Compact Element
In the mathematical area of order theory, the compact or finite elements of a partially ordered set are those elements that cannot be subsumed by a supremum of any non-empty directed set that does not already contain members above the compact element.
Note that there are other notions of compactness in mathematics; also, the term "finite" in its normal set theoretic meaning does not coincide with the order-theoretic notion of a "finite element".
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Famous quotes containing the words compact and/or element:
“The Puritans, to keep the remembrance of their unity one with another, and of their peaceful compact with the Indians, named their forest settlement CONCORD.”
—Ralph Waldo Emerson (1803–1882)
“We must be very suspicious of the deceptions of the element of time. It takes a good deal of time to eat or to sleep, or to earn a hundred dollars, and a very little time to entertain a hope and an insight which becomes the light of our life.”
—Ralph Waldo Emerson (1803–1882)