Is the value of n_0 in complexity questions precise or flexible?

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The value of n_0 in complexity questions does not need to be a precise point of intersection between the functions f(n) and cg(n). It can be any point where n > n_0, as the primary requirement is that f(n) must be less than or equal to cg(n) for all n greater than n_0. This flexibility allows for a broader interpretation of Big O notation, emphasizing the existence of a suitable n_0 rather than its exact location.

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Let's say f(n) = O(g(n)), i.e. f(n) < cg(n) for some n > n_0. Does the n_0 have to be a precise point of intersection of cg(n) and f(n) or just any point for which n > n_0?

Thanks in advance.
 
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Any such point n_0 is fine.
 


The value of n_0 does not have to be a precise point of intersection between cg(n) and f(n). It can be any point for which n > n_0. The purpose of n_0 is to indicate the point at which f(n) becomes less than or equal to cg(n). As long as this condition is met, the statement f(n) = O(g(n)) holds true. Therefore, the exact location of the intersection is not as important as the fact that it exists and satisfies the condition.
 

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