Let c be a cluster point of a subset A of R and let f : A → R be a function. Suppose for every sequence (an) in A such that lim a, = c, the sequence (f(an)) is a Cauchy sequence. Prove that limf (x) exists.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 72E
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Let c be a cluster point of a subset A of R and let f : A → R be a function. Suppose for every
sequence (an) in A such that lim a, =
c, the sequence (f(an)) is a Cauchy sequence. Prove
that limf (x) exists.
Transcribed Image Text:Let c be a cluster point of a subset A of R and let f : A → R be a function. Suppose for every sequence (an) in A such that lim a, = c, the sequence (f(an)) is a Cauchy sequence. Prove that limf (x) exists.
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