12,144
edits
Changes
MyWikiBiz, Author Your Legacy — Wednesday November 05, 2025
Jump to navigationJump to searchDirectory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)
Revision as of 15:05, 15 April 2013
, 15:05, 15 April 2013→6.37. Propositional Types
|}
|}
[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:
{| align="center" cellspacing="8" width="90%"
{| align="center" cellspacing="8" width="90%"
| <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>
|}
|}
{| align="center" cellspacing="8" width="90%"
{| align="center" cellspacing="8" width="90%"
| <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>
|}
|}
