Define a relation on Z as xRy if |x−y|<1.
I have shown this relation is symetric and reflexive and i am pretty sure its transitive because this is the equality relation isnt it? thats my first question and my second is how to show it is transitive.
I attempted a direct proof but i dont know how to link the two inequalities together to get that |x−z|<1 (im trying to show if xRy and yRz then xRz).
Any help would be appreciated, thanks! I am looking for the proof of this last property (transitivity).