Re: A Simple Notation

"paul c" <toledobythesea_at_oohay.ac> wrote in message news:4Ifji.90354$xq1.46042_at_pd7urf1no...
> Brian Selzer wrote:
> ...
>> The symmetry is rather pleasing.
>> ...
>
> Not saying that the above comment by itself deserves to be criticized, but
> I would say that apparent lack of symmetry doesn't necessarily mean a
> method doesn't have same, just that we are unable to see it in some
> mechanical interpretation that we happen to prefer for other reasons (such
> as, "it gets the answer we want!").
>

As far as I can tell, David's choice of [] for TRUE is arbitrary. It's his notation, and therefore it's his perogative to do as he pleases. But what is contained within the brackets is a conjunction of an arbitrary number of boolean values, so it makes sense to view [] as the negation of a nullary product just as it makes sense to view [A] as the negation of a unary product, or [A B] as the negation of a binary product, and so on. Now had David begun with OR and <OR>, then it would have made sense to view [] as the negation of a nullary sum. A nullary sum takes on the value of the additive identity which is 0 or FALSE, whereas a nullary product takes on the value of the multiplicative identity which is 1 or TRUE. So,

for OR and <OR>, [] should yield TRUE, but for AND and <AND>, [] should yield FALSE

> p
Received on Fri Jul 06 2007 - 08:55:48 CEST