upper limit
（ plural ）
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(mathematical analysis) 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.
upper limit
To determine the upper limit of a sequence of real numbers, remove successive initial terms to form tail subsequences, find the supremum of each tail, and then take the infimum of those supremums.
To determine the upper limit of a sequence of real numbers, remove successive initial terms to form tail subsequences, find the supremum of each tail, and then take the infimum of those supremums.
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