Re: abundance of irrationals!)

In article <fb701d3c.0504140910.19f43d42@xxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx (W. Mueckenheim) wrote:

> "*** T. Winter" <***.Winter@xxxxxx> wrote in message
> news:<IEvuBI.Krr@xxxxxx>...
>
> >
> > Yes, they come close by every number, but the does not contain every real
> > number. The limit of a series is not necessarily in the series. One
> > omission: pi is not in the sequence.
>
>
> (Say pi/4, because only the interval (0,1) is covered.)
> Neither is pi/4 in Cantor's antidiagonal which also may come
> arbitrarily close.
>
> >
> > > > > 0.1;
> > > > > 0.10; 0.11;
> > > > > 0.001; 0.101; 0.011; 0.111;
> > > > > ...
> > > > >
> > > > > Your infinity is realised:
> > > >
> > > > We do not "realise" infinities.
>
> Cantor assumed these to be really existing "whole numbers, larger than
> any natural number".

IIRC, he called them cardinalities, and gave a careful exposition of
what a cardinality was, and equivalence class of bijectable sets.
>
>
> > > That is realised in my sequence above.
> >
> > I have no idea what you mean with this sentence.
>
> The number of digits of these numbers
> 0.1;
> 0.10; 0.11;
> 0.001; 0.101; 0.011; 0.111;
> does surpass any any fixed natural number.

But is always another natural number.
>
> Regards, WM
.