# Re: what are keys and surrogates?

From: David BL <davidbl_at_iinet.net.au>
Date: Sun, 13 Jan 2008 11:20:27 -0800 (PST)

On Jan 13, 2:19 am, Keith H Duggar <dug..._at_alum.mit.edu> 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
>
> > From mathworld a relation
>
> > http://mathworld.wolfram.com/Relation.html
>
> > is defined as a subset of a cartesian product. If a
> > function is a relation why do they define a graph of
> > a function f as
>
> > { (x,f(x)) | x in domain of f },
>
> > as described in
>
> > http://mathworld.wolfram.com/FunctionGraph.html
>
> Simple. The "definition" you gave above and dishonestly
> attributed to Mathworld is wholly your own fabrication.

There was no dishonesty about it at all. As it turned out I had googled about and read a number of definitions of "graph of function", "relation" etc and hadn't paid attention to Mathworld's restricted definition (to the reals). Wikipedia for example defines "graph of function" without any such restriction

When I tried to copy and paste the definition from Mathworld, I found it didn't work - perhaps because the equations are images? So I typed what I thought was a more succinct description. I admit I should have been more careful. I find your suggestion that I would wilfully be dishonest quite astounding.

This however doesn't change the fact that most authors define a (mathematical) relation as a set of ordered tuples, which means a function is not a relation (assuming, as most do, that a function has a defined domain and codomain). Furthermore, I was correct when I stated that a graph of a function is a relation, according to the more general definition of graph of function, as described in Wikipedia. Received on Sun Jan 13 2008 - 20:20:27 CET

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