On 9 December 2012 08:41, Bo Jacoby <bojac...@yahoo.dk> wrote:
> Well, 'cm' is a product, c*m, where c=.0.01 and m is a meter.

All my life I have been under the impression that 'cm' is an
abbreviation for 'centimeter', used to denote the unit of length,
and not an arithmetic expression.  And that, similarly, 'cm²' is
a denotation for a unit derived from 'cm', and does not include
operations.

> The J convention is that expressions are evaluated from right to left:
>  a*b+c   means   a*(b+c).

How is J related to your treatment of 'cm' and 'cm²', and how  does
J convention lead to 'omitting parentheses'?

> It is better because is is simpler and more general.

How exactly?
I agree that if you have many operations, not having precedences
between them is a plus.  But in school algebra there are no many
operations, so the precedences hardly present a problem.  And, let
us not forget that in J the evaluation does not occur in strictly
one direction.  As for whether right-to-left is better than
left-to-right, I am not sure.  I see advantages in both systems.
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