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:
“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)
“The very definition of the real becomes: that of which it is possible to give an equivalent reproduction.... The real is not only what can be reproduced, but that which is always already reproduced. The hyperreal.”
—Jean Baudrillard (b. 1929)
“I’m beginning to think that the proper definition of “Man” is “an animal that writes letters.””
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)