• To: "'Bullard, Claude L (Len)'" <clbullar@i...>
• Subject: RE: Subtyping in XML
• From: Jeff Lowery <jlowery@s...>
• Date: Mon, 9 Sep 2002 14:27:01 -0700
• Cc: "Xml-Dev (E-mail)" <xml-dev@l...>

Real numbers aren't countable.  I think most people would agree that they
are a type.  I'm sure if I dug around I could find a formal proof that real
numbers exist. 

> -----Original Message-----
> From: Bullard, Claude L (Len) [mailto:clbullar@i...]
> Sent: Monday, September 09, 2002 2:23 PM
> To: 'John Cowan'
> Cc: jlowery@s...; aray@n...; xml-dev@l...
> Subject: RE:  Subtyping in XML
> 
> 
> Cantor The Mad.  Back to the denumerability thing 
> and quantum foaming at the mouth...
> 
> Ok.  Still, he said 
> 
> "types first and formost define a concept of membership.
> Such definitions must be formal and unambiguous."
> 
> So are you saying "unambiguous" means countable?
> 
> len
> 
> -----Original Message-----
> From: John Cowan [mailto:jcowan@r...]
> 
> "Bullard, Claude L (Len)" scripsit:
> 
> > Doesn't that make type synonymous with set?
> 
> No.  Types have to be specifiable: there are only countably 
> many types,
> but there are uncountably many sets, indeed $2^\aleph_0$ of them.
> An easy way to achieve this is to require that types have names.
> 

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