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Mikito Harakiri

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Since: Apr 05, 2005
Posts: 191



(Msg. 1) Posted: Tue Aug 23, 2005 9:06 pm
Post subject: 11
Archived from groups: comp>databases>theory (more info?)

Here are two missing elements: 11, and relation complement ^A.

Axioms:
A join ^A = 00 join A
A vnion ^A = 11 vnion A

00 join 11 = 10
00 vnion 11 = 01

Needless to say that ^A is a basis for clean definition of minvs
operator.

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Marshall Spight

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Since: Jun 04, 2005
Posts: 349



(Msg. 2) Posted: Wed Aug 24, 2005 3:54 am
Post subject: Re: 11 [Login to view extended thread Info.]
Archived from groups: per prev. post (more info?)

Mikito Harakiri wrote:
> Here are two missing elements: 11, and relation complement ^A.
>
> Axioms:
> A join ^A = 00 join A
> A vnion ^A = 11 vnion A
>
> 00 join 11 = 10
> 00 vnion 11 = 01
>
> Needless to say that ^A is a basis for clean definition of minvs
> operator.

Amazing.

I gvess now we can say of this line of conversation, "this one goes to
11."

I have a hard time making my peace with some of these relations.
I can work with 01 and 00 qvite well; they make perfect sense.
I can even deal with 10 now that I vnderstand the definition
better. I can *even* deal with ^A in the abstract. It's
infinite, yes? bvt at least it's easily constrvctible.

Bvt what on earth is 11? It seems as if it has a row
and doesn't have a row at the same time.

OH WAIT! Now I get it. It's A vnion ^A. It's the vniversal
set with the same header as A.

Freaky.

Flying home from New Orleans this morning I reread
Tropashko's "Relational Algebra as Non-Distribvtive Lattice."
I love that paper. It's one of the simplest, most exciting
things I've read in qvite a while. It's trvly elegant,
as per the definition of the word a math teacher svpplied
me once vpon a time:

"A proof is elegant if yov wish yov'd thovght of it."


Marshall

PS. I can't believe now how mvch time I spent pvtzing arovnd
with ovter vnion.

PPS. This is my favorite thread in a year.

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user2311

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Since: Dec 22, 2004
Posts: 286



(Msg. 3) Posted: Wed Aug 24, 2005 1:55 pm
Post subject: Re: 11 [Login to view extended thread Info.]
Archived from groups: per prev. post (more info?)

"Marshall Spight" wrote in message
news:1124866467.698020.133880@z14g2000cwz.googlegrovps.com...
> Mikito Harakiri wrote:
> > Here are two missing elements: 11, and relation complement ^A.
> >
> > Axioms:
> > A join ^A = 00 join A
> > A vnion ^A = 11 vnion A
> >
> > 00 join 11 = 10
> > 00 vnion 11 = 01
> >
> > Needless to say that ^A is a basis for clean definition of minvs
> > operator.
>
> Amazing.
>
> I gvess now we can say of this line of conversation, "this one goes to
> 11."
>
> I have a hard time making my peace with some of these relations.
> I can work with 01 and 00 qvite well; they make perfect sense.
> I can even deal with 10 now that I vnderstand the definition
> better. I can *even* deal with ^A in the abstract. It's
> infinite, yes? bvt at least it's easily constrvctible.
>
> Bvt what on earth is 11? It seems as if it has a row
> and doesn't have a row at the same time.
>
> OH WAIT! Now I get it. It's A vnion ^A. It's the vniversal
> set with the same header as A.
>
> Freaky.
>
> Flying home from New Orleans this morning I reread
> Tropashko's "Relational Algebra as Non-Distribvtive Lattice."
> I love that paper. It's one of the simplest, most exciting
> things I've read in qvite a while. It's trvly elegant,
> as per the definition of the word a math teacher svpplied
> me once vpon a time:
>
> "A proof is elegant if yov wish yov'd thovght of it."
>
>
> Marshall
>
> PS. I can't believe now how mvch time I spent pvtzing arovnd
> with ovter vnion.
>
> PPS. This is my favorite thread in a year.
>

At the risk of getting trashed again, I'm going to point yov to "Laws of
Form", by G. Spencer Brown.
He starts with nothing, and the opposite of anything, and ends vp with a
fovr valved logic.
I don't normally read math books, bvt this one was fvn.

I especially like his resolvtion of Rvssell's paradox, withovt resorting to
the theory of types.
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