| upper limit -
The upper limit of a sequence of real numbers is the real number which can be found as follows: remove the first term of the sequence in order to obtain the "first subsequence. " Then remove the first term of the first subsequence in order to obtain the "second subsequence. " Repeat the removal of first terms in order to obtain a "third subsequence," "fourth subsequence," etc. Find the supremum of each of these subsequences, then find the infimum of all of these supremums. This infimum is the upper limit.
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