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#41
 
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Re: Foreign keys -
01-15-2008
, 04:54 AM
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Always a physical issue. Never a theory issue.Agree? |
Roy
#42
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"Kira Yamato" <kirakun (AT) earthlink (DOT) net> wrote in message news:2008011502240916807-kirakun (AT) earthlinknet (DOT) .. On 2008-01-14 21:18:57 -0500, "Evan Keel" <evankeel (AT) sbcglobal (DOT) net> said: Always a physical issue. Never a theory issue.Agree? Foreign keys are functional dependencies across two relations. More specifically, let R1(K1, A1, B1) be a relation with attribute sets K1, A1 and B1 where K1 is R1's primary key and B1 is a foreign key to the relation R2(K2, A2) where K2 is R2's primary key and A2 is the set of its remaining attributes. Then the foreign key B1 represents the functional dependency B1 --> A2, which is the functional dependency across two relation I mentioned in the first sentence. Furthermore, through transitivity by the functional dependency K1 --> B1, the foreign key also represents the inter-relational functional dependency K1 --> A2. Am I correct to say this? I don't think so. A functional dependency A --> B is surjective, meaning not only that for every A there must be one and only one B, but also that for every B there must be at least one A. The relationship between B1 and A2 above is injective, as is the relationship between K1 and A2. |
Theory" (section 1.6) he does not include surjectivity as a requirement
for functional dependency.
--
-kira
#43
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"Kira Yamato" <kirakun (AT) earthlink (DOT) net> wrote in message news:2008011502240916807-kirakun (AT) earthlinknet (DOT) .. On 2008-01-14 21:18:57 -0500, "Evan Keel" <evankeel (AT) sbcglobal (DOT) net> said: Always a physical issue. Never a theory issue.Agree? Foreign keys are functional dependencies across two relations. More specifically, let R1(K1, A1, B1) be a relation with attribute sets K1, A1 and B1 where K1 is R1's primary key and B1 is a foreign key to the relation R2(K2, A2) where K2 is R2's primary key and A2 is the set of its remaining attributes. Then the foreign key B1 represents the functional dependency B1 --> A2, which is the functional dependency across two relation I mentioned in the first sentence. Furthermore, through transitivity by the functional dependency K1 --> B1, the foreign key also represents the inter-relational functional dependency K1 --> A2. Am I correct to say this? I don't think so. A functional dependency A --> B is surjective, meaning not only that for every A there must be one and only one B, but also that for every B there must be at least one A. The relationship between B1 and A2 above is injective, as is the relationship between K1 and A2. |
Theory" (section 1.6) he does not include surjectivity as a requirement
for functional dependency.
--
-kira
#44
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"Kira Yamato" <kirakun (AT) earthlink (DOT) net> wrote in message news:2008011502240916807-kirakun (AT) earthlinknet (DOT) .. On 2008-01-14 21:18:57 -0500, "Evan Keel" <evankeel (AT) sbcglobal (DOT) net> said: Always a physical issue. Never a theory issue.Agree? Foreign keys are functional dependencies across two relations. More specifically, let R1(K1, A1, B1) be a relation with attribute sets K1, A1 and B1 where K1 is R1's primary key and B1 is a foreign key to the relation R2(K2, A2) where K2 is R2's primary key and A2 is the set of its remaining attributes. Then the foreign key B1 represents the functional dependency B1 --> A2, which is the functional dependency across two relation I mentioned in the first sentence. Furthermore, through transitivity by the functional dependency K1 --> B1, the foreign key also represents the inter-relational functional dependency K1 --> A2. Am I correct to say this? I don't think so. A functional dependency A --> B is surjective, meaning not only that for every A there must be one and only one B, but also that for every B there must be at least one A. The relationship between B1 and A2 above is injective, as is the relationship between K1 and A2. |
Theory" (section 1.6) he does not include surjectivity as a requirement
for functional dependency.
