12,080
edits
Changes
MyWikiBiz, Author Your Legacy — Wednesday April 09, 2025
Jump to navigationJump to searchDirectory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)
Revision as of 01:00, 23 February 2013
, 01:00, 23 February 2013→6.36. Irreducibly Triadic Relations: markup
Line 9,339:
Line 9,339:
R012 = R112 = 112 = B2,+R013 = R113 = 113 = B2,+R023 = R123 = 123 = B2.+</pre>
The corresponding projections of <math>\operatorname{Proj}^{(2)} L_0\!</math> and <math>\operatorname{Proj}^{(2)} L_1\!</math> are identical. In fact, all six projections, taken at the level of logical abstraction, constitute precisely the same dyadic relation, isomorphic to the whole of <math>\mathbb{B} \times \mathbb{B}\!</math> and expressed by the universal constant proposition <math>1 : \mathbb{B} \times \mathbb{B} \to \mathbb{B}.\!</math> In summary:
The corresponding projections of <math>\operatorname{Proj}^{(2)} L_0\!</math> and <math>\operatorname{Proj}^{(2)} L_1\!</math> are identical. In fact, all six projections, taken at the level of logical abstraction, constitute precisely the same dyadic relation, isomorphic to the whole of <math>\mathbb{B} \times \mathbb{B}\!</math> and expressed by the universal constant proposition <math>1 : \mathbb{B} \times \mathbb{B} \to \mathbb{B}.\!</math> In summary:
−<pre>
+{| align="center" cellspacing="8" width="90%"
−|
−<math>\begin{array}{lllll}
−(L_0)_{12} & = & (L_1)_{12} & \cong & \mathbb{B}^2
+\\[4pt]
+(L_0)_{13} & = & (L_1)_{13} & \cong & \mathbb{B}^2
+\\[4pt]
+(L_0)_{23} & = & (L_1)_{23} & \cong & \mathbb{B}^2
+\end{array}</math>
+|}
−Thus, R0 and R1 are both examples of irreducibly triadic relations.
+Thus, <math>L_0\!</math> and <math>L_1\!</math> are both examples of irreducibly triadic relations.
−===6.37. Propositional Types===
===6.37. Propositional Types===
