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Re: are there uncountably infinite types?

From: Aki Yoshida <akitoshi.yoshida@sap.com>
Date: Wed, 20 Dec 2000 13:41:32 +0100
Message-ID: <000301c06a82$2f089c00$e968120a@wdf.sapag.de>
To: <mmatsa@us.ibm.com>
Cc: <www-xml-schema-comments@w3.org>
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

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
"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 07:45:49 UTC

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