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Frank Hamersley wrote:
> Bob Badour wrote:
>
>> Frank Hamersley wrote: >> >>> Bob Badour wrote:
>>>> In that line of thought, here's an interesting question that Date et >>>> al have posed before to the n-VL folks: >>>> >>>> If "exists but empty" is true and "doesn't exist" is false, what is >>>> null? >>> >>> Neither and both! >> >> I find that sort of handwaving to be a complete non-answer.
>> A much more intellectually honest reply would be: "I don't know."
>> or "Null has no similar analog in set theory."
No, it is quite explicit. Relations are sets. Relational algebra is the equivalent of set theory, and relational calculus is the equivalent of predicate calculus.
Thus, the equivalence of dee and true and of dum and false are very important. And the question of what relation value equates to null is a very good question.
>> True and 1 both have the exact same analog in set theory. False and 0 >> both have the exact same analog in set theory.
Are you suggesting that query transformations lack practical benefits?
>> This has a certain elegance and symmetry.
>> In canonical form: >> >> {} = 0 = false >> {{}} = 1 = true >> >> What is the similar analog for null?
{} is the empty set and is the set with cardinality 0.
{{}} is the set containing an empty set and is the canonical form of all
sets with cardinality 1.
{{},{{}}} is the canonical set with cardinality 2.
http://www.math.psu.edu/simpson/papers/philmath/node17.html
One can continue in this vein until Goedel stomps on one. http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems
With respect to {}{} either it is completely meaningless, or perhaps you
intend the juxtaposition of two sets to mean conjunction or disjunction,
in which case:
{}{} = {} = false
If null and false are the same, we can do away with null.
> As an aside (and with no malice aforethought) I am curious why the 0 and
> 1 figure at all? Forced to conform I would probably go with ...
>
> {}{} = -1 = null
0 and 1 figure by tying into the formalism for whole numbers as shown above. http://en.wikipedia.org/wiki/Foundations_of_mathematics
I direct your attention to:
http://en.wikipedia.org/wiki/Formalism#Mathematics
"Complete formalisation is in fact in the domain rather of computer science."
And finally, the relational model is itself a formal system:
http://en.wikipedia.org/wiki/Formal_system
See also:
http://en.wikipedia.org/wiki/Category:Mathematical_logic
> * (for another post perhaps) I don't see any great leap forward in the
> aspects of TTM that address the extinction of nulls.
If nulls cause great damange without serving any particularly useful purpose, why should one address their extinction? Received on Sun Apr 23 2006 - 08:58:14 CDT