Absolute Value
Absolute Value
Absolute value is an operation in mathematics, written as bars on either side of the expression. For example, the absolute value of −1 is written as −1.
Absolute value can be thought of in three ways. First, the absolute value of any number is defined as the positive of that number. For example, 8 = 8 and −8 = 8. Second, one absolute value equation can yield two solutions. For example, if we solve the equation x  = 2, not only does x = 2 but also x = −2 because 2 = 2 and −2 = 2.
Third, absolute value is defined as the distance, without regard to direction, that any number is from 0 on the real number line. Consider a formula for the distance on the real number line as k − 0, in which k is any real number. Then, for example, the distance that 11 is from 0 would be 11 (because 11 − 0 = 11). Likewise, the absolute value of 11 is equal to 11. The distance for −11 will also equal 11 (because −11 − 0 = −11 = 11), and the absolute value of −11 is 11.
Thus, the absolute value of any real number is equal to the absolute value of its distance from 0 on the number line. Furthermore, if the absolute value is not used in the above formula k − 0, the result for any negative number will be a negative distance. Absolute value helps improve formulas in order to obtain realistic solutions.
see also Number Line; Numbers, Real.
Michael Ota
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absolute value
absolute value, magnitude of a number or other mathematical expression disregarding its sign; thus, the absolute value is positive, whether the original expression is positive or negative. In symbols, if a denotes the absolute value of a number a, then a = a for a > 0 and a = a for a < 0. For example, 7= 7 since 7 > 0 and 7 = (7), or 7 = 7, since 7 < 0.
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absolute value
absolute value The magnitude of a number, regardless of its sign (positive or negative). For example, 25 is the absolute value of 25 and –25. Most spreadsheet programs include a function that returns the absolute value of a number.
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