deletions | additions       diff --git a/untitled.tex b/untitled.tex  index 9702e2f..e8b28e3 100644  --- a/untitled.tex  +++ b/untitled.tex 
...
Let us now do the following:  \begin{itemize}   \item Restrict ourselves to universes in which we can measure things with real numbers.  \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]. $\delta$.  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 $t\ge 0$, a relative error $\epsilon \ge 0$ and a probability $q\ge 0$ which is the probability of a random prediction to be successful [TODO: did I define this? Should I move this at the end and say that this is the probability given the previous constraints?] and let us denote by $f$ with $0 < f \le 1$ the fraction of the world where we can make predictions about what happens after the given time length $t$, with the relative error $\epsilon$ and having a probability $q$ that the prediction is correct.  Then, if the world is not designed, 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 a relative  error $\epsilon$, 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, we are just restating the present), $\epsilon = \infty$ (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 \ghilimele{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?]