Lower Limit

Let the least term  of a sequence be a term which is smaller than all but a finite number of the terms which are equal to . Then  is called the lower limit of the sequence.

A lower limit of a series

is said to exist if, for every ,  for infinitely many values of  and if no number less than  has this property.

REFERENCES:

Bromwich, T. J. I'A. and MacRobert, T. M. "Upper and Lower Limits of a Sequence." §5.1 in An Introduction to the Theory of Infinite Series, 3rd ed. New York: Chelsea, p. 40 1991.