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Concept
Constant (mathematics)
Summary
In mathematics, the word constant conveys multiple meanings. As an adjective, it refers to non-variance (i.e. unchanging with respect to some other value); as a noun, it has two different meanings:
A fixed and well-defined number or other non-changing mathematical object. The terms mathematical constant or physical constant are sometimes used to distinguish this meaning.
A function whose value remains unchanged (i.e., a constant function). Such a constant is commonly represented by a variable which does not depend on the main variable(s) in question.
For example, a general quadratic function is commonly written as:
where a, b and c are constants (coefficients or parameters), and x a 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 (and by extension the constancy of a, b and c) clear. 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. More generally, any polynomial term or expression of degree zero (no variable) is a constant.
Constant function and Nullary
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 of a horizontal line parallel to the x-axis. Such a function always takes the same value (in this case 5), because the variable does not appear in the expression defining the function.
The context-dependent nature of the concept of "constant" can be seen in this example from elementary calculus:
"Constant" means not depending on some variable; not changing as that variable changes. In the first case above, it means not depending on h; in the second, it means not depending on x. A constant in a narrower context could be regarded as a variable in a broader context.
Official source
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