limit superior

limit superior

[′lim·ət sə′pir·ē·ər]

(mathematics)

Also known as upper limit.

The limit superior of a sequence whose n th term is a_n is the limit as N approaches infinity of the least upper bound of the terms a_n for which n is greater than N ; denoted by

The limit superior of a function ƒ at a point c is the limit as ε approaches zero of the least upper bound of ƒ(x) for | x-c | ε and x ≠ c ; denoted by

For a sequence of sets, the set consisting of all elements that belong to infinitely many of the sets in the sequence. Also known as complete limit.

McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.