Re: 11

"Marshall Spight" <marshall.spight_at_gmail.com> wrote in message news:1124866467.698020.133880_at_z14g2000cwz.googlegroups.com...
> Mikito Harakiri wrote:
> > Here are two missing elements: 11, and relation complement ^A.
> >
> > Axioms:
> > A join ^A = 00 join A
> > A union ^A = 11 union A
> >
> > 00 join 11 = 10
> > 00 union 11 = 01
> >
> > Needless to say that ^A is a basis for clean definition of minus
> > operator.
>
> Amazing.
>
> I guess 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 quite well; they make perfect sense.
> I can even deal with 10 now that I understand the definition
> better. I can *even* deal with ^A in the abstract. It's
> infinite, yes? but at least it's easily constructible.
>
> But 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 union ^A. It's the universal
> set with the same header as A.
>
> Freaky.
>
> Flying home from New Orleans this morning I reread
> Tropashko's "Relational Algebra as Non-Distributive Lattice."
> I love that paper. It's one of the simplest, most exciting
> things I've read in quite a while. It's truly elegant,
> as per the definition of the word a math teacher supplied
> me once upon a time:
>
> "A proof is elegant if you wish you'd thought of it."
>
>
> Marshall
>
> PS. I can't believe now how much time I spent putzing around
> with outer union.
>
> PPS. This is my favorite thread in a year.
>

At the risk of getting trashed again, I'm going to point you to "Laws of Form", by G. Spencer Brown.
He starts with nothing, and the opposite of anything, and ends up with a four valued logic.
I don't normally read math books, but this one was fun.

I especially like his resolution of Russell's paradox, without resorting to the theory of types. Received on Wed Aug 24 2005 - 14:33:38 CEST