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Constant (mathematics) : ウィキペディア英語版
Constant (mathematics)

In mathematics, the adjective constant means non-varying. The noun constant may have two different meanings. It may refer to a fixed and well defined number or other mathematical object. The term mathematical constant (and also physical constant) is sometimes used to distinguish this meaning from the other one. A constant may also refer to a constant function or its value (it is a common usage to identify them). Such a constant is commonly represented by a variable which does not depend on the main variable(s) of the studied problem. This is the case, for example, for a constant of integration which is an arbitrary constant function (not depending on the variable of integration) added to a particular antiderivative to get all the antiderivatives of the given function.
For example, a general quadratic function is commonly written as:
:a x^2 + b x + c\, ,
where ''a'', ''b'' and ''c'' are constants (or parameters), while ''x'' is the variable, a placeholder for the argument of the function being studied. A more explicit way to denote this function is
:x\mapsto a x^2 + b x + c \, ,
which makes the function-argument status of ''x'' clear, and thereby implicitly the constant status of ''a'', ''b'' and ''c''. In this example ''a'', ''b'' and ''c'' are coefficients of the polynomial. Since ''c'' occurs in a term that does not involve ''x'', it is called the constant term of the polynomial and can be thought of as the coefficient of ''x''0; any polynomial term or expression of degree zero is a constant.
== Constant function ==

A constant may be used to define a constant function that ignores its arguments and always gives the same value. A constant function of a single variable, such as f(x)=5, has a graph that is a horizontal straight line, parallel to the x-axis. Such a function always takes the same value (in this case, 5) because its argument does not appear in the expression defining the function.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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