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:]
> Sent: Monday, September 09, 2002 2:23 PM
> To: 'John Cowan'
> Cc: ; ;
> Subject: RE: [xml-dev] 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:]
>
> "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.
>
