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:
“No one who cannot limit himself has ever been able to write.”
—Nicolas Boileau-Despréaux (1636–1711)
“The man who takes the liberty to live is superior to all the laws, by virtue of his relation to the lawmaker.”
—Henry David Thoreau (1817–1862)