From: V. Bruce Hunt <vbhunt@silverfox.com>

Date: Sat, 30 Oct 1999 18:01:03 +0000

Message-ID: <381B325F.A43A8D15@silverfox.com>

To: www-xml-schema-comments@w3.org

Date: Sat, 30 Oct 1999 18:01:03 +0000

Message-ID: <381B325F.A43A8D15@silverfox.com>

To: www-xml-schema-comments@w3.org

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 HuntReceived on Saturday, 30 October 1999 13:56:27 UTC

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