# Re: All hail Neo!

Date: Sun, 23 Apr 2006 13:58:14 GMT

Message-ID: <WJL2g.64598$VV4.1223196_at_ursa-nb00s0.nbnet.nb.ca>

Frank Hamersley 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.

*>*

> I suspect you are wearing the darkly tinted glasses of preconception.

*> Whilst I was trying to show a little wit, the current 3VL state of*

*> affairs still seems to me to fit that description.*

*>*

>> A much more intellectually honest reply would be: "I don't know."

*>*

> Not from this black duck (on this occasion)!

*>*

>> or "Null has no similar analog in set theory."

*>*

> I wasn't comparing/contrasting the RM with set theory. Perhaps for you

*> it is implicit?*

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.

>> True and 1 both have the exact same analog in set theory. False and 0 >> both have the exact same analog in set theory.

*>*

> Perhaps but insistence on a parallel form for the RM does not seem to

*> lead anywhere practical*...FWICT.*

Are you suggesting that query transformations lack practical benefits?

>> This has a certain elegance and symmetry.

*>*

> I agree that and readily subscribe to that in my own endeavours.

*>*

>> In canonical form: >> >> {} = 0 = false >> {{}} = 1 = true >> >> What is the similar analog for null?

*>*

> My prior knowledge of your/the notation is non existent but I can prolly

*> deduce its intent. So having a stab at it how about ...*

*>*

*> {}{} = 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 - 15:58:14 CEST