Question
let f be defined on [0 1] by the formula f(x)=1/n if x=m/n is rational f(x)= 0 if x is irrational f(x)=1 if x=0 (x=m/n
let f be defined on [0 1] by the formula
f(x)=1/n if x=m/n is rational
f(x)= 0 if x is irrational
f(x)=1 if x=0
(x=m/n is in lowest terms, n belong to p ). prove that f is continuous only at the irrational points of [0,1]
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Introduction to Real Analysis
Authors: Robert G. Bartle, Donald R. Sherbert
4th edition
471433314, 978-1118135853, 1118135857, 978-1118135860, 1118135865, 978-0471433316
