Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Matheology § 203
Replies: 3   Last Post: Feb 1, 2013 8:15 PM

 Messages: [ Previous | Next ]
 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: Matheology § 203
Posted: Feb 1, 2013 10:53 AM

On 1 Feb., 16:38, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:
> William Hughes <wpihug...@gmail.com> writes:
> > Let P(n) be
> >  0.111...  is not the nth line
> >  of

>
> >  0.1000...
> >  0.11000...
> >  0.111000...
> >  ...

>
> > Clearly for every natural number n
> > P(n) is true.

>
> > This means there is no natural
> > number m for which P(m) is true.

>
> > It is not simply that we cannot find m,
> > we know that m does not exist.

>
> Futhermore WM accepts, for example, that
> for every natural number n, 2 * n is even.
>
> Doesn't he?

Of course.
>
> But when asked how it is possible to know such a thing,
> he falls strangely silent.

For that theorem you need not know (actually) all natural numbers.
Induction is sufficient that holdes for (potentially) all natural
numbers, i.e., up to every natural number. There is no impredicative
definition involved.

Regards, WM

Date Subject Author
2/1/13 Alan Smaill
2/1/13 mueckenh@rz.fh-augsburg.de
2/1/13 Virgil