I was talking about exactitude in general, as a requirement for a physical interpretation of the integers.
> I think it is not impossible for us to prove that the universe was created by a god, if we found some hidden message in subatomic particles or cosmic dust or something.
That's actually a good point, there could be scientific proof of some intelligent creator in principle. The fact that there is no reason a priori to believe that we will find such a proof is a problem, but I don't think it would be enough to deem the theory unscientific. Otherwise, many actually used theories would be unscientific - for example, there is no scientific reason to expect supersimmetry to exist, but that doesn't make the search for supersimmetry unscientific.
> Multiverse theory, on the other hand, would qualify as unscientific by your reasoning.
Yes, multiverse theory is unscientific by my definition. I don't believe speculation about a multiverse can be considered science in any meaningful sense. Just like simulation theory, it is using science-sounding terminology for idle speculation (though the universe being a simulation could similarly be proven by the same kind of evidence as the intelligent creator idea, to be fair).
> These are predictions that we cannot "test" except by looking at the universe and seeing what we find, and even then we are not guaranteed a positive result
But this is exactly the definition of a test. It's true that you can't prove that something doesn't exist in this way, but saying that something is untestable goes beyond that. An untestable hypothesis is one that by definition doesn't make any predictions about the universe. Multiverse theory is in this bucket - whether you believe it to be true or not, you won't expect to see anything different in the world.
> Of course if something was actually infinite, you wouldn't be able to measure it to be so, but if the model (that you have shown to be correct in other case) predicts an actual infinity and you keep counting more and more orders of magnitude, does it not make sense to assume your model is correct?
Of course it's OK to assume your model is correct, and infinity will likely be the simplest assumption in this case. However, any model that predicts an infinity can be replaced with an equivalent model that makes all the same measurable predictions but replaces the infinity with some arbitrarily large but finite number (or arbitrarily small but not infinitesimal). This second model may well be harder to work with and will contain an extra assumption (an explicit upper bound for the infinite quantity), so I wouldn't advocate for its use. But it would have to be accepted that it is not empirically distinguishable from the infinity based model.