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Absolute Values

*"*The definition of the absolute value of a real number is most conveniently introduced at this point: if *a* [is a real number], then the *absolute value of a*, denoted by |*a*|, is [defined as follows:]

The absolute value has the following properties:*"* *(see ita-2-2-17-pg22)*

(Rosenlicht describes the first three properties below as trivial consequences of the definition, but I will review the concepts in detail.)

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AV 1.
The absolute value is greater than or equal to zero.
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AV 2.
The absolute value of a product is the product of the absolute values.
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AV 3.
The square of the absolute value is the square of the number.
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AV 4.
The absolute value of a sum is less than or equal to the sum of the absolute values.
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AV 5.
The absolute value of a difference is greater than or equal to the aboslute value of the difference of absolute values.
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Converted [ in part ] by *Mathematica*
December 4, 2007