--
-kira
#45
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"Kira Yamato" <kirakun (AT) earthlink (DOT) net> wrote in message news:2008011502240916807-kirakun (AT) earthlinknet (DOT) .. On 2008-01-14 21:18:57 -0500, "Evan Keel" <evankeel (AT) sbcglobal (DOT) net> said: Always a physical issue. Never a theory issue.Agree? Foreign keys are functional dependencies across two relations. More specifically, let R1(K1, A1, B1) be a relation with attribute sets K1, A1 and B1 where K1 is R1's primary key and B1 is a foreign key to the relation R2(K2, A2) where K2 is R2's primary key and A2 is the set of its remaining attributes. Then the foreign key B1 represents the functional dependency B1 --> A2, which is the functional dependency across two relation I mentioned in the first sentence. Furthermore, through transitivity by the functional dependency K1 --> B1, the foreign key also represents the inter-relational functional dependency K1 --> A2. Am I correct to say this? I don't think so. A functional dependency A --> B is surjective, meaning not only that for every A there must be one and only one B, but also that for every B there must be at least one A. The relationship between B1 and A2 above is injective, as is the relationship between K1 and A2. |
Theory" (section 1.6) he does not include surjectivity as a requirement
for functional dependency.
--
-kira
#46
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"Kira Yamato" <kirakun (AT) earthlink (DOT) net> wrote in message news:2008011502240916807-kirakun (AT) earthlinknet (DOT) .. On 2008-01-14 21:18:57 -0500, "Evan Keel" <evankeel (AT) sbcglobal (DOT) net> said: Always a physical issue. Never a theory issue.Agree? Foreign keys are functional dependencies across two relations. More specifically, let R1(K1, A1, B1) be a relation with attribute sets K1, A1 and B1 where K1 is R1's primary key and B1 is a foreign key to the relation R2(K2, A2) where K2 is R2's primary key and A2 is the set of its remaining attributes. Then the foreign key B1 represents the functional dependency B1 --> A2, which is the functional dependency across two relation I mentioned in the first sentence. Furthermore, through transitivity by the functional dependency K1 --> B1, the foreign key also represents the inter-relational functional dependency K1 --> A2. Am I correct to say this? I don't think so. A functional dependency A --> B is surjective, meaning not only that for every A there must be one and only one B, but also that for every B there must be at least one A. The relationship between B1 and A2 above is injective, as is the relationship between K1 and A2. |
Theory" (section 1.6) he does not include surjectivity as a requirement
for functional dependency.
--
-kira
#47
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"Kira Yamato" <kirakun (AT) earthlink (DOT) net> wrote in message news:2008011502240916807-kirakun (AT) earthlinknet (DOT) .. On 2008-01-14 21:18:57 -0500, "Evan Keel" <evankeel (AT) sbcglobal (DOT) net> said: Always a physical issue. Never a theory issue.Agree? Foreign keys are functional dependencies across two relations. More specifically, let R1(K1, A1, B1) be a relation with attribute sets K1, A1 and B1 where K1 is R1's primary key and B1 is a foreign key to the relation R2(K2, A2) where K2 is R2's primary key and A2 is the set of its remaining attributes. Then the foreign key B1 represents the functional dependency B1 --> A2, which is the functional dependency across two relation I mentioned in the first sentence. Furthermore, through transitivity by the functional dependency K1 --> B1, the foreign key also represents the inter-relational functional dependency K1 --> A2. Am I correct to say this? I don't think so. A functional dependency A --> B is surjective, meaning not only that for every A there must be one and only one B, but also that for every B there must be at least one A. The relationship between B1 and A2 above is injective, as is the relationship between K1 and A2. |
Theory" (section 1.6) he does not include surjectivity as a requirement
for functional dependency.
