Date: Mar 24, 2013 3:57 PM
Author: fom
Subject: Re: Matheology § 224

On 3/24/2013 10:30 AM, WM wrote:
> On 24 Mrz., 16:19, William Hughes <wpihug...@gmail.com> wrote:
>> On Mar 24, 4:09 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>>
>>
>>

>>> On 24 Mrz., 14:42, William Hughes <wpihug...@gmail.com> wrote:
>>
>>>> On Mar 24, 12:13 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>>
>>>>> On 24 Mrz., 11:02, William Hughes <wpihug...@gmail.com> wrote:
>>
>>>>>> On Mar 24, 10:23 am, WM <mueck...@rz.fh-augsburg.de> wrote:
>>
>>>>>>> On 23 Mrz., 23:58, William Hughes <wpihug...@gmail.com> wrote:
>>>>>>>> WH: this does not mean that one can do something
>>>>>>>> WH: that does not leave any of the lines of K
>>>>>>>> WH: and does not change the union of all lines.

>>
>>>>>>> This does not mean that one can really do so
>>
>>>>>> It does, however, mean that you have not shown
>>>>>> that one can or cannot.

>>
>>>> Have you shown that "one can or cannot".
>>
>>>> Yes or no please.
>>
>> Please answer the question.

>
> I did so. Given ZFC: one can - but in fact: one cannot.
>
> Please answer this question (the best way for our readers to
> understand the difference between pot. and act. infinity):
> What is the difference between the Binary Tree that constains only all
> finite paths and the Binary Tree that contains in addition all
> actually infinite paths?


The first does not exist.

When the lengths of the paths of a tree have a
common upper bound, the tree may be thought of
as consisting of only finite paths.

When the lengths of the paths of a tree have no
upper bound, finiteness corresponds only
with classes of paths that share a given initial
segment.