limit superior[′lim·ət sə′pir·ē·ər]
Also known as upper limit.
The limit superior of a sequence whose n th term is an is the limit as N approaches infinity of the least upper bound of the terms an 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.