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:
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)
“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)
“It’s a rare parent who can see his or her child clearly and objectively. At a school board meeting I attended . . . the only definition of a gifted child on which everyone in the audience could agree was “mine.””
—Jane Adams (20th century)