Definition
Let X be a set with a partial order ≤. As usual, let < be the relation on X such that x < y if and only if x ≤ y and x ≠ y.
Let x and y be elements of X.
Then y covers x, written x <· y, if x < y and there is no element z such that x < z < y. Equivalently, y covers x if the interval is the two-element set {x, y}.
When x <· y, it is said that y is a cover of x. Some authors also use the term cover to denote any such pair (x, y) in the covering relation.
Read more about this topic: Covering Relation
Famous quotes containing the word definition:
“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)
“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)
“... if, as women, we accept a philosophy of history that asserts that women are by definition assimilated into the male universal, that we can understand our past through a male lens—if we are unaware that women even have a history—we live our lives similarly unanchored, drifting in response to a veering wind of myth and bias.”
—Adrienne Rich (b. 1929)