The limit inferior of a sequence whose
nth term is
an is the limit as
N approaches infinity of the greatest lower bound of the terms
an for which
n is greater than
N; denoted by

. The limit inferior of a function
f at a point
c is the limit as
∊ approaches zero of the greatest lower bound of
f (
x ) for |
x -
c|<
∊ and x ≠
c; denoted by

.