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Math Help - Riemann Integrable

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    Riemann Integrable

    Suppose f is a riemann integrable function on [a,b]. If g is a bounded real valued function defined on [a,b] and g differs from f at infinitely many points in [a,b], should g be riemann integrable on [a,b]. Prove or disprove?
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Chandru1 View Post
    Suppose f is a riemann integrable function on [a,b]. If g is a bounded real valued function defined on [a,b] and g differs from f at infinitely many points in [a,b], should g be riemann integrable on [a,b]. Prove or disprove?
    This makes no sense. Let f(x)=3 and g(x)=\begin{cases} 1 & \mbox{if} \quad x\in\mathbb{Q}\\ 0 & \mbox{if} \quad x\notin\mathbb{Q}\end{cases}
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    Senior Member Shanks's Avatar
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    It shoud be "g differs from f at finitely many points in [a,b]", I think.
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Chandru1 View Post
    Suppose f is a riemann integrable function on [a,b]. If g is a bounded real valued function defined on [a,b] and g differs from f at infinitely many points in [a,b], should g be riemann integrable on [a,b]. Prove or disprove?
    Quote Originally Posted by Shanks View Post
    It shoud be "g differs from f at finitely many points in [a,b]", I think.
    Is that so? Or is it countably many. Or what?
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