Re: Do Data Models Need to built on a Mathematical Concept?
Date: 5 May 2003 08:43:15 -0700
Message-ID: <4b45d3ad.0305050743.30acb4de_at_posting.google.com>
> > Pg 65 of Schaum's Outline (0-07-038159-3), binary relation as follows:
> > A = (b,c)
> > B = (j,k,l)
> > AxB = ((b,j), (b,k), (b,l), (c,j), (c,k), (c,l))
> > then (b,j), (b,k) ... are binary relations.
>
> That's not the generally accepted definition of the term. Nor is it even
> what that specific book says; I checked. What is says is:
> "Let A and B be sets. A *binary relation* or, simple,
> a *relation* from A to B is a subset of A x B."
> So, to fix your example, the cardinality-2 set { (b,j), (b,k) } is
> a binary relation.
Ok, let me try to understand:
"A *binary relation* from A to B is a subset of A x B."
Since (NULL) is a subset of AxB, it is a binary relation!!!
Since ((b,j)) is a subset of AxB, it is a binary relation.
Since ((b,j), (b,k)) is a subset of AxB, it is a binary relation.
Since ((b,j), (b,k), (b,l)) is a subset of AxB, it is a binary
relation.
and so on....
If the above is the correct interpretation, I find the definition to be inaccurate in that it has not defined the fundamental form of a binary relation.
> To expand on the comparison a little:
> An example of a binary relation on Z x Z (the integers) is 'less than'.
> So the set of all integers a, b where a < b is a binary relation. If your
> explanation of the standard definition were correct, (which I do
> understand you specifically disagree with) then we would say
> '1<2' and '7<123' are binary relations.
I would say '1<2' is not A binary relation but composed of TWO direct binary relations. Most people only see the relationship between 1 and 2. I see it as 1 is related to its set(ie whole numbers) AND 2 is related to its set(ie whole numbers). The < is an indirect or derived relationship between 1 and 2.
Set theory books say X-Y-Z is a binary relation because there are two
link.
I have been saying X-Y is a binary relation because there are two
nodes.
But now my symbolic logic books say "If it connects two elements at a time it is said to be a dyadic relation, if three, triadic". Here they count things.
As best as I can determine, the word "binary" before the word
"relation" could be interpretted in two way:
1. indicates the number of relations.
2. a relation between 2 things.
Received on Mon May 05 2003 - 17:43:15 CEST