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:
“Sigh no more, ladies, sigh no more,
Men were deceivers ever,
One foot in sea and one on shore,
To one thing constant never:
Then sigh not so, but let them go,
And be you blithe and bonny,
Converting all your sounds of woe
Into Hey nonny, nonny.”
—William Shakespeare (1564–1616)
“The intension of a proposition comprises whatever the proposition entails: and it includes nothing else.... The connotation or intension of a function comprises all that attribution of this predicate to anything entails as also predicable to that thing.”
—Clarence Lewis (1883–1964)