equivalence class of an inequiality

Question

For the equivalence relation R={(x,y):x,y belong to the set of real numbers & |x-y|<4} how would you determine the equivalence class? I'm particularly confused as to how one would do so for an inequality function involving an absolute value. Thank you.

Answer 1

It's not an equivalence relation so you can't find equivalence classes.

Specifically, we have for example $$(0,3)\in R\quad\hbox{and}\quad (3,6)\in R\quad\hbox{but}\quad (0,6)\not\in R\ ,$$ so $R$ is not transitive.