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 are rarely able to interact only with folks like ourselves, who think as we do. No matter how much some of us deny this reality and long for the safety and familiarity of sameness, inclusive ways of knowing and living offer us the only true way to emancipate ourselves from the divisions that limit our minds and imaginations.”
—bell hooks (b. 1955)
“For by superior energies; more strict
Affiance in each other; faith more firm
In their unhallowed principles, the bad
Have fairly earned a victory o’er the weak,
The vacillating, inconsistent good.”
—William Wordsworth (1770–1850)