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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)
Revision as of 03:00, 7 January 2013
, 03:00, 7 January 2013→6.35. Reducibility of Sign Relations: markup
Suppose <math>L \subseteq X \times Y \times Z\!</math> is an arbitrary triadic relation and consider the information about <math>L\!</math> that is provided by collecting its dyadic projections. To formalize this information define the ''projective triple'' of <math>L\!</math> as follows:
Suppose <math>L \subseteq X \times Y \times Z\!</math> is an arbitrary triadic relation and consider the information about <math>L\!</math> that is provided by collecting its dyadic projections. To formalize this information define the ''projective triple'' of <math>L\!</math> as follows:
{| align="center" cellspacing="8" width="90%"
| <math>\operatorname{Proj}^{(2)}(L) ~=~ (\operatorname{proj}_{12}(L), \operatorname{proj}_{13}(L), \operatorname{proj}_{23}(L)).</math>
|}
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<pre>
If R is visualized as a solid body in the 3 dimensional space XxYxZ, then Proj (R) can be visualized as the arrangement or ordered collection of shadows it throws on the XY, XZ, and YZ planes, respectively.
If R is visualized as a solid body in the 3 dimensional space XxYxZ, then Proj (R) can be visualized as the arrangement or ordered collection of shadows it throws on the XY, XZ, and YZ planes, respectively.