Lower Limit

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

A lower limit of a series


is said to exist if, for every epsilon>0, |S_n-h|<epsilon for infinitely many values of n and if no number less than h has this property.

See also

Infimum Limit, Limit, Supremum Limit, Upper Limit

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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.

Referenced on Wolfram|Alpha

Lower Limit

Cite this as:

Weisstein, Eric W. "Lower Limit." From MathWorld--A Wolfram Web Resource.

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