 Equivalence of partial functions modulo finite changes

Two functions $f:A\to X$ and $g:B\to X$, whose domains lie in one ambient set, are equivalent modulo finite changes when $A△B$ is a finite set and the functions disagree at only finitely many points of $A\cap B$. The symmetric difference inclusion $A△C\subseteq (A△B)\cup (B△C)$ handles domains in a transitive chain. An exceptional set for values must also include points of $A\cap C$ absent from the middle domain $B$; these lie in the finite difference $A\setminus B$.