Re: RM and definition of relations/tuples
From: Martin Zapf <Martin_Zapf_at_gmx.net>
Date: Fri, 25 Nov 2005 11:22:37 +0100
Message-ID: <dm6olm$3ch$1_at_online.de>
>>I have a question to the Relational Model and the definition of
>>relations and tuples.
>>
>>
>>I learned the following definitions:
>>
>>A relation schema R is a set of Attributes R={A_1,A_2,...,A_n}
>>Each Attribute A has a domain dom(A)
>>
>>Here comes the problem, there are two definitions for relations/tuples
>>
>>1. defintion:
>>
>> A relation r for schema R is a mathematical relation (cartesian
>> product) over the
>> domains from the attributes of R.
>> So r:=dom(A_1)xdom(A_2)x...xdom(A_n)
>> A tuple is an element of r.
>>
>>2. definition
>>
>> A relation r for schem R is a set of tuples.
>> A tuple t is a function
>> t: R -> Union (dom(A_1),dom(A_2),...,dom(A_1))
>> t maps each Attribute of R to an value of its domain.
>> So a relation is a set of functions, which are called tuples.
>>
>>
>>I noticed, that the difference between this two definition is that
>>definition 1 forces a certain order for the Attributes and the values
>>for them in the tuples.
>>The 2. definition doesnt need any order for the attributes.
>>
>>
>>Im quite confussed, is there a "better" definition or should you always
>>use both?
Date: Fri, 25 Nov 2005 11:22:37 +0100
Message-ID: <dm6olm$3ch$1_at_online.de>
vc wrote:
> Martin Zapf wrote: >
>>I have a question to the Relational Model and the definition of
>>relations and tuples.
>>
>>
>>I learned the following definitions:
>>
>>A relation schema R is a set of Attributes R={A_1,A_2,...,A_n}
>>Each Attribute A has a domain dom(A)
>>
>>Here comes the problem, there are two definitions for relations/tuples
>>
>>1. defintion:
>>
>> A relation r for schema R is a mathematical relation (cartesian
>> product) over the
>> domains from the attributes of R.
>> So r:=dom(A_1)xdom(A_2)x...xdom(A_n)
>> A tuple is an element of r.
>>
>>2. definition
>>
>> A relation r for schem R is a set of tuples.
>> A tuple t is a function
>> t: R -> Union (dom(A_1),dom(A_2),...,dom(A_1))
>> t maps each Attribute of R to an value of its domain.
>> So a relation is a set of functions, which are called tuples.
>>
>>
>>I noticed, that the difference between this two definition is that
>>definition 1 forces a certain order for the Attributes and the values
>>for them in the tuples.
>>The 2. definition doesnt need any order for the attributes.
>>
>>
>>Im quite confussed, is there a "better" definition or should you always
>>use both?
> > > The first definition is closer to the "mathematical" relation where a > tuple is an *ordered* sequence. The second definition is what database > folks prefer to use (see Codd, Date, et al) where a tuple is a *set* of > attribbute:value pairs. One can be mapped to the other and I would not > worry too much about the difference unless you are doing some d.b. > theoretical research. >
I also figured that out, a mathematical relation (subset of catesian product) is ordered because the elements of a cartesian product are ordered sets by definition.
And yes I have to do some theoretical db stuff so Im asking myself: If there are two definitions for the same thing, what is the universal valid and precise definition for the RM? This two definitions cant come out of nowhere, can they. Received on Fri Nov 25 2005 - 11:22:37 CET