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

 Messages: [ Previous | Next ]
 Graham Cooper Posts: 4,495 Registered: 5/20/10
Re: UNCOUNTABILITY
Posted: Dec 22, 2012 10:01 PM

On Dec 23, 12:55 pm, William Hughes <wpihug...@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.
>

Herc turns his mobius strip over... even more to see there!

Herc

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