Yet it is not possible to effectively determine exactly where the initial well-ordered part ends and the part lacking a least element begins.
42.
The relation " is a substring of " defines a partial order on ? *, the least element of which is the empty string.
43.
Browsers speed up Web use by storing, or caching, recently viewed Web pages, or at least elements of them, on their user's hard drive.
44.
In addition, the domain of computation is equipped with an " ordering relation ", in which the " undefined result " is the least element.
45.
From the underlying idea of partially specified results as representing incomplete knowledge, one derives another desirable property : the existence of a "'least element " '.
46.
The notions of maximal and minimal elements are weaker than those of greatest element and least element which are also known, respectively, as maximum and minimum.
47.
Also note that the empty set usually has upper bounds ( if the poset is non-empty ) and thus a bounded complete poset has a least element.
48.
"What is clear is that an operation of this size and complexity could not be mounted without the collaboration of at least elements of governments, " he said.
49.
Note also that a join-semilattice which is directed complete is almost a complete lattice ( possibly lacking a least element )-- see completeness ( order theory ) for details.
50.
Another theory that some North Korea experts have offered is that the North Korean leadership, or at least elements within it, are embarrassed by South Korea's efforts to promote peace.
