Re: Cantor Confusion

In article <1164126713.968092.237570@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> mueckenh@xxxxxxxxxxxxxxxxx writes:
*** T. Winter schrieb:
> > There are infinite paths
> > in your tree, but they do not contain a node that represents (for
> > instance) 1/3. So, if the nodes represent numbers (as you have said),
>
> Do you have a reference?

Not needed. Just above you state that the nodes represent the bits 0 or
1. I have shown how you could concatenate the representation of a node
with the representations of its parent nodes to get a number.

A number consists of bits. Some numbers consist even of one bit. But
you must not mix up these terms.
A number like 1/2 consist of the bit sequence 0.1000.... That is a path
in my tree:

As an infinite bit sequence, yes, but there is *no* node in your tree
that represents that bit sequence.

> > 1/3 is not in your tree.

Of course it is, like 0.333... is in Cantor's list of decimals.

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 are not clear about what the numbers in
> > your tree are. Are they the nodes? Are they the paths? Sometimes
> > you say one thing other times you say something different. So to get
> > proper understanding. What are the things that represent numbers?
>
> Infinite paths.

I do not understand. You stated the nodes represent bits.

Yes. That's the stuff numbers are built from.

This makes it still less clear.
--
*** t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~***/
.

Quantcast