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:
“It is after all the greatest art to limit and isolate oneself.”
—Johann Wolfgang Von Goethe (1749–1832)
“The burden of being black is that you have to be superior just to be equal. But the glory of it is that, once you achieve, you have achieved, indeed.”
—Jesse Jackson (b. 1941)
“The so-called Transcendentalists are not the only people who deal in Transcendentals. On the contrary, we seem to see that the Utilitarians,—the every-day world’s people themselves, far transcend those inferior Transcendentalists by their own incomprehensible worldly maxims.”
—Herman Melville (1819–1891)