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 powers of the federal government ... result from the compact to which the states are parties, [and are] limited by the plain sense and intention of the instrument constituting that compact.”
—James Madison (1751–1836)
“Having become conscious of the truth he once perceived, man now sees only the awfulness or the absurdity of existence, he now understands the symbolic element in Ophelia’s fate, he now recognizes the wisdom of the woodland god, Silenus: it nauseates him.”
—Friedrich Nietzsche (1844–1900)