R is the set of all positive real numbers. Define r @ x if and only if |r| = [x]. I don't have the correct symbols to use for it, but i do not mean absolute value. |r| represents the greatest integer less than or equal to r. [x] represents the smallest integer greater than or equal to x.
Is this relation an equivalence relation? I'm struggling in why some relations ARE equivalence relations and some are not (some are partial order relations, for example). Why is this or isn't it an equivalence relation?