Re: Cantor and the binary tree



*** T. Winter wrote:
> In article <1117381085.891784.283560@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> mueckenh@xxxxxxxxxxxxxxxxx writes:
> > Examples.
> > Path 0,1000...is mapped on the node on level n = 0.
> > Path 0,01000... is mapped on the left node on level n = 1.
> > In this way all numbers (except 0 = 0.000...) which differ from all
> > other numbers by at least one digit are mapped on the nodes.
>
> Oh. On what node is 0,010101010... mapped? The numbers mapped on nodes
> at level n = 0 are of the form k/2, with k odd. The numbers mapped on
> nodes at level n = 1 are of the form k/4, with k odd. In general, the
> numbers mapped on the nodes of some level n are of the form k/(2^n),
> with k odd. On what level is there a node on which 1/3 is mapped?

I don't know how many bits the number 1/3 has. But if it is a number
then it has a path in my tree. And if it has a path in my tree then it
has a node to be mapped on. You must know, there are infinitely many
nodes in my tree.

Regards, WM

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