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:
“Was man made stupid to see his own stupidity?
Is God by definition indifferent, beyond us all?
Is the eternal truth man’s fighting soul
Wherein the Beast ravens in its own avidity?”
—Richard Eberhart (b. 1904)
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)
“One definition of man is “an intelligence served by organs.””
—Ralph Waldo Emerson (1803–1882)