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:
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
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 x0; any polynomial term or expression of degree zero is a constant.
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 , 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.
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