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[The following piece occurs in § 6.35.]

 

 

[The following piece occurs in § 6.35]

The set of triples of dyadic relations, with pairwise cartesian products chosen in a pre-arranged order from a triple of three sets <math>(X, Y, Z),\!</math> is called the ''dyadic explosion'' of <math>X \times Y \times Z.\!</math>  This object is denoted <math>\operatorname{Explo}(X, Y, Z ~|~ 2),\!</math> read as the ''explosion of <math>X \times Y \times Z\!</math> by twos'', or more simply as <math>X, Y, Z ~\operatorname{choose}~ 2,\!</math> and defined as follows:

The set of triples of dyadic relations, with pairwise cartesian products chosen in a pre-arranged order from a triple of three sets <math>(X, Y, Z),\!</math> is called the ''dyadic explosion'' of <math>X \times Y \times Z.\!</math>  This object is denoted <math>\operatorname{Explo}(X, Y, Z ~|~ 2),\!</math> read as the ''explosion of <math>X \times Y \times Z\!</math> by twos'', or more simply as <math>X, Y, Z ~\operatorname{choose}~ 2,\!</math> and defined as follows:

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| <math>\operatorname{Explo}(X, Y, Z ~|~ 2) ~=~ \operatorname{Pow}(X \times Y) \times \operatorname{Pow}(X \times Z) \times \operatorname{Pow}(Y \times Z).\!</math>

| <math>\operatorname{Explo}(X, Y, Z ~|~ 2) ~=~ \operatorname{Pow}(X \times Y) \times \operatorname{Pow}(X \times Z) \times \operatorname{Pow}(Y \times Z)\!</math>

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| <math>2^{XY} \times 2^{XZ} \times 2^{YZ} ~=~ 2^{(XY + XY + YZ)},\!</math>

| <math>2^{XY} \times 2^{XZ} \times 2^{YZ} ~=~ 2^{(XY + XY + YZ)}\!</math>

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