--
-kira
#48
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"Kira Yamato" <kirakun (AT) earthlink (DOT) net> wrote in message news:2008011502240916807-kirakun (AT) earthlinknet (DOT) .. On 2008-01-14 21:18:57 -0500, "Evan Keel" <evankeel (AT) sbcglobal (DOT) net> said: Always a physical issue. Never a theory issue.Agree? Foreign keys are functional dependencies across two relations. More specifically, let R1(K1, A1, B1) be a relation with attribute sets K1, A1 and B1 where K1 is R1's primary key and B1 is a foreign key to the relation R2(K2, A2) where K2 is R2's primary key and A2 is the set of its remaining attributes. Then the foreign key B1 represents the functional dependency B1 --> A2, which is the functional dependency across two relation I mentioned in the first sentence. Furthermore, through transitivity by the functional dependency K1 --> B1, the foreign key also represents the inter-relational functional dependency K1 --> A2. Am I correct to say this? I don't think so. A functional dependency A --> B is surjective, meaning not only that for every A there must be one and only one B, but also that for every B there must be at least one A. The relationship between B1 and A2 above is injective, as is the relationship between K1 and A2. |
Theory" (section 1.6) he does not include surjectivity as a requirement
for functional dependency.
--
-kira
#49
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"Kira Yamato" <kirakun (AT) earthlink (DOT) net> wrote in message news:2008011502240916807-kirakun (AT) earthlinknet (DOT) .. On 2008-01-14 21:18:57 -0500, "Evan Keel" <evankeel (AT) sbcglobal (DOT) net> said: Always a physical issue. Never a theory issue.Agree? Foreign keys are functional dependencies across two relations. More specifically, let R1(K1, A1, B1) be a relation with attribute sets K1, A1 and B1 where K1 is R1's primary key and B1 is a foreign key to the relation R2(K2, A2) where K2 is R2's primary key and A2 is the set of its remaining attributes. Then the foreign key B1 represents the functional dependency B1 --> A2, which is the functional dependency across two relation I mentioned in the first sentence. Furthermore, through transitivity by the functional dependency K1 --> B1, the foreign key also represents the inter-relational functional dependency K1 --> A2. Am I correct to say this? I don't think so. A functional dependency A --> B is surjective, meaning not only that for every A there must be one and only one B, but also that for every B there must be at least one A. The relationship between B1 and A2 above is injective, as is the relationship between K1 and A2. |
Theory" (section 1.6) he does not include surjectivity as a requirement
for functional dependency.
--
-kira
#50
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On 2008-01-15 04:37:23 -0500, "Brian Selzer" <brian (AT) selzer-software (DOT) com said: "Kira Yamato" <kirakun (AT) earthlink (DOT) net> wrote in message news:2008011502240916807-kirakun (AT) earthlinknet (DOT) .. On 2008-01-14 21:18:57 -0500, "Evan Keel" <evankeel (AT) sbcglobal (DOT) net> said: Always a physical issue. Never a theory issue.Agree? Foreign keys are functional dependencies across two relations. More specifically, let R1(K1, A1, B1) be a relation with attribute sets K1, A1 and B1 where K1 is R1's primary key and B1 is a foreign key to the relation R2(K2, A2) where K2 is R2's primary key and A2 is the set of its remaining attributes. Then the foreign key B1 represents the functional dependency B1 --> A2, which is the functional dependency across two relation I mentioned in the first sentence. Furthermore, through transitivity by the functional dependency K1 -- B1, the foreign key also represents the inter-relational functional dependency K1 --> A2. Am I correct to say this? I don't think so. A functional dependency A --> B is surjective, meaning not only that for every A there must be one and only one B, but also that for every B there must be at least one A. The relationship between B1 and A2 above is injective, as is the relationship between K1 and A2. Hmm... According to Atzeni/De Antonellis's book "Relational Database Theory" (section 1.6) he does not include surjectivity as a requirement for functional dependency. -- |
the same relation schema. A functional dependency is a statement, A --> B,
where A and B are sets of attributes. A relation satisfies the functional
depencency if and only if whenever two tuples agree on values for A they
also agree on values for B. Since both A and B appear in the same relation
schema, whenever there is a value for B, there must also be a value for A.
So it does not matter whether it is a stated requirement, surjectivity is a
property that functional dependencies exhibit.
Quote:
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-kira |
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