Date: Mar 22, 2013 5:36 AM Author: fom Subject: Re: Matheology § 224 On 3/22/2013 4:05 AM, WM wrote:

> On 22 Mrz., 08:30, William Hughes <wpihug...@gmail.com> wrote:

>> On Mar 22, 7:32 am, WM <mueck...@rz.fh-augsburg.de> wrote:

>>

>>

>>

>>

>>

>>> On 21 Mrz., 16:41, William Hughes <wpihug...@gmail.com> wrote:

>>

>>>> On Mar 21, 4:11 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

>>

>>>>> On 21 Mrz., 14:29, William Hughes <wpihug...@gmail.com> wrote:

>>

>>>>>> On Mar 21, 2:11 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

>>

>>>>>>> On 21 Mrz., 14:02, William Hughes <wpihug...@gmail.com> wrote:

>>

>>>>>>>>> In fact? That's amazing. So we cannot prove that all lines of the

>>>>>>>>> infinite set of lines are unnecessary?

>>

>>>>>>>> We can prove that something is true for every

>>>>>>>> member of an infinite set. We cannot

>>>>>>>> prove that something is true for the set

>>>>>>>> itself unless the set is finite.

>>

>>>>>>> But I am not interested in the set itself. Not at all! My claim is

>>>>>>> that every member of the set of lines can be removed

>>

>>>>>> Yes, removed one at a time

>>

>>>>>>> such that no member remains

>>

>>>>>> nope, working one at a time you will not get

>>>>>> to the point that no member remains.

>>

>>>>> Induction does not need time.

>>>>> The conclusion from n on n+1, if valid, is valid for every natural at

>>>>> one instance.

>>

>>>> Yes, valid for every natural, but not valid

>>>> for the *set* of all naturals.-

>>

>>> I do not talk about this *set* when removing lines. My proof shows

>>> that every line can be removed from the list without removing any

>>> natural number from the list.

>>

>> No your proof shows that *any* *one* line can be removed from the

>> list.

>> However, you are talking about removing more

>> than one line, i,e. a *set* of lines.

>

> No, I do not speak of a set when I say one, two, or three or

> infinitely many lines. Don't confuse the set of all lines with all

> lines of the set.

>

> Do you believe that one line can be considered without considering it

> as a set,but two or more lines cannot be considered as elements of a

> set, but only as the set?

> How inconsistent!

As I recall, WM recently made some insulting

remarks concerning the need for others to

learn about set inclusions.

> And even removing no line cannot be done other than by removing the

> empty set?

>

If it is meaningful to remove something, and if it is

meaningful to say that something has been removed, and

if nothing that constitutes a something actually has been

removed, then the only thing left to have been removed must

be the one thing that actually has nothing that could be

a something.

>> If you want to

>> remove all of the lines you have to remove the set of all

>> lines that are indexed by a natural number.

>

And, this would imply that the unfindable line that

has no index does, in fact, have an index. Otherwise 'all'

does really have the usual meaning attributed to 'all'. In

turn, WM is assuming that his non-standard usage is what is

taught by everyone else's parents, teachers, etc.

> But I don't want to remove a set. When has it been prohibited to

> handle elements of a set? Where is that laid down in the axioms of

> ZFC?

At the risk of being repetitious:

As I recall, WM recently made some insulting

remarks concerning the need for others to

learn about set inclusions.