500 A Law and order
y
x
A × B
Fig. A.6. Cartesian product A × B; A := {x ∈ N | x ∈ [1; 3] ∨x = 4} and B := {y ∈ N | y ∈ [1; 2] ∨ y = 3}.
y
x
A × B
Fig. A.7. Cartesian product A × B; A := {1, 2, 3} and B := [1; 2[∪{3}.
y
x
A × B
Fig. A.8. Cartesian product A × B; A := [1; 2]∪]3; 4[ and B := [0; 1] ∪ [3; 4[.
In order to interpret the Cartesian product A × B as a set of third kind, we have to understand
better the power set P (A) of a set, the intersection and union of set systems, and the partitioning of
a set system into subsets called fibering.