Given any set a set-theoretical partition of is any subset of the power set such that , such that for all with and such that . The elements of are called the blocks of .
Set-theoretical partitions of are in one-to-one correspondence to equivalence relations on . From a partition of one obtains an equivalence relation by defining for all that if and only if there exists such that . Conversely, given an equivalence relation on the set of all equivalence classes is a set-theoretical partition of .
Note that the only set-theoretical partition of the empty set is the empty set itself. We speak of the empty partition.