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From: Moebius <invalid@example.invalid>
Newsgroups: sci.math
Subject: Re: hot to write out this summation:
Date: Mon, 1 Jul 2024 20:10:42 +0200
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Am 01.07.2024 um 19:54 schrieb Chris M. Thomasson:
> On 7/1/2024 10:12 AM, Moebius wrote:

> I was just thinking that each iterate of the .(0)(1) is a real number... 

Ok, you really make me laugh, sorry.

The point is that you are using an _undefined_ expression here.

It's like claiming [in the context of the real numbers] that 1/x tends 
to 1/0 as x tends to 0, or something like that.

I other words, there IS NO "iterate of the .(0)(1)" as there is no 
(referent of) ".(0)(1)". At least not in my book. :-P

You already wrote down what you meant:

r[0] = .01
r[1] = .0011
r[2] = .000111
r[3] = .00001111
....

Why not use the expression ".0...01...1" as a general "term" für your 
r's? Ok, we do not see that the number of "0"s is always identical with 
the numbers of "1" here.

Maybe a little diagram might be helpful:

.. 0 ... 0 1 ... 1
   ------- -------
   n-times n-times

Starting with the index 1 we might (alternatively) state:

s[1] = .01
s[2] = .0011
r[3] = .000111
s[4] = .00001111
....

Then we'd have:

s[n] = . 0 ... 0 1 ... 1
          ------- -------
          n-times n-times

(for n = 1, 2, 3, ...).