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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No, this is not true. For example, let $f$ be the constant $1$ function, and define $g$ by $g(2n) = 1/n$ and $g(2n+1) = 1$.
answered Oct 6, 2015 at 22:08
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$\begingroup$ Very Good. Thank you. Haven't thought about these kind of functions. $\endgroup$ Commented Oct 6, 2015 at 22:13