limit superior

limit superior [′lim·ət sə′pir·ē·ər]

(mathematics)

Also known as upper limit.

The limit superior of a sequence whosenth term isa_nis the limit asNapproaches infinity of the least upper bound of the termsa_nfor whichnis greater thanN; denoted by

The limit superior of a function ƒ at a pointcis the limit as ε approaches zero of the least upper bound of ƒ(x) for |x-c| ε andx≠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.