Another set with cardinality |Z|

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

  • Next message: Robert Israel: "Re: Another set with cardinality |Z|" 
    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
  • Next message: Robert Israel: "Re: Another set with cardinality |Z|"

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