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:
“The back meets the front.”
—Hawaiian saying no. 2650, ‘lelo No’Eau, collected, translated, and annotated by Mary Kawena Pukui, Bishop Museum Press, Hawaii (1983)
“General jackdaw culture, very little more than a collection of charming miscomprehensions, untargeted enthusiasms, and a general habit of skimming.”
—William Bolitho (1890–1930)