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 an = c, the sequence (f(an)) is a Cauchy sequence. Prove that lim f (x) exists.
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 an = c, the sequence (f(an)) is a Cauchy sequence. Prove that lim f (x) exists.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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