Let f : R R be defined by setting f(x) := x if x is rational,

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Let f : R → R be defined by setting f(x) := x if x is rational, and f(x) = 0 if x is irrational.
(a) Show that f has a limit at x = 0.
(b) Use a sequential argument to show that if c ≠ 0, then f does not have a limit at c.

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Introduction to Real Analysis

ISBN: 978-0471433316

4th edition

Authors: Robert G. Bartle, Donald R. Sherbert

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Question Posted: Apr 07, 2016 10:58 AM

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Let f : R R be defined by setting f(x) := x if x is rational,

Question:

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a Since fx 0 x we can take to show that fx 0 b If c 0 i...View the full answer

Introduction to Real Analysis

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