Re: Relative Cardinality



Jiri Lebl wrote:
> mueckenh@xxxxxxxxxxxxxxxxx wrote:
> > > I also thought of another irrational number that escapes your logic.
> > > Take the number:
> > > 0.9909000900000009000... That is the number whose digital
> > > representation has 9s in the places that are powers of 2. It is the
> > > "sum(n=0 to oo) 9*10^(-(2^n))". So then I can say what the 10^10^100's
> > > digit is, it is 0. Also the 2^100^100^100^100^100^100^100^100's digit
> > > is 9. And the next digit after that is 0. I wonder why this number
> > > doesn't exist and why it cannot be on any list.
> >
> > Interesting number. Thank you for posting this question which is one of
> > the few non-polemic questions I received. Can you say which digit is on
> > the position floor(pi*10^10^100)?
>
> 0, and it is not hard to see.

Therefore, this number does exist and can be on a list. But I have not
yet spent much time on researching which numbers can exist.

Regards, WM

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