Re: Cantor and the binary tree



*** T. Winter wrote:
> In article <1116939502.814879.192170@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> mueckenh@xxxxxxxxxxxxxxxxx writes:
> > If we accept that, in binary digits, SUM{n = 1 ... oo} 2^-n = 0.111...
> > = 1
>
> You may note that that is *not* an infinite sum...

It is defined as an infinite tree.
>
> > .
> > 0 1
> > 0 1 0 1
> > ..................
> ...

> Also we find that up to line n, summing up to that node along the path
> gives a value for k/(2^n) for some integer k. Therefore a number along
> a node is always equal to a rational with a denominator that is a power
> of two. It is simply impossible to assume that one of these numbers
> becomes 1/3.

What is the difference to an infinite decimal expansion? A number
0.333... is always equal to a rational with a denominator that is a
power of ten. It is simply impossible to assume that this number
becomes 1/3. Or is there any occult advantage of the decimal system
over the binary system?

Regards, WM

.

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