Tetraspace comments on Introduction to Cartesian Frames

Tetraspace 26 Oct 2020 20:22 UTC
3 points

This means you can build an action that says something like “if I am observable, then I am not observable. If I am not observable, I am observable” because the swapping doesn’t work properly.

Constructing this more explicitly: Suppose that $a_{1} e \in S$ and $a_{2} e \in W ∖ S$ . Then $i f (S, a_{2}, a_{1})$ must be empty. This is because for any action $a_{3}$ in the set $i f (S, a_{2}, a_{1})$ , if $a_{3} e$ was in $S$ then it would have to equal $a_{2} e$ which is not in $S$ , and if $a_{3} e$ was not in $S$ it would have to equal $a_{1} e$ which is in $S$ .

Since $i f (S, a_{2}, a_{1})$ is empty, $S$ is not observable.