Re: abundance of irrationals!)

"*** 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".


> > 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.

Regards, WM
.