MathGloss
A
partition
of a set
X
X
X
is a subset
S
\mathcal S
S
of the
power set
P
(
X
)
\mathcal P(X)
P
(
X
)
such that
A
∈
S
A\in \mathcal S
A
∈
S
implies that
A
≠
∅
A\neq \emptyset
A
=
∅
;
For every
x
∈
X
x\in X
x
∈
X
, there is a unique
A
∈
S
A\in \mathcal S
A
∈
S
such that
x
∈
A
x\in A
x
∈
A
. (Equivalently, the union of the sets
A
∈
S
A\in \mathcal S
A
∈
S
is
X
X
X
and the intersection of any two elements of
S
\mathcal S
S
is empty.)