Cauchy Sequences
... In any metric space S, a divergent Cauchy sequence, because it “converges to a hole,” detects a hole into which S could fit another point. A metric space that has no such holes is called a complete metric space: Definition 4 A metric space S is complete iff every Cauchy sequence in S has a limit in ...
... In any metric space S, a divergent Cauchy sequence, because it “converges to a hole,” detects a hole into which S could fit another point. A metric space that has no such holes is called a complete metric space: Definition 4 A metric space S is complete iff every Cauchy sequence in S has a limit in ...
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... respectively. It is well known that S1(ns k) is the number of permutations of Zn = {1, 2, ..., n] with k cycles and that S(n9 k) is the number of partitions of the set Zn into k blocks [1, Ch. 5], [2, Ch. 4]. These combinatorial interpretations suggest the following extensions. Let n, fc be positive ...
... respectively. It is well known that S1(ns k) is the number of permutations of Zn = {1, 2, ..., n] with k cycles and that S(n9 k) is the number of partitions of the set Zn into k blocks [1, Ch. 5], [2, Ch. 4]. These combinatorial interpretations suggest the following extensions. Let n, fc be positive ...
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