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:
“Guilty, guilty, guilty is the chant divorced parents repeat in their heads. This constant reminder remains just below our consciousness. Nevertheless, its presence clouds our judgment, inhibits our actions, and interferes in our relationship with our children. Guilt is a major roadblock to building a new life for yourself and to being an effective parent.”
—Stephanie Marston (20th century)
“The mother’s and father’s attitudes toward the child correspond to the child’s own needs.... Mother has the function of making him secure in life, father has the function of teaching him, guiding him to cope with those problems with which the particular society the child has been born into confronts him.”
—Erich Fromm (1900–1980)