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:
“There is no limit to what a man can do so long as he does not care a straw who gets the credit for it.”
—C.E. (Charles Edward)
“The momentary charge at Balaklava, in obedience to a blundering command, proving what a perfect machine the soldier is, has, properly enough, been celebrated by a poet laureate; but the steady, and for the most part successful, charge of this man, for some years, against the legions of Slavery, in obedience to an infinitely higher command, is as much more memorable than that as an intelligent and conscientious man is superior to a machine. Do you think that that will go unsung?”
—Henry David Thoreau (1817–1862)