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Topic: Matheology § 210
Replies: 80   Last Post: Feb 8, 2013 5:45 PM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology � 210
Posted: Feb 5, 2013 6:49 PM

In article
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 5 Feb., 21:55, William Hughes <wpihug...@gmail.com> wrote:
> > On Feb 5, 6:02 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> >
> > <snip>
> >

> > >... one cannot even put all natural numbers in
> > > correspondence with all natural numbers.

> >
> > However, one can put every natural number in
> > correspondence with every natural number.

>
> One can have that by belief or decreed by the powers that be.
> n <--> n is the finite expression of this belief. But its validity is
> dubious because one cannot have possibly in a possible list that
> contains every finite initial sequence of the sequence of natural
> numbers the sequence s of every finite initial segment of the sequence
> of natural numbers.

If one cannot even justify an n to n correspondence for naturals n, then
one has thrown out a large baby with a very little bathwater, as one has
automatically thrown out induction as well.

Induction requires that one be able to conclude that something holds for
all n in |N.

But if one cannot anything for all n in |N, no induction!
--

Date Subject Author
2/5/13 mueckenh@rz.fh-augsburg.de
2/5/13 fom
2/5/13 mueckenh@rz.fh-augsburg.de
2/5/13 William Hughes
2/5/13 mueckenh@rz.fh-augsburg.de
2/5/13 William Hughes
2/5/13 Virgil
2/5/13 fom
2/5/13 Virgil
2/5/13 fom
2/6/13 mueckenh@rz.fh-augsburg.de
2/6/13 fom
2/6/13 mueckenh@rz.fh-augsburg.de
2/6/13 Virgil
2/6/13 fom
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 Virgil
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 William Hughes
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 William Hughes
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 William Hughes
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 William Hughes
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 William Hughes
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 William Hughes
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 William Hughes
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 William Hughes
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 Virgil
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 William Hughes
2/8/13 mueckenh@rz.fh-augsburg.de
2/8/13 Virgil
2/8/13 fom
2/8/13 mueckenh@rz.fh-augsburg.de
2/8/13 Michael Stemper
2/8/13 mueckenh@rz.fh-augsburg.de
2/8/13 Virgil
2/8/13 Virgil
2/7/13 Virgil
2/7/13 Virgil
2/7/13 fom
2/8/13 mueckenh@rz.fh-augsburg.de
2/8/13 Virgil
2/7/13 Virgil
2/7/13 fom
2/7/13 Virgil
2/7/13 fom
2/7/13 Virgil
2/8/13 mueckenh@rz.fh-augsburg.de
2/8/13 Virgil
2/7/13 Virgil
2/7/13 fom
2/7/13 Virgil
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 fom
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 fom
2/7/13 Virgil
2/8/13 mueckenh@rz.fh-augsburg.de
2/7/13 Virgil
2/7/13 fom
2/7/13 fom
2/7/13 fom
2/7/13 fom
2/7/13 fom
2/7/13 fom
2/6/13 Virgil
2/5/13 Virgil
2/6/13 mueckenh@rz.fh-augsburg.de
2/6/13 Virgil
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 Virgil
2/8/13 Scott Berg