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Big O notation deals with asymptotic behavior of a function - in other words, as N goes to infinity. If we're accepting the premise that N has an upper bound, the rest of the discussion is meaningless.

Presumably the argument is an abstract one, not applying to any particular machine that actually exists.

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Big O notation is often used with assumptions like adding numbers is always constant time. You can't physically build a machine where addition between any two numbers is constant time, but that doesn't matter.

It depends what you mean by "numbers": all integers or just 64-bit ones?

My point is relevant to additions that are the same type as n as n has no upper bound. n will never be a 64 bit integer.

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