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)
“And what is an authentic madman? It is a man who preferred to become mad, in the socially accepted sense of the word, rather than forfeit a certain superior idea of human honor. So society has strangled in its asylums all those it wanted to get rid of or protect itself from, because they refused to become its accomplices in certain great nastinesses. For a madman is also a man whom society did not want to hear and whom it wanted to prevent from uttering certain intolerable truths.”
—Antonin Artaud (1896–1948)