## Re: [xsl] Testing 2 XML documents for equality - a solution

 Subject: Re: [xsl] Testing 2 XML documents for equality - a solution From: Mukul Gandhi Date: Thu, 31 Mar 2005 04:36:32 -0800 (PST)
```Hi Dimitre,
I am really not good at mathematics at this level. I
did studied about relations like "symmetric, reflexive
and transitive" time back. But I did so just to score
indeed enlightening for me to know they have real
practical use (in XML & XSLT!). I cannot define my
problem in these terms.. As my knowledge is limited.

I would be happy if you can define in these precise
terms the problem I am trying to solve(based on my
earlier posts to this thread). I'll keep it as a
reference for future use. I defined the problem (I am
trying to solve) from an average programmer's point of
view.. And I think that it is quite understandable to
an average programmer ;)

Regards,
Mukul

--- Dimitre Novatchev <dnovatchev@xxxxxxxxx> wrote:
>
> We are in a vicious circle here. You explain one
> undefined notion
> ("document equality") with two other undefined terms
> ("identical node
> structure" and "abstract structure")...
>
> Whenever one defines "equality", this means a
> symmetric, reflexive and
> transitive relation on the set of X^2 of pairs of
> values from a set X.
>
> One *must* define a breakdown of X^2 into classes of
> equivalence
> (non-intersecting subsets of X^2 that cover X^2
> completely (to put it
> in other words: whose union is X^2)  ) . Then, by
> definition, every
> pair of elements belonging to a class of equivalence
> are considered
> equivalent.
>
> Without doing this, one cannot speak about
> "equality" at all. There
> are cases when more than one breakdown into classes
> of equivalence may
> exist on the same set (e.g. the classes of
> equivalence on the set of
> natural numbers N may be defined as all k+1 sets of
> numbers {x mod k =
> r, where r = 0, 1, ..., k-1} In this case there are
> an infinite number
> of different equivalent relations on N^2, just let k
> vary from 2  to
> infinity). This example shows clearly that if you
> haven't defined
> precisely about which equivalence relation you are
> speaking, then you
> have no equivalence relation at all.
>
> In this concrete case "document equality" remains
> undefined.
> Therefore, the problem based on it is also
> undefined. Any activity to
> solve an undefined problem is groundless and
> imaginary -- something
> like hallucination.
>
>
> Cheers,
> Dimitre.

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