# Re: cdt glossary [Graph] (was: what are keys and surrogates?)

From: JOG <jog_at_cs.nott.ac.uk>
Date: Sun, 13 Jan 2008 13:57:31 -0800 (PST)

On Jan 13, 8:04 pm, David BL <davi..._at_iinet.net.au> wrote:
> On Jan 13, 3:48 am, JOG <j..._at_cs.nott.ac.uk> wrote:
>
>
>
> > On Jan 12, 8:14 am, David BL <davi..._at_iinet.net.au> wrote:
>
> > > On Jan 12, 2:24 pm, JOG <j..._at_cs.nott.ac.uk> wrote:
>
> > > > On Jan 12, 1:05 am, David BL <davi..._at_iinet.net.au> wrote:
> > > > > Really! I have seen a (mathematical) relation formally defined as a
> > > > > subset of a cartesian product (and not an ordered tuple) on many
> > > > > occasions.
>
> > > > Bit confused by this - a cartesian product generates a set of ordered
> > > > tuples (over which a function is a subset), and all the hyperlinks you
> > > > listed seemed to follow that description.
>
> > > Do you agree that most authors define a binary relation as a set of
> > > ordered pairs? In an earlier post you said a function is the ordered
> > > triple (D,C,G). How do you reconcile saying that a function is a
> > > (binary) relation?
>
> > Relations are formally described by the ordered triple (D,C,G), but
> > are often informally described by just G.
>
> So all those authors that define a binary relation as a set of ordered
> pairs are being informal? I don't agree with that.
>
> Check out the section under formal definitions in
>
> http://en.wikipedia.org/wiki/Relation_%28mathematics%29
>
> Are you saying that definition 1 is informal?

I don't see why you'd think so - in the article, first the domains, x1...xn, are stated. Then the graph is specified as a subset of the cartesian product of x1..xn. Seems relatively formal to me - domains and a graph (albeit for an n-ary as opposed to a binary relation). Received on Sun Jan 13 2008 - 22:57:31 CET

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