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

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Virgil

Posts: 8,833
Registered: 1/6/11
Re: UNCOUNTABILITY
Posted: Dec 23, 2012 12:12 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

In article
<ee1d96e2-fbb9-4c48-a02e-cef0a3204464@s14g2000yqg.googlegroups.com>,
William Hughes <wpihughes@gmail.com> wrote:

> On Dec 22, 7:04 pm, Virgil <vir...@ligriv.com> wrote:
> > In article
> > <2263ace1-dfa7-466d-8341-c50692402...@v7g2000yqv.googlegroups.com>,
> >  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
Read Re: UNCOUNTABILITY
george
12/20/12
Read Re: UNCOUNTABILITY
Zaljohar@gmail.com
12/20/12
Read Re: UNCOUNTABILITY
Barb Knox
12/20/12
Read Re: UNCOUNTABILITY
ross.finlayson@gmail.com
12/20/12
Read Re: UNCOUNTABILITY
Zaljohar@gmail.com
12/20/12
Read Re: UNCOUNTABILITY
ross.finlayson@gmail.com
12/20/12
Read Re: UNCOUNTABILITY
Graham Cooper
12/21/12
Read Re: UNCOUNTABILITY
mueckenh@rz.fh-augsburg.de
12/21/12
Read Re: UNCOUNTABILITY
Virgil
12/20/12
Read Re: UNCOUNTABILITY
Graham Cooper
12/20/12
Read Re: UNCOUNTABILITY
mueckenh@rz.fh-augsburg.de
12/20/12
Read Re: UNCOUNTABILITY
Zaljohar@gmail.com
12/21/12
Read Re: UNCOUNTABILITY
mueckenh@rz.fh-augsburg.de
12/21/12
Read Re: UNCOUNTABILITY
Zaljohar@gmail.com
12/21/12
Read Re: UNCOUNTABILITY
mueckenh@rz.fh-augsburg.de
12/21/12
Read Re: UNCOUNTABILITY
Virgil
12/21/12
Read Re: UNCOUNTABILITY
William Hughes
12/22/12
Read Re: UNCOUNTABILITY
mueckenh@rz.fh-augsburg.de
12/22/12
Read Re: UNCOUNTABILITY
William Hughes
12/22/12
Read Re: UNCOUNTABILITY
Virgil
12/22/12
Read Re: UNCOUNTABILITY
William Hughes
12/22/12
Read Re: UNCOUNTABILITY
Graham Cooper
12/23/12
Read Re: UNCOUNTABILITY
Virgil
12/23/12
Read Re: UNCOUNTABILITY
William Hughes
12/24/12
Read Re: UNCOUNTABILITY
Graham Cooper
12/24/12
Read Re: UNCOUNTABILITY
mueckenh@rz.fh-augsburg.de
12/24/12
Read Re: UNCOUNTABILITY
Virgil
12/23/12
Read Re: UNCOUNTABILITY
mueckenh@rz.fh-augsburg.de
12/23/12
Read Re: UNCOUNTABILITY
Virgil
12/23/12
Read Re: UNCOUNTABILITY
mueckenh@rz.fh-augsburg.de
12/23/12
Read Re: UNCOUNTABILITY
William Hughes
12/24/12
Read Re: UNCOUNTABILITY
mueckenh@rz.fh-augsburg.de
12/24/12
Read Re: UNCOUNTABILITY
Virgil
12/23/12
Read Re: UNCOUNTABILITY
Virgil
12/22/12
Read Re: UNCOUNTABILITY
Virgil
12/21/12
Read Re: UNCOUNTABILITY
Zaljohar@gmail.com
12/22/12
Read Re: UNCOUNTABILITY
mueckenh@rz.fh-augsburg.de
12/22/12
Read Re: UNCOUNTABILITY
William Hughes
12/22/12
Read Re: UNCOUNTABILITY
Virgil
12/21/12
Read Re: UNCOUNTABILITY
Zaljohar@gmail.com
12/21/12
Read Re: UNCOUNTABILITY
mueckenh@rz.fh-augsburg.de
12/21/12
Read Re: UNCOUNTABILITY
Virgil
12/22/12
Read Re: UNCOUNTABILITY
Zaljohar@gmail.com
12/22/12
Read Re: UNCOUNTABILITY
Virgil
12/22/12
Read Re: UNCOUNTABILITY
Zaljohar@gmail.com
12/22/12
Read Re: UNCOUNTABILITY
mueckenh@rz.fh-augsburg.de
12/22/12
Read Re: COUNTABILITY of a set requires N to surject to it
Virgil
12/22/12
Read Re: UNCOUNTABILITY
mueckenh@rz.fh-augsburg.de
12/22/12
Read Re: UNCOUNTABILITY
Virgil
12/23/12
Read Re: UNCOUNTABILITY
mueckenh@rz.fh-augsburg.de
12/23/12
Read Re: UNCOUNTABILITY
Virgil
12/21/12
Read Re: UNCOUNTABILITY
Virgil
12/20/12
Read Re: UNCOUNTABILITY
Virgil
12/20/12
Read Re: UNCOUNTABILITY
Graham Cooper
12/20/12
Read Re: UNCOUNTABILITY
Graham Cooper
12/21/12
Read Re: UNCOUNTABILITY
mueckenh@rz.fh-augsburg.de
12/21/12
Read Re: UNCOUNTABILITY
Virgil
12/21/12
Read Re: UNCOUNTABILITY
Graham Cooper
12/21/12
Read Re: UNCOUNTABILITY
Graham Cooper

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