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I want to prove the following: $$\frac{\Omega(f(n))}{\Omega(g(n))} \subseteq \Omega(\frac{f(n)}{g(n)})$$ I wonder if its true?
What about using $n$ and $n^2$?
Any suggestions? Thanks!

Ofir Attia
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  • The statement is false. It sounds like you have a counterexample in mind; what do you mean "what about using $n$ and $n^2$"? – Antonio Vargas Apr 08 '14 at 15:09

1 Answers1

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The statement is false.

$$f(n)=n^4,g(n)=n^2\\ n^4\in \Omega(f(n)),n^3\in \Omega(g(n))\\\frac{n^4}{n^3} \subseteq \Omega(\frac{n^4}{n^2})\\\\n \nsubseteq \Omega(n^2)$$

Evyatar Elmaliah
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