Formal Definition
A subset S of the natural numbers is called recursive if there exists a total computable function f such that f(x) = 1 if x ∈ S and f(x) = 0 if x ∉ S . In other words, the set S is recursive if and only if the indicator function 1S is computable.
Read more about this topic: Recursive Set
Famous quotes containing the words formal and/or definition:
“The conviction that the best way to prepare children for a harsh, rapidly changing world is to introduce formal instruction at an early age is wrong. There is simply no evidence to support it, and considerable evidence against it. Starting children early academically has not worked in the past and is not working now.”
—David Elkind (20th century)
“It is very hard to give a just definition of love. The most we can say of it is this: that in the soul, it is a desire to rule; in the spirit, it is a sympathy; and in the body, it is but a hidden and subtle desire to possess—after many mysteries—what one loves.”
—François, Duc De La Rochefoucauld (1613–1680)