Limit Superior and Limit Inferior

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:

    “Today, the notion of progress in a single line without goal or limit seems perhaps the most parochial notion of a very parochial century.”
    —Lewis Mumford (1895–1990)

    “The First Amendment is not a blanket freedom-of-information act. The constitutional newsgathering freedom means the media can go where the public can, but enjoys no superior right of access.”
    —George F. Will (b. 1934)

    “I find very reasonable the Celtic belief that the souls of our dearly departed are trapped in some inferior being, in an animal, a plant, an inanimate object, indeed lost to us until the day, which for some never arrives, when we find that we pass near the tree, or come to possess the object which is their prison. Then they quiver, call us, and as soon as we have recognized them, the spell is broken. Freed by us, they have vanquished death and return to live with us.”
    —Marcel Proust (1871–1922)