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:
“There is a limit to the application of democratic methods. You can inquire of all the passengers as to what type of car they like to ride in, but it is impossible to question them as to whether to apply the brakes when the train is at full speed and accident threatens.”
—Leon Trotsky (1879–1940)
“A superior person brings out the best in others.”
—Chinese proverb.
Confucian Analects.
“Few persons who have ever sat for a portrait can have felt anything but inferior while the process is going on.”
—Anthony Powell (b. 1905)