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F(x)+g(x) is also periodic

  1. Jul 8, 2009 #1

    correct me if I am wrong, but as far as I know if 2 functions f(x) and g(x) are periodic with Tf and Tg periods. f(x)+g(x) is also periodic with least common multiple of Tf and Tg.

    But; what if that least common multiple doesn't exist?

    is "sin(x) + sin(pi*x)" periodic?

    there is no x ( except for zero ) which makes both sin(x) and sin(pi*x) zero at the same x.

  2. jcsd
  3. Jul 8, 2009 #2


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    Re: periodicity

    The quotient of the periods, Tf/Tg has to be rational in order for the sum to be periodic.
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