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Jefine f RR by f(x) = 1 if x is rational, f(x) = 0 if x is irrational. Prove that there exists a sequence {n} converging to a real number xo such that xn xo f(xn) - f(xo) for all n E R and such that the sequence is unbounded. Xnxo

Jefine f RR by f(x) = 1 if x is rational, f(x) = 0 if x is irrational. Prove that there exists a sequence {n} converging to a real number xo such that xn xo f(xn) - f(xo) for all n E R and such that the sequence is unbounded. Xnxo

Advanced Engineering Mathematics
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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Jefine f RR by f(x) = 1 if x is rational, f(x) = 0 if x is irrational. Prove that there exists a sequence {n} converging to a real number to such that xn ‡ xo f(xn) - f(xo) for all n E R and such that the sequence is unbounded. Xnxo
Transcribed Image Text:Jefine f RR by f(x) = 1 if x is rational, f(x) = 0 if x is irrational. Prove that there exists a sequence {n} converging to a real number to such that xn ‡ xo f(xn) - f(xo) for all n E R and such that the sequence is unbounded. Xnxo
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