# Re: what are keys and surrogates?

From: Jan Hidders <hidders_at_gmail.com>
Date: Sun, 20 Jan 2008 05:12:56 -0800 (PST)

On 19 jan, 19:14, Keith H Duggar <dug..._at_alum.mit.edu> wrote:
> David BL wrote:
> > Jan Hidders wrote:
> > > Keith H Duggar wrote:
> > > > Jan Hidders wrote:
> > > > > David is making a valid and correct point.
>
> > > > No he wasn't. Perhaps you forgot too quickly that his original
> > > > point (which he repeated in various ways) was:
>
> > > >    "it [is] more precise to say that the
> > > >     graph of a function is a relation"
>
> > > > not that there are different definitions of "function".
>
> > > > > 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.
>
> > > > The only one to thus far claim that functions are associated
> > > > with their graphs was David! Let's draw a simplified picture
> > > > of the formalisms discussed and the various combinations one
> > > > might choose
>
> > > >    F1 = function is {(x,y)}
> > > >    F2 = function is (D,C,G={(x,y)})
> > > >    R1 = binary relation is {(x,y)}
> > > >    R2 = binary relation is (D1,D2,G={(x,y)})
>
> > > > possible combinations
>
> > > >    (F1 R1) (F1 R2)
> > > >    (F2 R1) (F2 R2)
>
> > > > You yourself have pointed out under both (F1 R1) and (F2 R2)
> > > > "a function is a relation". Furthermore, you also claim your
> > > > experience indicates mathematicians choose either (F1 R1) or
> > > > (F2 R2) not (F1 R2) nor (F2 R1) ie the one David holds high.
>
> > > > Finally, who can know what David meant by "more precise" but
> > > > I would choose (F2 R2) as more precise than his pet (F2 R1).
>
> > They are formalisms; all are valid.
>
> > > > Based on the above (mostly your own claims here simplified),
> > > > would you not agree that "a function is a relation" is both
> > > > more common and more precise than "the graph of a function
> > > > is a relation"?
>
> > > Before I answer that let me first agree that your simplified picture
> > > is correct. But as far as I understand him I don't think that David
> > > actually disagrees with that picture.
>
> > Agreed.
>
> > > Do I think that the "a function is a relation" definition is both more
> > > common? Yes, I do. Do I think that it is more precise? The statement
> > > "the graph of a function is a relation" has the benefit of being true
> > > for several definitions of the notion of function. As such it might be
> > > preferable in the context of the c.d.t glossary where it is important
> > > to make clear what the different definitions are. Of course it is not
> > > really a definition but just the description of a certain property and
> > > in that sense less precise. But also here, I doubt that David would
> > > actually disagree with that.
>
> > Agreed.
>
> > I should have make the implicit assumptions in my original statement
> > explicit, so it would be...
>
> >      "If we assume F2, R1 then it is more precise
> >       to say that the graph of a function is a relation".
>
> Why not simply
>
>   "Or If we assume F2 and R1 then the
>    graph of a function is a relation." ?
>
> Why would you still want to qualify it as "more precise"?
> By doing so you would continue to maintain a precise-boy
> facade ie one who claims their language is "more precise"
> solely to demonstrate "knowledge" and "correct" others.

So you actually agree with him, but you don't like the way he said it? You think he sounded arrogant? Is that really why you are getting so worked up about this? Could be. That's not the impression that I had. Remember that it is very easy on usenet to read more into words than what was actually intended.

• Jan Hidders
Received on Sun Jan 20 2008 - 14:12:56 CET

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