is negative (in which case negating x {\displaystyle x} makes − x {\displaystyle -x} positive), and | 0 | = 0 {\displaystyle |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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