Limit Superior And Limit Inferior
In mathematics, the limit inferior (also called infimum limit, liminf, inferior limit, lower limit, or inner limit) and limit superior (also called supremum limit, limsup, superior limit, upper limit, or outer limit) of a sequence can be thought of as limiting (i.e., eventual and extreme) bounds on the sequence. The limit inferior and limit superior of a function can be thought of in a similar fashion (see limit of a function). The limit inferior and limit superior of a set are the infimum and supremum of the set's limit points, respectively. In general, when there are multiple objects around which a sequence, function, or set accumulates, the inferior and superior limits extract the smallest and largest of them; the type of object and the measure of size is context-dependent, but the notion of extreme limits is invariant.
Read more about Limit Superior And Limit Inferior: Definition For Sequences, The Case of Sequences of Real Numbers, Real-valued Functions, Functions From Metric Spaces To Metric Spaces, Sequences of Sets, Generalized Definitions
Famous quotes containing the words limit, superior and/or inferior:
“We live in oppressive times. We have, as a nation, become our own thought police; but instead of calling the process by which we limit our expression of dissent and wonder “censorship,” we call it “concern for commercial viability.””
—David Mamet (b. 1947)
“The traveler to the United States will do well ... to prepare himself for the class-consciousness of the natives. This differs from the already familiar English version in being more extreme and based more firmly on the conviction that the class to which the speaker belongs is inherently superior to all others.”
—John Kenneth Galbraith (b. 1908)
“The world proceeds from the same spirit as the body of man. It is a remoter and inferior incarnation of God, a projection of God in the unconscious.”
—Ralph Waldo Emerson (1803–1882)