In order-theoretic mathematics, a partially ordered set in is chain complete if every chain in it has a least upper bound. It is ω-complete when every increasing sequence of elements (a type of countable chain) has a least upper bound; the same notion can be extended to other cardinalities of chains.
Read more about Chain Complete: Examples, Properties
Famous quotes containing the words chain and/or complete:
“It could not have come down to us so far,
Through the interstices of things ajar
On the long bead chain of repeated birth,
To be a bird while we are men on earth,”
—Robert Frost (1874–1963)
“Could slavery suggest a more complete servility than some of these journals exhibit? Is there any dust which their conduct does not lick, and make fouler still with its slime?”
—Henry David Thoreau (1817–1862)