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'''Definition.'''  An ''enumerated set'' <math>(S, f)\!</math> is a numbered set with a bijective <math>f.\!</math> &hellip;

'''Definition.'''  An ''enumerated set'' <math>(S, f)\!</math> is a numbered set with a bijective <math>f.\!</math> &hellip;

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'''Definition.'''  The ''<math>n\!</math>-fold sum'' (''co-product'', ''disjoint union'') of the sets <math>X_1, \ldots, X_n\!</math> is notated and defined as follows:

The "n fold sum" ("co product", "disjoint union") of the sets X1, ... , Xn is notated and defined as follows:

Ui Xi  = X1 + ... + Xn  = 1^X1 U ... U n^Xn.

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| <math>\coprod_{i=1}^n X_i ~=~ X_1 + \ldots + X_n ~=~ 1 \widehat{~} X_1 \cup \ldots \cup n \widehat{~} X_n.\!</math>

The "n fold product" ("cartesian product") of the sets X1, ... , Xn is notated and defined as follows:

The "n fold product" ("cartesian product") of the sets X1, ... , Xn is notated and defined as follows: