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Topic: UNCOUNTABILITY
Replies: 59   Last Post: Dec 24, 2012 2:06 PM

 Messages: [ Previous | Next ]
 Virgil Posts: 8,833 Registered: 1/6/11
Re: UNCOUNTABILITY
Posted: Dec 23, 2012 12:12 AM

In article
William Hughes <wpihughes@gmail.com> wrote:

> On Dec 22, 7:04 pm, Virgil <vir...@ligriv.com> wrote:
> > In article
> >  William Hughes <wpihug...@gmail.com> wrote:
> >

> > > Note, that
> > > subcountable
> > > does not mean countable.

> >
> > I am not at all sure of what you mean by subcountable.

>
> A set X is subcountable if we can associate a different natural number
> with every element x of X, call it f(x) In classical mathematics
> subcountable
> implies countable because f(X) must be a subset of the natural
> numbers.
> However, if we take a contructivist viewpoint, then we do not know
> that f(X) is a subset (it may not be contructable). So in
> constructive
> mathematics the fact that X is subcountable, does not mean we can
> find a bijection between X and some subset of the naturals, so X might
> not be countable. E.g. in constructive mathematics the (constructive)
> reals
> are subcountable but not countable.
>
> So the fact that a set is uncountable need not mean it is "bigger"
> than
> the natural numbers.

But the constraints of your "constructive mathematics' are not required
in classical mathematics when not doing your constructive mathematics,
so are not relevant in classical mathematics.
--

Date Subject Author
12/19/12 george
12/20/12 Zaljohar@gmail.com
12/20/12 Barb Knox
12/20/12 ross.finlayson@gmail.com
12/20/12 Zaljohar@gmail.com
12/20/12 ross.finlayson@gmail.com
12/20/12 Graham Cooper
12/21/12 mueckenh@rz.fh-augsburg.de
12/21/12 Virgil
12/20/12 Graham Cooper
12/20/12 mueckenh@rz.fh-augsburg.de
12/20/12 Zaljohar@gmail.com
12/21/12 mueckenh@rz.fh-augsburg.de
12/21/12 Zaljohar@gmail.com
12/21/12 mueckenh@rz.fh-augsburg.de
12/21/12 Virgil
12/21/12 William Hughes
12/22/12 mueckenh@rz.fh-augsburg.de
12/22/12 William Hughes
12/22/12 Virgil
12/22/12 William Hughes
12/22/12 Graham Cooper
12/23/12 Virgil
12/23/12 William Hughes
12/24/12 Graham Cooper
12/24/12 mueckenh@rz.fh-augsburg.de
12/24/12 Virgil
12/23/12 mueckenh@rz.fh-augsburg.de
12/23/12 Virgil
12/23/12 mueckenh@rz.fh-augsburg.de
12/23/12 William Hughes
12/24/12 mueckenh@rz.fh-augsburg.de
12/24/12 Virgil
12/23/12 Virgil
12/22/12 Virgil
12/21/12 Zaljohar@gmail.com
12/22/12 mueckenh@rz.fh-augsburg.de
12/22/12 William Hughes
12/22/12 Virgil
12/21/12 Zaljohar@gmail.com
12/21/12 mueckenh@rz.fh-augsburg.de
12/21/12 Virgil
12/22/12 Zaljohar@gmail.com
12/22/12 Virgil
12/22/12 Zaljohar@gmail.com
12/22/12 mueckenh@rz.fh-augsburg.de
12/22/12 Virgil
12/22/12 mueckenh@rz.fh-augsburg.de
12/22/12 Virgil
12/23/12 mueckenh@rz.fh-augsburg.de
12/23/12 Virgil
12/21/12 Virgil
12/20/12 Virgil
12/20/12 Graham Cooper
12/20/12 Graham Cooper
12/21/12 mueckenh@rz.fh-augsburg.de
12/21/12 Virgil
12/21/12 Graham Cooper
12/21/12 Graham Cooper