From: Morris Matsa <mmatsa@us.ibm.com>

Date: Wed, 20 Dec 2000 22:50:08 -0500

To: "Aki Yoshida" <akitoshi.yoshida@sap.com>

Cc: <www-xml-schema-comments@w3.org>

Message-ID: <OFAAE430C5.43DAA10B-ON852569BC.000854C0@somers.hqregion.ibm.com>

Date: Wed, 20 Dec 2000 22:50:08 -0500

To: "Aki Yoshida" <akitoshi.yoshida@sap.com>

Cc: <www-xml-schema-comments@w3.org>

Message-ID: <OFAAE430C5.43DAA10B-ON852569BC.000854C0@somers.hqregion.ibm.com>

For question 1: Thank you for the history, I wasn't involved when there were real numbers, and it seems to explain the sentence. You seem to be confirming that now there is no longer a way to make a type with an uncountably infinite value space. If this is so, should the spec be amended slightly? It now says (see below) "others are uncountably infinite" which is at least misleading. > For Question 2: > A uriReference can be infinitely long just as an integer can. So, it's still > countable. For question 2: I disagree. I'll tell you why I feel the way that I do, and please tell me where I'm going wrong. (I'm still not sure anybody would care even if I'm right.) The way I see it, the difference between integers and uriReferences is that while there are infinitely many integers, the lexical representation of any given integer is finite, although arbitrarily long (the same is true for rational numbers and all other finite and countably infinite sets, given the correct lexical representation). This is not true for uriReferences --- a given uriReference can be infinitely long (the same is true for irrational numbers, real numbers, and all other uncountably infinite sets, regardless of lexical representation). Consider a trivial one-to-one mapping between real numbers between 0 and 1 and a subset of uriReferences: Take the decimal representation of the real number and add a slash between every two digits, eliminating the leading "0." [Admittedly, this is a mapping between decimal representations of real numbers and uriReferences, and there are more representations of real numbers than there are real numbers (e.g. 0.09999... = 0.10000...), so eliminate the redundant representations and reduce the subset of the uriReferences involved, and the point is the same.] If you prefer, use a diagonalization argument on a similar subset. Do you still think that the value space of uriReferences is countable? I'm rusty on this stuff so I'll believe you - please explain. (I also wonder if it matters given that the lexical space of all uriReferences encodable in the universe is finite.) Morris "Aki Yoshida" <akitoshi.yoshida@sap.com> on 12/20/2000 07:41:32 AM To: Morris Matsa/Somers/IBM@IBMUS cc: <www-xml-schema-comments@w3.org> Subject: Re: are there uncountably infinite types? For Question 1: An earlier draft had a datatype called "real" whose value space included irrational numbers. Although thatdraft provided no way to lexically represent these values, from the value-space point of view, these values were there and therefor, this datatype was classified as uncountably infinite. In contrast, the value space for the current decimal datatype is constrained by i * 10^-n, where both i and n are integers (which is countably infinite). Therefore, the decimal type is classified as countably infinite. If instead we didn't make the above value constraint, we would have an uncountably infinite decimal. For Question 2: A uriReference can be infinitely long just as an integer can. So, it's still countable. Best regards, Aki Yoshida --------------------------------------------------------------- From: "Morris Matsa" <mmatsa@us.ibm.com> Date: Tue, 19 Dec 2000 18:27:43 -0500 Subject: are there uncountably infinite types? Part 2 of the spec (http://www.w3.org/TR/xmlschema-2/#dt-cardinality) says that: "Every value space has associated with it the concept of cardinality. Some value spaces are finite, some are countably infinite while still others are uncountably infinite." Table C.1 "Fundamental Facets", also in part 2 of the spec, (http://www.w3.org/TR/xmlschema-2/#app-fundamental-facets) lists all of the built-in datatypes and their cardinalities, and none of them are uncountably infinite. Elsewhere, the spec tells us how to figure out the cardinality of the value spaces of user-defined data types (http://www.w3.org/TR/xmlschema-2/#dc-defn), none of which end up uncountably infinite. 1. My first question is how any type can ever end up uncountably infinite, as the spec claims? 2. My second question is a minor one - I was wondering whether all of the primitive types should be defined as not being uncountably infinite. For example, I looked at uriReference, and it seems uncountably infinite. It is defined (http://www.w3.org/TR/xmlschema-2/#uriReference) as "a Uniform Resource Identifier (URI) Reference as defined in Section 4 of [RFC 2396], as amended by [RFC 2732]." From skimming RFC2396 it seems that a URI mostly reduces to a sequence of path segments. In section 3.3. of RFC 2396 (http://www.ietf.org/rfc/rfc2396.txt) it says "The path may consist of a sequence of path segments separated by a single slash "/" character." This does not say, as the Schema spec would, "a finite sequence of path segments", so it seems that URIs may be infinitely long, in which case the value space of uriReference would be uncountably infinite. Am I right?Received on Wednesday, 20 December 2000 22:48:25 UTC

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