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:
“Love not me for comely grace,
For my pleasing eye or face,
Nor for any outward part:
No, nor for a constant heart!”
—Unknown. Love Not Me for Comely Grace (l. 1–4)
“Morality and its victim, the mother—what a terrible picture! Is there indeed anything more terrible, more criminal, than our glorified sacred function of motherhood?”
—Emma Goldman (1869–1940)