Definition
A partially ordered set (poset) P is said to satisfy the ascending chain condition (ACC) if every strictly ascending sequence of elements eventually terminates. Equivalently, given any sequence
there exists a positive integer n such that
Similarly, P is said to satisfy the descending chain condition (DCC) if every strictly descending sequence of elements eventually terminates, that is, there is no infinite descending chain. Equivalently every descending sequence
of elements of P, eventually stabilizes.
Read more about this topic: Ascending Chain Condition
Famous quotes containing the word definition:
“... if, as women, we accept a philosophy of history that asserts that women are by definition assimilated into the male universal, that we can understand our past through a male lensif we are unaware that women even have a historywe live our lives similarly unanchored, drifting in response to a veering wind of myth and bias.”
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“According to our social pyramid, all men who feel displaced racially, culturally, and/or because of economic hardships will turn on those whom they feel they can order and humiliate, usually women, children, and animalsjust as they have been ordered and humiliated by those privileged few who are in power. However, this definition does not explain why there are privileged men who behave this way toward women.”
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“Was man made stupid to see his own stupidity?
Is God by definition indifferent, beyond us all?
Is the eternal truth mans fighting soul
Wherein the Beast ravens in its own avidity?”
—Richard Eberhart (b. 1904)