## 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.

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.