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Re: Matheology § 162
Posted:
Nov 28, 2012 12:07 PM
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On 28 Nov., 16:13, William Hughes <wpihug...@gmail.com> wrote:
> On Nov 28, 10:59 am, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > On 28 Nov., 13:48, William Hughes <wpihug...@gmail.com> wrote:
>
> > > On Nov 28, 2:43 am, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > > > Induction proves also: Every set of natural numbers is finite.
> > > > Why do you overlook this simple proof?
>
> > > No, what induction proves is that every set of natural numbers
> > > with a largest number is finite.
>
> > And induction proves that every set of natural numbers has a largest
> > number. For every finite n also n + 1 is finite
>
> Look! Over There! A Pink Elephant!
>
> >and the set containing
> > both, n and n + 1 ist finite too.
>
> There is of course no such thing as
> "the set containing both n and n+1".
Here it is: {n, n+1}
> You need to prove that all such sets
> have a largest number, not just the sets
> you can get by starting with {} and
> adding one element at a time.
Induction does not say more than: 1 is natural number, and if n is a
natural number, then n+1 is a natural number.
If {1, 2, 3, ..., n} is a set of natural numbers, then
{1, 2, 3, ..., n, n+1} is a set of natural numbers.
> (You can do this by fiat, E.g. the
> only sets are those you get starting with {}
> and adding one element at a time;
Induction cannot do more.
> but induction will not answer the question
> one way or the other.)
Anyhow, this question is unimportant.
Have you meanwhile convinced yourself that analysis is capable
expanding infinity by a series of powers of 10? This is tantamount to
a decimal representation.
Regards, WM
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