Given a sequence of real numbers , the infimum limit (also called the limit inferior or lower
limit), written
and pronounced 'lim-inf,' is the limit of

as . Note that by definition,
is nondecreasing, and so either has
a limit or tends to .
For example, suppose ,
then for
odd, ,
and for
even, .
Another example is ,
in which case
is a constant sequence .