Another set with cardinality |Z|

From: Eray Ozkural exa (erayo_at_bilkent.edu.tr)
Date: 09/23/04 

Date: 22 Sep 2004 19:23:35 -0700

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. Is the easiest method proof by contradiction?

Regards, 

--
Eray Ozkural

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