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So I'm trying to learn how to simplify Big O notations, these are the ones i'm working on (also sorry if i mess up the format, i'm new)

So the first one i have is: f(n) = n g(n) = n/loglog 12

I have to determine whether f is O(g), Omega(g), or Theta(g).

I also want to account for Big O vs Little O (which is also something i'm having trouble understanding but i think the idea is simply strictly greater than or strictly less than).

How i simplified: f(n) = n, g(n) = n/loglog12 -> g(n) = n f is Theta(g) ?? since simplified it is, f(n) = n and g(n) = n?

Am i doing this right?

fatalwanderer
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  • No, you're not doing it right. $g(n)=n/\log\log12$ does not imply that $g(n)=n$, as you claim. – David Richerby Oct 05 '15 at 22:21
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    You're on the right track, but your approach is messy. Maybe write down the definition of big-O and see if you can prove whether or not f is big-O of g, using the exact definition. – usul Oct 05 '15 at 22:40

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