In mathematics, a constant function is a function whose values do not vary and thus are constant. For example the function f(x) = 4 is constant since f maps any value to 4. More formally, a function f : A → B is a constant function if f(x) = f(y) for all x and y in A.
Every empty function is constant, vacuously, since there are no x and y in A for which f(x) and f(y) are different when A is the empty set.
In the context of polynomial functions, a non-zero constant function is called a polynomial of degree zero.
A function is said to be identically zero if it takes the value 0 for every argument; it is then trivially a constant function.
Read more about Constant Function: Properties
Famous quotes containing the words constant and/or function:
“What, to the American slave, is your Fourth of July? I answer: A day that reveals to him, more than all other days in the year, the gross injustice and cruelty to which he is the constant victim. To him your celebration is a sham.”
—Frederick Douglass (c.1817–1895)
“The art of living is to function in society without doing violence to one’s own needs or to the needs of others. The art of mothering is to teach the art of living to children.”
—Elaine Heffner (20th century)