Author: Uri Blass
Date: 12:05:27 05/14/01
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On May 14, 2001 at 13:58:50, Robert Hyatt wrote:
<snipped>
>As far as the "mythical" requirement that N be unbounded, I give this explicit
>definition of Big-oh:
>
>"We say a function g(n) is O(f(n)) for another f(n) if there exist constants
>c and N such that for all n>=N, we have g(n) <= cf(n).
>
>I don't see any _requirement_ that n or N be unbounded.
If n is bounded and gets only a finite number of values then it is clear that
always g(n) is O(1) by this definition
In this case g(n) can get only a finite number of values and
you can define c=max({g(n)}
You get g(n)<=c for all n>=1 and it means by definition that g(n)=O(1).
Uri
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