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:
“It is after all the greatest art to limit and isolate oneself.”
—Johann Wolfgang Von Goethe (1749–1832)
“A superior person does not remember a petty person’s trespasses.”
—Chinese proverb.