The Case of Sequences of Real Numbers
In mathematical analysis, limit superior and limit inferior are important tools for studying sequences of real numbers. Since the supremum and infimum of an unbounded set of real numbers may not exist (the reals are not a complete lattice), it is convenient to consider sequences in the affinely extended real number system: we add the positive and negative infinities to the real line to give the complete totally ordered set, which is a complete lattice.
Read more about this topic: Limit Superior And Limit Inferior
Famous quotes containing the words case, real and/or numbers:
“The woods were as fresh and full of vegetable life as a lichen in wet weather, and contained many interesting plants; but unless they are of white pine, they are treated with as little respect here as a mildew, and in the other case they are only the more quickly cut down.”
—Henry David Thoreau (1817–1862)
“The real world is not easy to live in. It is rough; it is slippery. Without the most clear-eyed adjustments we fall and get crushed. A man must stay sober: not always, but most of the time.”
—Clarence Day (1874–1935)
“The only phenomenon with which writing has always been concomitant is the creation of cities and empires, that is the integration of large numbers of individuals into a political system, and their grading into castes or classes.... It seems to have favored the exploitation of human beings rather than their enlightenment.”
—Claude Lévi-Strauss (b. 1908)