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How are metric spaces used in the definition of a Cauchy sequence?

In: Math and Arithmetic, Topology, Abstract Algebra [Edit categories]

Answer:

Let B, D be a metric space, e be any positive number, m be an integer such that m Є N where N is the set of all positive integers, and let {s_b}, b Є N and {s_c}, c Є N be sequences where both b and c are greater than m. Then the sequence {s_b} is a Cauchy sequence in the set B with metric D if for any element e Є B, an m exists where D(s_b,s_c) < e

That's just a fancy way of saying converging sequences are Cauchy sequences, but not necessarily the other way around.

See related links for some definitions.

First answer by Mrkbh. Last edit by Mrkbh. Contributor trust: 685 [recommend contributor ]. Question popularity: 2 [recommend question].

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