deletions | additions       diff --git a/untitled.tex b/untitled.tex  index 6ee833a..d6fb3f3 100644  --- a/untitled.tex  +++ b/untitled.tex 
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\item Fix $\delta \gt 0$ and say that we care about measuring things which are larger than $\delta$ [TODO: replace epsilon with delta where needed]. This means that we can have three sizes $a$, $b$ and $c$ with $a=b$ and $b=c$ but $a\not=c$. This should be fine as long as we're aware that equality here actually means that the difference is smaller than $\delta$.  \item Fix a time length $s$ and ignore things which happen rarely.  \end{itemize}  We could use any reasonable definition of "measuring" and "happen rarely". Then we could say that the important things are the ones which are larger than $\delta$ and which do not happen rarely. Let us also fix an arbitrary time length $t\ge 0$, an acceptable error $\epsilon \ge 0$ and a probability $q\ge 0$ for our predictions [TODO: did I define this?] and let us denote by $f$ with $0 < f \le 1$ the fraction of the world where we can make predictions using the given time length $t$, the acceptable error $\delta$, $\epsilon$,  having a probability $p$ that the prediction is correct. Then, if the world is not created, we have a countable number of finite observable [TODO: is observable the right term?] descriptions out of a $\reale$ total number of descriptions. Then, for any continuous distribution, the probability of having a finite description with which we can make predictions for a time length of $t$, with an error $\delta$, $\epsilon$,  with a probability $p$ and for a fraction of the world $f$, is $0$. To have a non-zero probability either $t = 0$ (which means that we are not making any prediction), $\delta $\epsilon  = \infty$ (which means that our predictions have no connection to the reality), $p=0$ (which means that our predictions always fail) or $f=0$. We can discard the first option since then we would have no predictions. We can also discard the second and the third since such a description would not be useful in any way. The only remaining option is that $f=0$; as argued above, a description with $f=0$ can actually make sense. Therefore, with probability $1$, we have $f=0$ and the world has an infinite model. [TODO: Should I replace $f=0$ with "the minimal fraction absolutely needed", because having a space-time is a property of the entire universe, so f may not be zero? On the other hand, it does not allow any prediction. Should I add a footnote?] 
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From the above, we have two options. Either our universe is created and then we might be able to make predictions for a non-trivial part of the universe we can observe (assuming that we have enough details about the state of the universe), or the universe is not created and then, although we can make predictions for a small part of the universe, we can't make predictions outside of it, no matter how much information about the state of the universe we would have; also, this small part would be an insignificant fraction of what we could observe.  We seem to be able to make predictions for mostly everything that we can observe, even if we may not be able to make many predictions for very distant things. We also have no sign that the laws of the universe would be significantly different outside of Earth, so it seems that the limiting factor is that we don't know the state of the universe. Then the second option is probably false and the first one is probably true.  [TODO: Fix ``quotes".]  [TODO: Fix spaces between math mode and punctuation.]  [TODO: Fix the usage of I and we.]