Describe the equivalence class

Question

Let R be the relation on Z × (Z \ {0}) defined by (a, b)R(c, d) if and only if ad = bc. Show that R is an equivalence relation on Z × (Z \ {0}) and describe the equivalence class [(0, 1)]

Answer 1

This is the equivalence relation used to construct rational numbers from the set of integers. The equivalence class of [(0,1)] is basically just the number 0 in the set of rational numbers. So all fractions of the form 0/b, where b is a non-zero integer.