Note that
[0] ≠ [1], [0] = [2r] and [1] = [2r + 1], r ∈ Z Infact, what we have seen above is true
for an arbitrary equivalence relation R in a set X Given an arbitrary equivalence
relation R in an arbitrary set X, R divides X into mutually disjoint subsets Ai called
partitions or subdivisions  of X satisfying:
(i)
all elements of Ai are related to each other, for all i (ii)
no element of Ai is related to any element of Aj , i ≠ j