Re: So what's null then if it's not nothing?

"Hugo Kornelis" <hugo_at_pe_NO_rFact.in_SPAM_fo> wrote in message news:hk81q19t85t60ho59gjkch3rdgv2aoq9ct_at_4ax.com...
> On Mon, 12 Dec 2005 04:24:43 GMT, David Cressey wrote:
>
> >
> >"Hugo Kornelis" <hugo_at_pe_NO_rFact.in_SPAM_fo> wrote in message
> >news:mr6pp1dthae49qdiudmgcp8eh66tmve5pp_at_4ax.com...
> >
> >
> >> If a data type accomodates not only True and False but Unknown as well
> >> (represented in whatever way), I'd hesitate to call it Boolean, since
> >> most people associate the term Boolean with the most simple Boolean
> >> algebra, that has only True and False. But on the other hand, if all
> >> rules for a Boolean algebra are met, there's technically no reason to
> >> object to the name Boolean for this data type.
> >
> >In order to move this discussion forward, I believe it's going to be
> >necessary to distinguish between
> >Boolean arithmetic and Boolean algebra.
>
> Hi David,
>
> And what exactly is the difference?

This isn't exact, but it's as close as I can come:

Arithmetic is when you apply known operators to known operands, in order to come up with known results.

Algebra is when you apply operations to equations in one or more unknowns, in order to simplify the equations, and generally, solve for the unknowns.

In the Boolean domain, given two operands (or one in the case of NOT) and the truth tables, it's simple mechanics to arrive at the answer. This is what computers do. It's Boolean arithmetic.

Given propositions with multiple unknowns, like those horrible mind twisters that have clues like
"The man who smokes Camels lives next to the man who likes Jazz", you can use Boolean algebra to solve for the unknowns.

Now it's a remarkable fact (well, remarkable to me) that you can simulate an algebraic system on a machine that is only capable of performing arithmetic and following programs.

Anyway, a statement like "this statement is false" can be in expressed in Boolean algebra, but not Boolean arithmetic. Received on Thu Dec 15 2005 - 00:05:43 CET