, especially order theory
, the covering relation of a partially ordered set
is the binary relation
which holds between comparable
elements that are immediate neighbours. The covering relation is commonly used to graphically express the partial order by means of the Hasse diagram
.
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.
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"But why's the rum gone?" - Johnny Depp as "Captain Jack Sparrow", The Pirates of the Carribean: The Curse of the Black Pearl
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