Re: Another set with cardinality |Z|

From: Robert Low (mtx014_at_linux.services.coventry.ac.uk)
Date: 09/23/04 

Date: 23 Sep 2004 08:20:57 GMT

Eray Ozkural exa <erayo@bilkent.edu.tr> wrote:
>Let's have an algorithm that starts with
>0.1 in binary, and constructs a tree in breadth-first fashion
>
> 0.1
> 0.01 0.11
>0.001 0.011....
>
>You get the idea... It's obvious that this tree has the same
>cardinality as Z, since this is a nonhalting algorithm (or since I can
>give an integer to every node, etc.) Now, I want to prove that such a
>subdivision procedure cannot generate all x in (0,1) in an intuitive
>way.

You only get terminating expansions from this algorithm, and most
of the numbers in (0,1) aren't of that form. 

-- 
Rob.  http://www.mis.coventry.ac.uk/~mtx014/

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