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Big omega definition: $f(x)=\Omega(g(x))$ if $f(x) \ge c g(x)$

Is it correct to switch it around to proof:

$$g(x) \le c f(x)$$

I am afraid that moving the '$c$' to the other side may change the entire idea.


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Why did you use Big Theta instead of Big Omega in line 1? –  Ganesh Dec 11 '12 at 2:06
oops, sorry it should be omega –  user1234440 Dec 11 '12 at 2:08
i just editted it –  user1234440 Dec 11 '12 at 2:08
Your result is essentially right. Suppose $x>x_0$ throughout , where $x_0$ is the positive constant used in defining $\Omega$. Note also that $c$ is positive by definition. If $f(x) \geq cg(x)$ then $g(x) \leq f(x)/c$. We can define $k=1/c$, where $k$ is another positive constant. So $g(x) \leq kf(x)$. –  Ganesh Dec 11 '12 at 2:20

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