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Need explanation for CLRS Solution 3-3.

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I am currently studying "Order of growth" from 3rd edition. I was not able to understand the solution for the problem 3-3(b) problem : Give an example of a single non-negative function f(n) such that for all functions g(n) in part (a), f(n) is neither O(g(n)) nor <omega>(g(n))..

On some places it is given as the solution is given as (1 + Sin(n))*2^2^(n+2)

If somebody can explain its derivation, that will be good.


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