151k views
3 votes
Define lim sup sn and lim inf sn.

A. lim sup sn is the maximum limit, lim inf sn is the minimum limit.
B. lim sup sn is the limit superior, lim inf sn is the limit inferior.
C. lim sup sn is the positive limit, lim inf sn is the negative limit.
D. lim sup sn is the lower limit, lim inf sn is the upper limit.

User Alex Styl
by
7.3k points

1 Answer

2 votes

Final answer:

The terms 'lim sup' and 'lim inf' refer to the limit superior and limit inferior of a sequence, respectively. The limit superior is the supremum of subsequential limits while the limit inferior is the infimum of subsequential limits.

Step-by-step explanation:

The correct answer to the question is B. lim sup sn is the limit superior, lim inf sn is the limit inferior. These are concepts used in mathematical analysis to describe the limiting behavior of a sequence. The limit superior, or lim sup, of a sequence (sn) refers to the supremum (least upper bound) of the set of subsequential limits, essentially capturing the limit of the upper peaks of the sequence as it progresses to infinity. Conversely, the limit inferior, or lim inf, of a sequence (sn) designates the infimum (greatest lower bound) of all subsequential limits, representing the limit of the lower bounds of the sequence.

User Akshay Khandelwal
by
8.3k points