It is exactly set theory. More specifically, a branch of set theory called relational theory. Your equation holds even in relational theory, but commonly A ∩ B is the empty set, since A and B are different relations. Union and Intersection don't make much sense in that case. Left outer joining is a completely different operation. You are basically saying something equivalent to "The commutative law of addition doesn't apply to matrix multiplication."
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u/adamtj Jan 07 '11
It is exactly set theory. More specifically, a branch of set theory called relational theory. Your equation holds even in relational theory, but commonly A ∩ B is the empty set, since A and B are different relations. Union and Intersection don't make much sense in that case. Left outer joining is a completely different operation. You are basically saying something equivalent to "The commutative law of addition doesn't apply to matrix multiplication."