Re: Two results of set geometry

On Oct 5, 1:04 pm, Tony Orlow <t...@xxxxxxxxxxxxx> wrote:
William Hughes wrote:
On Oct 4, 11:44 am, Tony Orlow <t...@xxxxxxxxxxxxx> wrote:
William Hughes wrote:
On Oct 3, 11:10 am, Tony Orlow <t...@xxxxxxxxxxxxx> wrote:
William Hughes wrote:
On Sep 29, 11:00 am, Tony Orlow <t...@xxxxxxxxxxxxx> wrote:
Fine. The rationals are an actually infinite number, and as long as all
bit positions are finite, that's ultimately all you have anyway. I'm not
saying that's all there is, but I am saying that's all that lies within
the "infinite" tree.
So from the fact that .1010010001... is in the infinite tree
we conclude that not only are all the initial segments of .
1010010001...
rational but so is .1010010001...
- William Hughes
That is not a fact, but an assumption. All of that string does not exist
in a tree with only finite bit positions.
The string .1010010001... does exist is the
tree. This follows directly from the definition of when
a string is in the tree.
Spare me the "There is no node of the tree
at which .101001001... exists". This is true,
but does not show that .1010010001... is not in the tree.
- William Hughes
It shows that it is never completely contained in the tree,

The statement was

"does not show that .1010010001... is not in the tree"

The definition of when .1010010001... is in the tree
has nothing to do with "completely contained in the tree"
(whatever that means).

And when the balls are in the vase, they are npot completely contained
in the container. Is it kind of like when you're in your car, but are
hanging your arm out the window? Are there bits out there beyond the
extent of the tree?

Nope. Any bits beyond the extent of the tree would have
to be past the last level of the tree. Guess what?
As usual you have some vague idea about what
"completely" means that has to do with the "last"
something. The definition has nothing to do with
a last something.





if every
node is at a finite position, and therefore leaves a finite difference
between the path and the infinite string. I could "spare" you, but if
there does not exist a node in the tree where that value is reached,
then that value is not reached within the tree.

The statement was

"does not show that .1010010001... is not in the tree"

The definition of when .1010010001... is in the tree
has nothing to do with a value being "reached within the tree".

So, if a part of it is in the tree, then it is in the tree?

Nope, that is not the definition of "is in the tree"
If a sting is in the tree then every part of it is in the tree.
(do not try to change "every part of it is the tree" to
"is completely in the tree" without defining what you
mean by "is completely in the tree")
but this has nothing to do with a value
"being reached within the tree".

- William Hughes

.

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