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Re: Another AC anomaly?
Posted:
Dec 16, 2009 9:42 AM
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On 16 Dez., 03:44, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote:
>
> > {1} U {1, 2} U {1, 2, 3} U ... = ({1} U {1, 2} U {1, 2, 3} U ...) U {1,
> > 2, 3, ...}
That is a matter of taste.
>
> > There is no space in the binary tree to contain infinite paths in
> > addition to the sequeneces of all finite paths.
> > The sequence 0.0, 0.00, 0.000, ... when being completely constructed,
> > is already the path 0.000...
> > You cannot add it separately.
>
> A sequence of paths is not a path.
But a union of paths is.
>
> > Therefore: When all finite paths have been constructed within aleph_0
> > steps, then all paths have been constructed.
>
> Here, again, you err. You can not construct something in aleph_0 steps; you
> will never complete your construction. You *cannot* get at aleph_0 step by
> step.
But you can make a bijection with all elements of omega?
>
> > This hold for every limit of every sequence of finite paths.
>
> A limit is not a step by step process.
Then assume it is a mapping from omega.
Regards, WM
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