The infimum limit, also called the limit inferior or lower limit, of a sequence of real numbers 
,
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 
.
When 
,
the sequence converges to the real number
 |
Otherwise, the sequence does not converge.
