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)
“No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.”
—Florence Nightingale (1820–1910)
“... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
—George Eliot [Mary Ann (or Marian)