Re: Codd provided appropriate mathematics ... (was Re: Relational and MV (response to "foundations of relational theory"))
From: Dawn M. Wolthuis <dwolt_at_tincat-group.com>
Date: Fri, 27 Feb 2004 17:05:30 -0600
Message-ID: <c1oigg$pie$1_at_news.netins.net>
or
Date: Fri, 27 Feb 2004 17:05:30 -0600
Message-ID: <c1oigg$pie$1_at_news.netins.net>
And the only data of any consequence is that which
can be found by googling, right? Time to haul all of the data out of
RDBMS's ;-)
Here are a couple of defs of a relation (in
mathematics):
A relation is a subset of the Cartesian cross-product of sets S1x…xSn,
…
A relation is a set of ordered tuples, (s1, s2, …
sn). The sets S1…Sn can have
elements of any type, including other relations.
Often a relation is just defined in terms of two sets S1 x S2
because S2 could then be Sa x Sb x Sc, for example.
A function is a special case of a relation where each element
in S1 maps to exactly one element in S2. In that case, the set s1 is
referred to as the domain of the function and the subset of S2 includd in
the function is the range. I work with "functional databases" which are
(from a mathematics standpoint) a subset of relational databases. However,
because they permit not only stored functions, but functions on functions and
functions that would not be considered relational operators, the implementations
of the functional model have more functionality (so to speak), in general,
but fewer locks for programmers to get around (I mean,
respect).
smiles. --dawn
"Mikito Harakiri" <mikharakiri_at_iahu.com> wrote in message
news:WwP%b.24$zB2.129_at_news.oracle.com...
Received on Sat Feb 28 2004 - 00:05:30 CETHere is unorthodox view. I queried Mathworld for "Relation" and fidn't find any. Hence the conclusion: "There is no Relation in math!""Tom Hester" <$$tom_at_metadata.com> wrote in message news:308d6$403fbc8a$45033832$31596_at_msgid.meganewsservers.com...No, the relational model is based on the notion of relation in symbolic logic. The interpretation of a relation may be required to be 1st order function free, resulting in a 1NF model; but there is no requirement that relations be 1NF for a database to be relational; and there has been a great deal of relational database theory developed around non-1NF (that is non first order function free) models. I simply gave a single reference to a single article. There are many books...This is supposed to be a theoretical news list but it seems to me that the relational bigots are incredibly ignorant of relational theory.