# Re: what are keys and surrogates?

Date: Thu, 17 Jan 2008 01:56:45 -0800 (PST)

Message-ID: <a59e1ba2-570d-4b2a-8b92-852cda9e78d2_at_q77g2000hsh.googlegroups.com>

On 17 jan, 02:39, Keith H Duggar <dug..._at_alum.mit.edu> wrote:

> On Jan 14, 8:23 pm, David BL <davi..._at_iinet.net.au> wrote:

*>
**>
**>
**> > On Jan 15, 9:08 am, Jan Hidders <hidd..._at_gmail.com> wrote:
**> > > On 14 jan, 03:22, David BL <davi..._at_iinet.net.au> wrote:
**> > > > On Jan 14, 7:25 am, mAsterdam <mAster..._at_vrijdag.org> wrote:
**> > > > > David BL schreef:
**> > > > > > Keith H Duggar wrote:
**> > > > > >> David BL wrote:
**> > > > > >>> Keith H Duggar wrote:
**> > > > > >>>> David BL wrote:
**> > > > > >>>>> Marshall wrote:
**> > > > > >>>>>> An interesting note, by the way:
**> > > > > >>>>>> functions are relations ...
**> > > > > >>>>> Isn't it more precise to say that the graph of a
**> > > > > >>>>> function is a relation?
**> > > > > >>>> No, it isn't.
**> > > > > >>>>http://mathworld.wolfram.com/Function.html
**>
**> > > In my experience as somebody who works in a Comp. science and
**> > > Mathematics department the mathematicians that prefer the (D,C,G)
**> > > definition of a function, also prefer the definition of relation that
**> > > makes the domains explicit, and so define a binary relation as a
**> > > triple (D_1,D_2,G). In that case a function is actually again a
**> > > special case of a relation. But this is all by no means
**> > > uncontroversial. If you look at the entry for mathematical relation in
**> > > Wikipedia you will see that there have been edit wars over this, and
**> > > even one resulting in a ban.
**>
**> > LOL.
**>
**> > I agree that in a "single work" one should be consistent one way or
**> > the other so that a function is indeed a relation.
**>
**> Finally you were able to admit "that a function is indeed
**> a relation". Sadly you felt compelled to add the nonsense
**> "single work" qualifier in a failed last-ditch attempt to
**> save precise-boy face.
*

Why the aggression? David is making a valid and correct point. There are many possible valid definitions of the notion of function, even within mathematics, and it is not always the case that functions are identified with their graphs.

- Jan Hidders