Re: Another Bidirectional Join Example

From: Cimode <cimode_at_hotmail.com>
Date: 31 Mar 2007 04:10:02 -0700
Message-ID: <1175339402.106092.320660_at_o5g2000hsb.googlegroups.com>


On 31 mar, 07:02, "Marshall" <marshall.spi..._at_gmail.com> wrote:
> On Mar 30, 9:32 pm, "David Cressey" <cresse..._at_verizon.net> wrote:
>
> > Another example of the bidirectional self join is the "borders on"
> > relationship between two countries.
>
> > If France borders on Spain, it follows that Spain borders on France. If
> > Andorra does not border on Luxembourg, it follows that Luxembourg does not
> > border on Andorra.
>
> > Perhaps this one is easier to discuss than the soccer games example.
>
> Minor related comments:
>
> This "bidirectionality" is exactly the difference between edges in
> a directed graph and an undirected graph.
>
> A relation that exhibits this property is called "symmetric."
> A relation R on AxA is symmetric if for all (a, b) in R,
> (b, a) is in R.
>
> I'm toying with how to express some of the queries
> we've mentioned in my own notation. (Perhaps someone
> can do the same in TTM?)
Agreed.

I have always had a some trouble accepting the idea of a *de facto* symetric relation without a formal mathematical demonstration.

Mathematical formalism dictates that in order to demonstrate the specific characteristic of a relation, one has to initially assume there are in 2 relations then establish that the relations are the indeed the same for the property of symetry to be established. Quite complex problem on which I have been biting my nails for a few years. I hope this makes sense.

> Marshall
Received on Sat Mar 31 2007 - 13:10:02 CEST

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