Definition
Given a set S and two binary operators · and + on S, we say that the operation ·
- is left-distributive over + if, given any elements x, y, and z of S,
-
- x · (y + z) = (x · y) + (x · z);
- is right-distributive over + if, given any elements x, y, and z of S:
-
- (y + z) · x = (y · x) + (z · x);
- is distributive over + if it is left- and right-distributive.
Notice that when · is commutative, then the three above conditions are logically equivalent.
Read more about this topic: Distributive Property
Famous quotes containing the word definition:
“Perhaps the best definition of progress would be the continuing efforts of men and women to narrow the gap between the convenience of the powers that be and the unwritten charter.”
—Nadine Gordimer (b. 1923)
“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)
“Scientific method is the way to truth, but it affords, even in
principle, no unique definition of truth. Any so-called pragmatic
definition of truth is doomed to failure equally.”
—Willard Van Orman Quine (b. 1908)