Re: 11

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. Received on Wed Aug 24 2005 - 08:54:27 CEST