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Quasi-Cauchy sequences. (English) Zbl 1204.26003

Summary: A quasi-Cauchy sequence is one in which the distance between successive terms tends to zero. This is a far weaker property than that of being Cauchy, although students in undergraduate real analysis classes often struggle with the distinction between the two concepts. Nevertheless, quasi-Cauchy sequences have many interesting properties. In this paper we investigate such sequences in both the real number system and in general metric spaces.

MSC:

26A06 One-variable calculus
97I30 Sequences and series (educational aspects)
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