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
grades. I had no idea then their practical use.. It is
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(_at_)gmail(_dot_)com> 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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