Constant (mathematics)

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:

ax^{2}+bx+c\,,

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

x\mapsto ax^{2}+bx+c\,,

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 $x 0$ . More generally, any polynomial term or expression of degree zero (no variable) is a constant.^: 18

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