Re: Cantor Confusion


*** T. Winter schrieb:


> > No, there is *no* node in your tree that represents 1/3. Because there
> > is *no* node in your tree that represents an infinite sequence. On the
> > other hand, Cantor's diagonal proof is about infinite sequences.
>
> You do not require that one digit represents the number 1/3 in Cantor's
> list. You do not require that any digit there represents an infinite
> sequence.

Of course not.

> But you require that one digit (node) represents 1/3 in the tree?
> But you require that one digit (node) in my tree represents an
> infinite sequence?

Of course.

That is unfair.

> Are you trolling, ***?

Not at all.

> There is no node in the tree which represents 0.000... and no node
> which represents 0.1 But these real numbers are represented in the
> tree by paths.

I do not understand. You state that the bits are the nodes.

Yes. And an infinte sequence of bits is the representation of a real
number.

I have
shown how you can extend that to the nodes representing numbers.

I do no want not extend anything to nodes representing numbers. The
paths represent numbers.

And
I also have shown how the numbers represented by the nodes all have
a finite sequence of bits. There is *no* node that represents 1/3.

No. There is no digits in Cantor's list representing 1/3.

And when you switch to paths representing numbers you have something
completely different.

I did not switch to paths but defined from the beginning that the paths
represent the numbers.

Let's assign to a finite path the number of the
node where the last edge terminates.

There is no last edge, because the paths are infinite, like the decimal
representations used in Cantor's list.

Also in this case 1/3 is not in
your paths.

Then 1/3 is not in Cantor's list.

There are no numbers assigned to the non-terminating
infinite paths.

Then there are no numbers assigned to non-terminating decimal
representations.

I think you wish that the edges represent the bits,
not the nodes.

No, I do not wish that. (I could do so, but it would again confuse you.
So we it as it is.)

Regards, WM

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