Tom Melly <tom### [at] tomandlucouk> wrote:

> "David Fontaine" <dav### [at] faricynet> wrote in message
> news:3A81CCBB.635F3E91@faricy.net...

>> Think of the problem of surface area of a 3d solid. Hence multiplication
>> operations should be "groups" when figuring out the order of operations.
> It
>> gets progressively more obscure, but I think a similar arument can be made
> for
>> all precedences.

> Well, yes, but obscure is the important point. Okay, you might be able to
> make a clear arguement for * over + but what about - and + or / and * ?
> There maybe an arguement, but it isn't a clear one. However, any arguement
> that says 2*3 is not 6 is plainly batty.

Actually, there are plenty of number systems where this is plainly *not*
true.  There are the simple systems where 6 is undefined (base 4, for
example, where 2+3 = 11, or the mod 5 number system, where 2*3 = 2) and then
there are more complex things, where the definitions which you use for the
multiplicative and additive operators get weird.  I can't give a good
example here, since A. It takes a lot of math, and B. It's been close to a
decade since I did discrete algebra.  How number systems behave is highly
dependant upon the assumptions you place upon them.

Now, if you're talking about the integer, rational, or real number lines,
then yes, 2*3 = 6.  However, those are not the only number system available
to us.  I use mod systems all the time in POV, for example.

Geoff

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