什麼是絕對值

Absolute value From Wikipedia, the free encyclopedia • Have questions? Find out how to ask questions and get answers. • Jump to: navigation, search In mathematics, the absolute value (or modulus[1]) of a real number is its numerical value without regard to its sign. So, for example, 3 is the absolute value of both 3 and −3. In computer programming, the mathematical function used to perform this calculation is usually given the name abs().
Generalizations 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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The graph of the absolute value function for real numbers. Contents [hide] 1 Real numbers2 Complex numbers3 Absolute value functions4 Ordered rings5 Distance6 Derivatives7 Fields8 Vector spaces9 Algorithms10 Notes11 References12 See also
[edit] Real numbers For any real number a the absolute value or modulus of a is denoted[2] by | a | and is defined as

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As can be seen from the above definition, the absolute value of a is always either positive or zero, but never negative.
From a geometric point of view, the absolute value of a real number is the distance along the real number line of that number from zero, and more generally the absolute value of the difference of two real numbers is the distance between them. Indeed the notion of an abstract distance function in mathematics can be seen to be a generalization of the absolute value of the difference (see "Distance" below).
The following proposition, gives an identity which is sometimes used as an alternative (and equivalent) definition of the absolute value:
PROPOSITION 1:

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The absolute value has the following four fundamental properties:
PROPOSITION 2:

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Subadditivity Other important properties of the absolute value include:
PROPOSITION 3:

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(equivalent to subadditivity) Two other useful inequalities are:

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The above are often used in solving inequalities; for example:

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absolute value means after absolute the value of it will become positive no matter it was a negative value or a positive value
however sometimes if it is an unknown, it should devide into cases to cal the value of the unknown.

2007-10-02 18:10:37 補充：
read my ans is easier to understand. the first one is very complicated. you ask about absolute value is that you are f4 and study a amaths le?