deletions | additions       diff --git a/untitled.tex b/untitled.tex  index 7568373..6d3de62 100644  --- a/untitled.tex  +++ b/untitled.tex 
...
Note that the fraction of the world that can be modelled is increasing, but is limited, so it converges at some value. Also, the prediction error (it's not important to define it precisely here) is decreasing and is limited, so it converges. If the fraction converges at $1$ and the prediction error converges at $0$, then we are in the first case, because we reach a point when the fraction is so close to $1$ and the error is so close to $0$ that one would find them good enough. If the fraction or the error converges to different values then we are in the second case.  There is also a third case, when one can improve the axiom set in ways that seem meaningful, without growing the fraction of the world that is covered by the set and without decreasing the prediction error. As an example, imagine a world with an infinite number of earth-like planets that lie on one line and with humans living on the first one. The laws of this hypothetical world, as observed by humans, would be wildly different from one planet to the other. As an example of milder differences, starting at $10$ meters above ground, gravity would be described with a different function on each planet. On some planets it would follow the inverse of a planet-specific polynomial function of the distance, on others it would follow the inverse of an exponential function, on others it would behave in some way if the distance to the center of the planet in meters is even and in another way if the distance is odd, and so on. Let us also assume that humans can travel between these planets freely in some bubble that preserves the laws of the first planet well enough that humans can live, but that also lets them observe a projection of  what happens outside. In this case one could study each planet and add a specific description of the laws for each, but at any moment in time the humans in this world would only have a finite part of an infinite set of laws, so we wouldn't be able to say that they cover a non-zero fraction of the laws or a non-zero fraction of the world. If one would think that they cover a non-zero fraction because (say) they cover a non-trivial part of the fundamental forces, then we could also vary the type of all forces from one planet to the other or we could add a new set of forces for each planet. The point is that we can have a case when the fraction of the universe that can be axiomatized at any moment is zero and one can't improve this fraction, even if one is able to model new meaningful things about the universe and the part of the world that is covered by the axiom set is continuously extended.