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:
“Can you find out the deep things of God? Can you find out the limit of the Almighty?”
—Bible: Hebrew, Job 11:7.
“He said, truly, that the reason why such greatly superior numbers quailed before him was, as one of his prisoners confessed, because they lacked a cause,—a kind of armor which he and his party never lacked. When the time came, few men were found willing to lay down their lives in defense of what they knew to be wrong; they did not like that this should be their last act in this world.”
—Henry David Thoreau (1817–1862)
“It is a fundamental characteristic of civilization that man most profoundly mistrusts those living outside his own milieu, so that not only does the Teuton regard the Jew as an incomprehensible and inferior being, but the football player likewise so regards the piano player.”
—Robert Musil (1880–1942)