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Is it true?

$an^{2} = O(n^{2})$  for a>0

Also, what is the difference between Small-oh and Big-oh?

Also, why we consider theta, omega as Big-oh sometimes, in the above problem, the answer is Big-theta but it is equal to big-oh. Why is it so?
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Small Oh and Big Oh have different definitions, they are clearly given in Cormen.
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can you please verify that asymptotic equation given above.

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https://en.wikipedia.org/wiki/Big_O_notation#Formal_definition

Look at this definition given here and see if what you are asking makes sense. If you still don't get it, I'll help you out.

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got it