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 lowerlim_(n->∞) S_n = lim_(n->∞)__ S_n = h is said to exist if, for every ϵ>0, left bracketing bar S_n - h right bracketing bar <ϵ for infinitely many values of n and if no number less than h has this property.
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