Re: what are keys and surrogates?

On Jan 17, 10:39 am, Keith H Duggar <dug..._at_alum.mit.edu> wrote:
> On Jan 14, 8:23 pm, David BL <davi..._at_iinet.net.au> wrote:
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> > 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.
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> > LOL.
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> > 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.
>
> KHD.F6
You have a naive idea that the question of whether a function is a relation has some absolute significance when in fact it merely comes down to the formalism.

I pointed out correctly that mathematicians usually formally define a binary relation as only a set of ordered pairs, and that coincides with a graph of a function, as formally defined in many mathematical texts.

If you feel compelled, have your last pathetic word on this. I intend to ignore you from now on. Received on Thu Jan 17 2008 - 04:48:06 CET