| 词条 | Subsequential limit |
| 释义 | {{unreferenced|date=December 2012}} In mathematics, a subsequential limit of a sequence is the limit of some subsequence. Every subsequential limit is a cluster point, but not conversely. In first-countable spaces, the two concepts coincide. The supremum of the set of all subsequential limits of some sequence is called the limit superior, or limsup. Similarly, the infimum of such a set is called the limit inferior, or liminf. See limit superior and limit inferior. If (X,d) is a metric space and there is a Cauchy sequence such that there is a subsequence converging to some x, then the sequence also converges to x. {{Mathanalysis-stub}} 2 : Limits (mathematics)|Sequences and series |
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