Limit Superior
Limit superior and limit inferior of a net of real numbers can be defined in a similar manner as for sequences. Some authors work even with more general structures than the real line, like complete lattices.
For a net we put
Limit superior of a net of real numbers has many properties analogous to the case of sequences, e.g.
where equality holds whenever one of the nets is convergent.
Read more about this topic: Net (mathematics)
Famous quotes containing the words limit and/or superior:
“Today, the notion of progress in a single line without goal or limit seems perhaps the most parochial notion of a very parochial century.”
—Lewis Mumford (1895–1990)
“There are few things more disturbing than to find, in somebody we detest, a moral quality which seems to us demonstrably superior to anything we ourselves possess. It augurs not merely an unfairness on the part of creation, but a lack of artistic judgement.... Sainthood is acceptable only in saints.”
—Pamela Hansford Johnson (1912–1981)