In mathematics, a subsequential limit of a sequence is the limit of some subsequence. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and In Mathematics, a sequence is an ordered list of objects (or events In Mathematics, a subsequence of some Sequence is a new sequence which is formed from the original sequence by deleting some of the elements without disturbing the It is the same as a cluster point. In Mathematics, informally speaking a limit point of a set S in a Topological space X is a point x in X that can be "approximated"

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. In Mathematics, the limit inferior and limit superior (also called infimum limit and supremum limit, or liminf and limsup

It can be shown that 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. In Mathematics, a Cauchy sequence, named after Augustin Cauchy, is a Sequence whose elements become arbitrarily close to each other as the sequence

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