6. Let f:[0,1→ R be defined by f(x) = {1 if x E Q lo if x e Q° a) Prove that f is not Riemann Integral (b) Note that the boundedness condition is satisfied, yet, the function is f in 6a is not Riemann Integral

6. Let f:[0,1→ R be defined by f(x) = {1 if x E Q lo if x e Q° a) Prove that f is not Riemann Integral (b) Note that the boundedness condition is satisfied, yet, the function is f in 6a is not Riemann Integral

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.4: Ordered Integral Domains

Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....

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6. Let f: [0,1] → R be defined by
(1 ifxε φ
f(x) = {o if x € Q°
a) Prove that f is not Riemann Integral
(b) Note that the boundedness condition is satisfied, yet the function is fin 6a is not Riemann
Integral

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