Again, yes, I know. I understand what the model is. I'm saying it's not useful to point out that you can choose contradicting axioms to base your model on. And make no mistake, the two axioms that you are proposing do contradict each other.

So again, the issue is not that you can't compare numbers of arbitrary magnitude in constant time -- I never said that. The issue is that it is a contradiction to say that it takes linear time to inspect all the digits of a number AND that it only takes constant time to compare O(n) digits of two numbers.

You're essentially saying that you can axiomatize your mathematical universe with nonsense axioms, which yes, you could do, but that's not useful to point out.