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 § 200
Replies: 40   Last Post: Jan 29, 2013 7:33 PM

 Messages: [ Previous | Next ]
 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: Matheology § 200
Posted: Jan 27, 2013 8:42 AM

On 27 Jan., 14:04, William Hughes <wpihug...@gmail.com> wrote:
> On Jan 27, 9:40 am, WM <mueck...@rz.fh-augsburg.de> wrote:
>

> > On 27 Jan., 01:55, William Hughes <wpihug...@gmail.com> wrote:
>
> > > On Jan 26, 10:51 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > > > The set of indexes is 1 + the decadic
> > > > logarithm of L.

>
> > > Nope, 1+ the decadic logarithm of L is the cardinality
> > > of the set of indexes.

>
> > I know.
>
> So do not make silly statements
> about what the set of indexes is.
>
> You are taking the limit of
>
>
> You are not taking the limit of sets
> but the limit of cardinalites of sets.

You are wrong. Look it up, in case you have forgotten. For instance
here
http://www.hs-augsburg.de/~mueckenh/GU/GU12c.PPT#403,25,Folie 25

The sets are {2, 1}, {2}, {4, 3, 2}, {4, 3}, {6, 5, 4, 3}, {6, 5,
4}, ...
This is a sequence of sets. If the digits in their order are
interpreted as a number (the usual and most natural way to do), then
the limit is oo. The cardinality of the indexes of this limit in
analysis is aleph_0.

The sequence of cardinalities is 2, 1, 3, 2, 4, 3, ... The limit of
this sequence is aleph_0 too.

> The limit you calculate is not a limit set, nor the
> cardinality of a limit set.

Analysis shows that the cardinality of the digits is 1 + logn. This
does not break down for n = oo.

Regards, WM