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are there uncountably infinite types?

From: Morris Matsa <mmatsa@us.ibm.com>
Date: Tue, 19 Dec 2000 18:27:43 -0500
To: www-xml-schema-comments@w3.org
Message-ID: <OF89575397.D26F8E02-ON852569BA.006F8028@somers.hqregion.ibm.com>

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 Tuesday, 19 December 2000 18:28:40 UTC

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