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# Absolute Value Definition

The absolute value or modulus of a real number x, denoted |x|, is the non-negative value of x without regard to its sign. Namely, |x| = x if x is positive, and |x| = −x if x is negative (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. Essentially, absolute value turns all negative numbers positive and leaves positive numbers and zero unchanged. The absolute value of a number may be thought of as its distance from zero.

The absolute value of a number is the distance between the number and the origin. This is a more refined definition of absolute value as it connects the notion of absolute value to the absolute value of a complex number and the magnitude of a vector. Generalizations of the absolute value for real numbers occur in a wide variety of mathematical settings. For instance, 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.

### Sources

Absolute Value. 16 May 2020, en.wikipedia.org/wiki/Absolute_value.

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