Define f : R → R by f(x) = 0 if x∈ R\Q f(x)=1/q if x=p/q with (p, q) = 1. Prove that f is continuous on R \ Q and discontinuous on Q.
Define f : R → R by f(x) = 0 if x∈ R\Q f(x)=1/q if x=p/q with (p, q) = 1. Prove that f is continuous on R \ Q and discontinuous on Q.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.5: Permutations And Inverses
Problem 5E: Let f:AA, where A is nonempty. Prove that f a has right inverse if and only if f(f1(T))=T for every...
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Define f : R → R by
f(x) = 0 if x∈ R\Q
f(x)=1/q if x=p/q with (p, q) = 1.
Prove that f is continuous on R \ Q and discontinuous on Q.
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