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:
“The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.”
—William James (1842–1910)
“According to our social pyramid, all men who feel displaced racially, culturally, and/or because of economic hardships will turn on those whom they feel they can order and humiliate, usually women, children, and animals—just as they have been ordered and humiliated by those privileged few who are in power. However, this definition does not explain why there are privileged men who behave this way toward women.”
—Ana Castillo (b. 1953)
“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)