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)
“I have never looked at foreign countries or gone there but with the purpose of getting to know the general human qualities that are spread all over the earth in very different forms, and then to find these qualities again in my own country and to recognize and to further them.”
—Johann Wolfgang Von Goethe (1749–1832)