# Re: Principle of Orthogonal Design

From: Bob Badour <bbadour_at_pei.sympatico.ca>

Date: Sun, 27 Jan 2008 09:28:11 -0400

Message-ID: <479c86f1$0$4043$9a566e8b_at_news.aliant.net>

> It's even further over my head.

> I really need to understand the word "trivial" as used above in a more

Date: Sun, 27 Jan 2008 09:28:11 -0400

Message-ID: <479c86f1$0$4043$9a566e8b_at_news.aliant.net>

David Cressey wrote:

> "Jan Hidders" <hidders_at_gmail.com> wrote in message

*> news:c4a59c20-5686-4f4a-aa43-512cdee1df64_at_d70g2000hsb.googlegroups.com...
**>
*

>>mAsterdam schreef: >> >>>This is all way over my head. Jan, you may be used to >>>sailing these waters; I am not. I think it is interesting, >>>but very time-consuming. >>>Am I talking rubbish? I try not to, but I don't know - nobody >>>else chimes in. You keep replying, but hey, you are a nice guy :-)

*>*> It's even further over my head.

*>*>>>>>>DEFINITION: A join dependency is said to be a proper if it does not >>>>>>hold that any of its components is a subset of another component. >>>>> >>>>>Proper is a nicer than non-trivial. >>>> >>>>Note that it's semantically different. Not all proper join >>>>dependencies are non-trivial, and not all non-trivial join >>>>dependencies are proper. >>> >>>Thanks, I have to read more carefully. >>> >>>Trivial dependencies are the ones implied by the >>>candidate keys. >> >>Not precisely. Trivial dependencies are those that hold in any schema. >>For example the FK a,b -> a is always true as long as you have >>attributes 'a' and 'b' in the header. Another example is the JD >>[ {a,b}, {b,c}, {a,b,c} ] if the attributes in the header are {a,b,c}. >>This is always a lossless decomposition, but also a very redundant >>one. Another is the JD [ {a,b,c} ].

*>*> I really need to understand the word "trivial" as used above in a more

*> careful manner than I do.**>**> Unfortunately, my intuitive grasp of the word "trivial" comes from hearing**> it used by engineers rather than mathematicians. When engineers use the**> word "trivial", there is almost always an overtone of snobbism present. A**> problem is "trivial" if it's unworthy of the attention of someone so**> important as the person speaking. It should be assigned to a "junior"**> person.**>**> In mathematics, the "trivial case" is almost always easy, but easiness is**> not what relegates it to triviality. It's more like "orthogonality to the**> peculiarities of the item under discussion", or something like that.**>**> So I need to understand "trivial dependencies", in a really tight fashion.**> My loose understanding of one form of trivial dependence is that a component**> of a composite key is trivially dependent on that key. In this case,**> "trivial" means, to me, that the dependency provides no additonal**> information about anything. The sort of thing that, in common parlance,**> would draw the response, "well, duh!"**>**> But I don't have a general understanding of what makes trivial dependencies**> trivial.*I might suggest: "Inferable from the definition."

Presumably one can infer (calculate/prove) from the definition of FK that: FK a,b -> a

Or did he mean FD above instead of FK? Received on Sun Jan 27 2008 - 14:28:11 CET