===== Cartesian product =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $X,Y$ ... small set |
| @#FFBB00: definiendum | @#FFBB00: $ p\in X \times Y $ |
| @#DDDDDD: range       | @#DDDDDD: $ x\in X$ |
| @#DDDDDD: range       | @#DDDDDD: $ y\in Y$ |
| @#55EE55: postulate   | @#55EE55: $ \exists x,y.\,p=\langle x,y\rangle $ |

==== Discussion ====
^ $ X \times Y\subset \mathcal{P}(\mathcal{P}(X \cap Y))$ ^
=== Definitions ===

In accordance to the defintion of the n-tuple in [[Ordered pair]], we set

^ $ X_1\times X_2\times X_3 \equiv (X_1\times X_2)\times X_3 $ ^

and inductively for 

^ $ X_1\times X_1\times X_3\times \ \dots\ \times X_{n-1}\times X_n \equiv ((\dots((X_1\times X_2)\times X_3)\times\ \dots\ )\times X_{n-1})\times X_n $ ^
==== Parents ====
=== Requirements ===
[[Ordered pair]]
=== Related ===
[[Product type]]