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:
“Can you find out the deep things of God? Can you find out the limit of the Almighty?”
—Bible: Hebrew, Job 11:7.
“He said, truly, that the reason why such greatly superior numbers quailed before him was, as one of his prisoners confessed, because they lacked a cause,—a kind of armor which he and his party never lacked. When the time came, few men were found willing to lay down their lives in defense of what they knew to be wrong; they did not like that this should be their last act in this world.”
—Henry David Thoreau (1817–1862)