| context | $X,Y$ … small set |
| definiendum | $ p\in X \times Y $ |
| range | $ x\in X$ |
| range | $ y\in Y$ |
| postulate | $ \exists x,y.\,p=\langle x,y\rangle $ |
| $ X \times Y\subset \mathcal{P}(\mathcal{P}(X \cap Y))$ |
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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 $ |
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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 $ |
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