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From: Steve Kass
Newsgroups: comp.databases.theory
Subject: Re: Extending my question. Was: The relational model and relationalalgebra
- why did SQL become the industry standard?
Date: Fri, 14 Feb 2003 00:13:14 -0500
Organization: MindSpring Enterprises
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Bob,
Thanks - that's exactly the way to model this, and in fact, the two models
reflect the usual mathematical definition of multiset as a function (set
of ordered
pairs), with the convenience of omitting rows where the function value
is zero.
Steve
Bob Badour wrote:
>"Mikito Harakiri" wrote in message
>news:XPW2a.15$O%2.103@news.oracle.com...
>
>
>>"Steve Kass" wrote in message
>>news:b2h96p$ma2$1@slb9.atl.mindspring.net...
>>
>>
>>>Mikito,
>>>
>>> It's pointless to talk about the limit of a set S without setting
>>>
>>>
>forth
>
>
>>>some context. If you are talking about sets, the limit of {0,x} as the
>>>real number x goes to zero is {0}. Why is the change of cardinality
>>>"nasty"? There is no mathematical reason to think that the
>>>cardinality function must be continuous.
>>>
>>>
>>Steve,
>>
>>Let me try to provide an example as a context.
>>
>>Consider a database of all polynomial roots. In multiset model we have
>>
>>table Polynomial (
>> id integer,
>> power integer,
>> coeff number
>>)
>>
>>CONSTRAINT c1 UNIQUE KEY (id, power)
>>CONSTRAINT c2 CHECK ( power >= 0 )
>>
>>table Roots (
>> polynomial id number,
>> root number
>>)
>>
>>In the set model, I would have to make all tuples in the Roots relation to
>>be distinct, and, therefore, add some extra column. When sets advocates
>>
>>
>talk
>
>
>>about a tuple reflecting some real-world relationship, how would they
>>interpret this extra column? If numbers are real, it might be the
>>enumeration induced by the total ordering of the roots. What if the
>>
>>
>numbers
>
>
>>are complex?
>>
>>
>
>table Roots (
> polynomial id number,
> root number,
> degree integer
>)
>
>CONSTRAINT c3 UNIQUE KEY (polynomial id, root)
>CONSTRAINT c4 CHECK ( degree > 0 )
>CONSTRAINT c5 CHECK P in Polynomial (
> P.power = sum(R.degree | { R in Roots, P.id = R.polynomial id})
>)
>
>I would interpret 'degree' as the number of coincident roots at 'root', and
>my interpretation does not depend on the specific set of values in the
>'number' type.
>
>
>
>