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This question already has an answer here:

Considering functions f and g, is the following true?

$ (f \in O(g)) \implies (f \in \Theta(g)) \lor (f \in o(g))$

If not, can you please state an example? Despite thinking hard, i could not find one.

Thanks a lot!

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marked as duplicate by Raphael Oct 7 '15 at 7:12

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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No, this is not true. For example, let $f$ be the constant $1$ function, and define $g$ by $g(2n) = 1/n$ and $g(2n+1) = 1$.

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  • $\begingroup$ Very Good. Thank you. Haven't thought about these kind of functions. $\endgroup$ – NoMorePen Oct 6 '15 at 22:13

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