Let f be a uniformly continuous function on a set E. Prove that for any Cauchy sequence {n} CE, the sequence {f(n)} is also Cauchy.
Let f be a uniformly continuous function on a set E. Prove that for any Cauchy sequence {n} CE, the sequence {f(n)} is also Cauchy.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 64E
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![Let f be a uniformly continuous function on a set E. Prove that for any Cauchy sequence
{n} CE, the sequence {f(n)} is also Cauchy.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fff2dd156-38c9-4dbd-9b97-4c0a3b6e00c0%2F753254fb-9ff6-4db8-9a2e-cdbcaa525e35%2Fguqcl9n_processed.png&w=3840&q=75)
Transcribed Image Text:Let f be a uniformly continuous function on a set E. Prove that for any Cauchy sequence
{n} CE, the sequence {f(n)} is also Cauchy.
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