# Re: what are keys and surrogates?

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