Re: what are keys and surrogates?

From: Keith H Duggar <duggar_at_alum.mit.edu>
Date: Sat, 12 Jan 2008 09:19:11 -0800 (PST)
Message-ID: <1b4c1d0b-d4cc-4eb5-b2ed-e0edb68fc93b_at_q39g2000hsf.googlegroups.com>


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. Shall we reprint what is /actually/ given by Mathworld?

graph f(x) def {(x,f(x)) E R^2 : x E U}
graph f(x1,...,xN) def {

   (x1,...,xN,f(x1,...xN)) E R^(N+1) : (x1,...,xN) E U}

Do you see the "E R^(N+1)" above? That usage of "graph" you employ applies only to real-valued functions not to functions generally.

Just admit you tried to be precise-boy cool and came out a fool instead. Do not allow yourself become yet-another person who can't swallow their pride and admit they were wrong. Believe me, it's liberating; try it; try it now.

KHD.F6 Received on Sat Jan 12 2008 - 18:19:11 CET

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