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:
“We live in oppressive times. We have, as a nation, become our own thought police; but instead of calling the process by which we limit our expression of dissent and wonder “censorship,” we call it “concern for commercial viability.””
—David Mamet (b. 1947)
“In literary circles, the men of trust and consideration, bookmakers, editors, university deans and professors, bishops, too, were by no means men of the largest literary talent, but usually of a low and ordinary intellectuality, with a sort of mercantile activity and working talent. Indifferent hacks and mediocrities tower, by pushing their forces to a lucrative point, or by working power, over multitudes of superior men, in Old as in New England.”
—Ralph Waldo Emerson (1803–1882)