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)
“To a superior race of being the pretensions of mankind to extraordinary sanctity and virtue must seem ... ridiculous.”
—William Hazlitt (1778–1830)