In
mathematics, the
limit inferior and
limit superior of a
sequence can be thought of as limiting (i.e., eventual and extreme) bounds on the sequence. They can be thought of in a similar fashion for a
function (see
limit of a function). For a set, they 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. Limit inferior is also called
infimum limit,
liminf,
inferior limit,
lower limit, or
inner limit; limit superior is also known as
supremum limit,
limit supremum,
limsup,
superior limit,
upper limit, or
outer limit.