Partitions
A partition of a set S is a collection of disjoint nonempty subsets of S
that have S as their union.
Theorem. Let R be an equivalence relation on a set S. Then the
equivalence classes of R form a partition of S.
What is the partition of the set of non-negative integers formed by the
relation “… is congruent to … modulo 3”?
It is the following 3 sets:
A0={0,3,6,9,12,…}, A1={1,4,7,10,13,…}, A2={2,5,8,11,14,…}