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:
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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)
“Literature does not exist in a vacuum. Writers as such have a definite social function exactly proportional to their ability as writers. This is their main use.”
—Ezra Pound (1885–1972)