Meets of General Subsets
If (A,∧) is a meet-semilattice, then the meet may be extended to a well-defined meet of any non-empty finite set, by the technique described in iterated binary operations. Alternatively, if the meet defines or is defined by a partial order, some subsets of A indeed have infima with respect to this, and it is reasonable to consider such an infimum as the meet of the subset. For non-empty finite subsets, the two approaches yield the same result, whence either may be taken as a definition of meet. In the case where each subset of A has a meet, in fact (A,≤) is a complete lattice; for details, see completeness (order theory).
Read more about this topic: Join And Meet
Famous quotes containing the words meets and/or general:
“Though an unpleasant sort of person, and even a queer threatener withal, yet, if one meets him, one must get along with him as one can; for his ignorance is extreme. And what under heaven indeed should such a phantasm as Death know, for all that the Appearance tacitly claims to be somebody that knows much?”
—Herman Melville (1819–1891)
“To judge from a single conversation, he made the impression of a narrow and very English mind; of one who paid for his rare elevation by general tameness and conformity. Off his own beat, his opinions were of no value.”
—Ralph Waldo Emerson (1803–1882)