greatest element in a sentence

Examples

1. Hence, the greatest element of " S " is an upper bound of " S " that is contained within this subset.
2. Even if a set has some upper bounds, it need not have a greatest element, as shown by the example of the negative real numbers.
3. Dually, a meet-semilattice is "'bounded "'if it has a greatest element, the meet of the empty set.
4. 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.
5. The existence of a certain Galois connection now implies the existence of the respective least or greatest elements, no matter whether the corresponding posets satisfy any completeness properties.
6. This example also demonstrates that the existence of a least upper bound ( the number 0 in this case ) does not imply the existence of a greatest element either.
7. A greatest element of a partially ordered subset must not be confused with " maximal elements " of the set, which are elements that are not smaller than any other elements.
8. If " S " contains a greatest element, then that element is the supremum; otherwise, the supremum does not belong to " S " ( or does not exist ).
9. Some great buildings dominate the architectural landscape, as the Rouyn-Noranda campus of the Universit?du Qu�bec, which could be seen by many aspects as the greatest element of contemporary architecture of the region.
10. Yet, the two posets are not isomorphic : [ & minus; 1, 1 ] has both a least and a greatest element, which are not present in the case of the real numbers.