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:
“Was man made stupid to see his own stupidity?
Is God by definition indifferent, beyond us all?
Is the eternal truth man’s fighting soul
Wherein the Beast ravens in its own avidity?”
—Richard Eberhart (b. 1904)
“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)
“The physicians say, they are not materialists; but they are:MSpirit is matter reduced to an extreme thinness: O so thin!—But the definition of spiritual should be, that which is its own evidence. What notions do they attach to love! what to religion! One would not willingly pronounce these words in their hearing, and give them the occasion to profane them.”
—Ralph Waldo Emerson (1803–1882)