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In the class we have seen three equivalent definitions for f(n)=O(g(n)). The first of these was: f(n)=O(g(n)) if and only if there is some constant

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In the class we have seen three equivalent definitions for f(n)=O(g(n)). The first of these was: f(n)=O(g(n)) if and only if there is some constant C>0 as well as a positive integer threshold n0 such that for every n>n0 we have f(n)0, the above condition is equivalent to: f(n)=O(g(n)) if and only if there is some constant C>0 such that for every n>0 we have f(n)0," then () is not equivalent with (). For this you need to give an example for f and g (however pathologic it is), where (*) holds but (**) does not

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