# Re: A Simple Notation

Date: Thu, 05 Jul 2007 13:07:44 GMT

Message-ID: <A26ji.4526$wu5.3127_at_trndny03>

"Brian Selzer" <brian_at_selzer-software.com> wrote in message
news:wd5ji.20671$RX.16718_at_newssvr11.news.prodigy.net...

*>
*

> "David Cressey" <cressey73_at_verizon.net> wrote in message

*> news:kv4ji.6553$za5.2586_at_trndny09...
**> > In Boolean algebra, you could, if you wanted to, express everything by
**> > just
**> > using brackets, as follows:
**> >
**> > [A B] means NOT (A AND B)
**> >
**> > This notation can be extended to 3 or more operands, as follows:
**> >
**> > [A B C] means NOT (A AND B AND C)
**> >
**> > "AND" is associative, so there's no confusion.
**> >
**> > You can reduce the notation to 1 operand as follows:
**> >
**> > [A] means NOT (A)
**> >
**> > And to zero operands as follows:
**> >
**> > [] means TRUE
**> > [[]] means FALSE
**> >
**>
**> I would switch these because the nullary product is 1, or TRUE, and the
**> nullary Cartesian product is {()}, or DEE. I think that you would agree
**> that [DEE] should be FALSE.
**>
*

*> [] should mean FALSE
**> [[]] should mean TRUE
*

I contemplated what you suggest, and I chose to let the representation of TRUE be []. You can read it as "not nothing". Regardless, we agree that [[]] represents NOT ([]). What do you gain by going the other way?