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Re: Matheology § 162
Posted:
Nov 28, 2012 10:13 AM
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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".
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.
(You can do this by fiat, E.g. the
only sets are those you get starting with {}
and adding one element at a time;
but induction will not answer the question
one way or the other.)
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