i.e. a well-defined algorithm exists to construct Cantor dust but the Cantor dust cannot be constructed/built from the algorithm in a finite number of steps. Hence, Cantor dust represents potential infinity rather than actual infinity. This problem has nagged at me for a while. Regards, Vasili On Fri, Jan 30, 2009 at 4:40 PM, Galchin, Vasili <vigalchin@gmail.com>wrote:
I don't think it exists from a constructivist viewpoint because it has to be constructed in a finite number of steps.
Vasili
On Fri, Jan 30, 2009 at 3:52 PM, Bas Spitters <spitters@cs.ru.nl> wrote:
On Friday 30 January 2009 08:18:39 Galchin, Vasili wrote:
Here is a definition of Cantor dust .... http://en.wikipedia.org/wiki/Cantor_set.
My question is from a constructivist viewpoint does this set
really
exist and if so, why?
Yes, it exists. In fact, it is a continuous image of 2^N. It is Bishop compact, fan-like and compact overt (choose your taste of constructivism).
Bas