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Give examples of two continuous functions $f(n)$ and $g(n)$ of positive real inputs $n$, such that

  • $f(n)$ not equal to $O(g(n))$,
  • $g(n)$ not equal to $O(f(n))$,
  • $f(n)$ not equal to $Omega(g(n))$ and
  • $g(n)$ not equal $omega(f(n))$.

Hint: You can specify some of the values of $f(n)$ and/or $g(n)$ depending on some condition on $n$, such as when $n$ is even or odd, but make sure that your function is continuous and defined for all positive real $n$.

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    Related: http://math.stackexchange.com/questions/199344/a-function-that-is-neither-on-nor-n2012-09-21
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    Pythagoras it seems, paithyakara ....2012-09-27
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    @frustratedguy What are you trying to say?2012-09-27

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