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:
“The Mind that lies fallow but a single Day, sprouts up in Follies that are only to be killed by a constant and assiduous Culture.”
—Joseph Addison (1672–1719)
“The function of muscle is to pull and not to push, except in the case of the genitals and the tongue.”
—Leonardo Da Vinci (1425–1519)