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:
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—Epicurus (c. 341–271 B.C.)
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—Antonin Artaud (1896–1948)
“If the only new thing we have to offer is an improved version of the past, then today can only be inferior to yesterday. Hypnotised by images of the past, we risk losing all capacity for creative change.”
—Robert Hewison (b. 1943)