# Constant (mathematics)

## Function or value which does not change / From Wikipedia, the free encyclopedia

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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.^{[1]} - A function whose value remains unchanged (i.e., a
*constant function*).^{[2]}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.^{[3]}^{: 18 }