- & - : (X « Y) x (X « Z) ® (X « (YxZ))
"x:X, y:Y, z:Z. (x,(y,z)) Î R&S Û xRz Ù ySz
Since the inverse may be defined similarly, any triadic relation T Í XxYxZ may be decomposed into
the relational join R&S of two binary relations R Í XxY and S Í XxZ.
On 16 Aug 2021, at 14:00, Jon Awbrey <jaw...@att.net> wrote:
Cf: ⚠ It’s A Trap ⚠
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The relational join operator, &, takes two binary relations to a triadic one, as defined thus:
- & - : (X « Y) x (X « Z) ® (X « (YxZ))
"x:X, y:Y, z:Z. (x,(y,z)) Î R&S Û xRz Ù ySz
Since the inverse may be defined similarly, any triadic relation T Í XxYxZ may be decomposed into
the relational join R&S of two binary relations R Í XxY and S Í XxZ.
Sorry for the typographical issues above, but it seems that by symmetry there are actually THREE decompositions for T \subseteq X x Y x Z:
R_1 \subseteq X x Y, S_1 \subseteq X x Z
R_2 \subseteq Y x X, S_1 \subseteq Y x Z
R_3 \subseteq Z x X, S_1 \subseteq Z X Y
correct?
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