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:
“If only he would not pity us so much,
Weaken our fate, relieve us of woe both great
And small, a constant fellow of destiny,
A too, too human god, self-pity’s kin
And uncourageous genesis . . .”
—Wallace Stevens (1879–1955)
“We are thus able to distinguish thinking as the function which is to a large extent linguistic.”
—Benjamin Lee Whorf (1897–1934)