I have to prove an equivalence relation..
$x$ is related to $y$ in the reals if $|x-y|\le3$
Reflexivity was easy. Symmetry was just a matter of breaking up the +ve and -ve case and it worked out. I'm a little rusty at this and I'm completely stumped on how to show that it's transitive.. By thinking about the numbers, it seems like it should work but the problem is that it needs to be in the general case..
Any help would be greatly appreciated!
Do you think that transitivity will hold for $x=7$, $y=9$, $z=11$?