DanielFilan comments on Finite Factored Sets: Orthogonality and Time

[DanielFilan]

From def 16:

… if ${\chi }_C^F(x,S)=x$ for all $x\in X$

Should I take this to mean “if ${\chi }_C^F(x,s)=x$ for all $x\in X$ and $s\in S$”?

[EDIT: no, I shouldn’t, since ${\chi }_C^F(x,S)$ and $x$ are both subsets of $S$]

[DanielFilan]

OK I think this is a typo, from the proof of prop 10 where you deal with condition 5:

Thus ${\chi }_C^F(x,s)\in x$.

I think this should be ${\chi }_C^F(x,s)\subseteq x$.

[Scott Garrabrant]

Fixed, Thanks.