Re: Uncountably infinite datatypes can be computational.

Bruce:
In the last few days we took a decision to change the "decimal" datatype
and make
the scale and precision facets optional.  If they are not specified, a
decimal number
can have any number of digits before and after the decimal point.

Will this, along with wording changes you recommend, take care of your
concern?

All the best, Ashok


"V. Bruce Hunt" <vbhunt@silverfox.com>@w3.org on 10/30/99 02:01:03 PM

Please respond to bhunt@silverfox.com

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Subject:  Uncountably infinite datatypes can be computational.



Hi,

In reading along in the XML schema 2 - datatypes specification, I came
across the sentence in Section 2.4.1.3 that says,

"No computational datatype is uncountably infinite. "

I suggest that the editors have a very narrow meaning for "computational
datatype" and are intending to convey the thought that no "finite numerical
computational" datatype is uncountably infinite based on current finite
numerical precision high performance native number system implementations
in todays computers.   There are of course infinite precision computational
packages and symbolic
computational packages; both categories deal effectively with uncountably
infinite datatypes.

The real numbers are the most common form of an uncountably infinite
datatype.  Many symbolic computational packages  such as Macsyma and
Mathematica "compute" with representations of uncountably infinite
datatypes and obtain results that can be delivered to any desired level of
numerical precision and routinely deliver results in terms that are
completely (in the mathematical sense) precise.  Examples include
integration, differentiation, laplace transforms, and algebraic
manipulation.

Clearly these are good examples of uses of a computational datatype that
are uncountably infinite.  I would suggest a correction to more clearly
define your intention.

In addition, the XML-schema group would be well served to expand the
explained domain of discourse with
a fourth bullet  in this section:

value spaces that are uncountably infinite and exact.

It is perfectly reasonable and is likely to become highly desirable to
represent  value spaces that are "uncountably infinte and exact" to
represent exact "symbolic" mathematical computations using XML-schema.  For
example, the ability to make room for such extensions now should permit a
future in which MathML contrains a datatype to, for example, the real
numbers (engineering and physics calculations) or the complex numbers (
electrical engineering ) or probability spaces ( the real numbers from 0
through 1 inclusive [for queueing theory]) and is quite satisfied to have a
result that is an expression of "pi" ( the ratio of the circumference of a
circle to its diameter ) or "e" ( the base of the natural logarithms) or
even "i"( the square root of  minus one).

To be clear, I am not suggesting that the working group take on defining
value spaces that are uncountably infinite and exact however I believe it
incumbent on the working group to clearly indicate that they can be defined
(and many are computable).  In addition, you may well wish to mark them for
later clarification and a potential area for future standardization.

sincerely

Bruce Hunt
(See attached file: vbhunt.vcf)