Asymptotic notations

Question

Is $ (5 - n^3) \in \Omega (n^2) $ ?

Answer 1

Yes. $ (5 - n^3) \in \Omega (n^2) $

$  \Omega (n^2) $ is set of all the functions which have power $ n^2 $ or more than that. 

Hence $ (5 - n^3) $ is in the $  \Omega (n^2) $. 

Hence, $ (5 - n^3) \in \Omega (n^2) $.

Comments

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Answer 2

It is not a question of asymptotic complexity as an algorithm cannot perform negative work. It is a question about growth of functions.

We know as n gets higher Ω($n^{2}$) approaches + infinity , whereas (5-$n^{3}$) approaches - infinity.

This can be visualized on a cartesian plane. Hence the given expression is false because Ω($n^{2}$) will always be greater than (5-$n^{3}$)  for higher values of n.

Answer 3

yes true n^3 > n^2