# Re: what are keys and surrogates?

From: Jan Hidders <hidders_at_gmail.com>
Date: Sun, 20 Jan 2008 12:53:52 -0800 (PST)

On 20 jan, 18:18, Keith H Duggar <dug..._at_alum.mit.edu> wrote:
> Jan Hidders wrote:
> > Keith H Duggar 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?
>
> Perhaps you should read the origin of this sub-thread again.
> No, Jan, I do not agree with his /originating/ statement
>
>   "it [is] more precise to say that the
>    graph of a function is a relation".
>
> I thought that should be crystal clear at this point so I am
> unable to understand your confusion on this point. It should
> also be clear that "more precise" is key to my disagreement.
> Furthermore, it should be obvious, based on his exact words,
> that David would still claim it to be "more precise" were he
> to make the claim today. And, no, "more precise" is not part
> of "the way he said it" it is material to his claim.
>
> > You think he sounded arrogant?
>
> No, not even close. I think DBL sounded ignorant and foolish
> as one who has only a superficial grasp of the concepts they
> wrongly believe they have mastered. I would have thought you
> could have deduced that from the quote Mark Twain I included
> in my original reply.
>
> > Is that really why you are getting so worked up about this?
>
> You and David have both classified my posts as "aggressive"
> and now you classify me as "worked up". That fascinates me.
>
> I would not have classified someone who responds at their
> leisure (up to two days) as "worked up". I would not have
> classified someone who responds to David elsewhere thusly
>
>
>
> Keith H Duggar wrote:
> > David BL wrote:
> > > Keith H Duggar wrote:
> > > > There was once another poster that trolled around always
> > > > discussing how she felt about this or that post or this
> > > > or that poster.
> > > Depending on how one reads that, it could be seen as
> > > implying Reinier is trolling. Was that your intention?
>
> > No, that was not my intention. I should have been more
> > precise.
>
> > > IMO he is not.
>
> > I agree. I do not believe rpost is trolling. Thanks
> > for pointing out this ambiguous language.
>
> as "aggressive". I would not classify succinct, clear, and
> logical arguments as aggressive. I would not even classify
> core-aimed psychological barbs such as "precise-boy" (that
> still makes me chuckle) as aggressive anymore than some of
> the previous barbs I've invented such as "wikipeducation".
> I would not classify someone playfully aligning paragraphs
> to certain fixed width columns as "worked up".
>
> No. If anything I would have classified myself as cold and
> calculating and my posts re DBL as inexorable pursuance.
>
> > Could be. That's not the impression that I had.
>
> As I wrote above neither did I.
>
> > Remember that it is very easy on usenet to read more into
> > words than what was actually intended.
>
> I agree. I believe you and David have read certain emotion
> into my posts and motivations into me that are absent.

Since my words seem to have the opposite effect of what I was hoping for, I think it is better to end this conversation.

• Jan Hidders
Received on Sun Jan 20 2008 - 21:53:52 CET

Original text of this message