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:
“Greatness collapses of itself: such limit the gods have set to the growth of prosperous states.”
—Marcus Annaeus Lucan (39–65)
“At length he would call to let us know where he was waiting for us with his canoe, when, on account of the windings of the stream, we did not know where the shore was, but he did not call often enough, forgetting that we were not Indians.... This was not because he was unaccommodating, but a proof of superior manners. Indians like to get along with the least possible communication and ado. He was really paying us a great compliment all the while, thinking that we preferred a hint to a kick.”
—Henry David Thoreau (1817–1862)