On 4/28/2022 9:29 AM, David Petry wrote:
> On Thursday, April 21, 2022 at 5:03:43 AM UTC-7, WM wrote:
>> zelos...@gmail.com schrieb am Donnerstag, 21. April 2022 um 12:34:25 UTC+2:
>>> Hey WM, let's start fresh. You keep claiming there are such things as "dark numbers"
>>>
>>> Define it in in terms of FOL and then prove that there exists two disjoint non-empty sets that has the union of natural numbers, where one set is your supposed claimed "dark" and the other is not, undark?
>> This task is more difficult than the proof that there are dark fractions. If you have understood that it is impossible to enumerate all fractions, because starting from
>>
>> 1/1, 1/2, 1/3, 1/4, ...
>> 2/1, 2/2, 2/3, 2/4, ...
>> 3/1, 3/2, 3/3, 3/4, ...
>> 4/1, 4/2, 4/3, 4/4, ...
>> 5/1, 5/2, 5/3, 5/4, ...
>> ...
>>
>> every attempt to collect all fractions in the first column will fail:
>>
>> 1/1, 2/1, 1/3, 1/4, ... 1/1, 3/1, 1/3, 1/4, ... 1/1, 3/1, 4/1, 1/4, ... 1/1, 3/1, 4/1, 1/4, ...
>> 1/2, 2/2, 2/3, 2/4, ... 1/2, 2/2, 2/3, 2/4, ... 1/2, 2/2, 2/3, 2/4, ... 1/2, 5/1, 2/3, 2/4, ...
>> 3/1, 3/2, 3/3, 3/4, ... 2/1, 3/2, 3/3, 3/4, ... 2/1, 3/2, 3/3, 3/4, ... 2/1, 3/2, 3/3, 3/4, ...
>> 4/1, 4/2, 4/3, 4/4, ... 4/1, 4/2, 4/3, 4/4, ... 1/3, 4/2, 4/3, 4/4, ... 1/3, 4/2, 4/3, 4/4, ...
>> 5/1, 5/2, 5/3, 5/4, ... 5/1, 5/2, 5/3, 5/4, ... 5/1, 5/2, 5/3, 5/4, ... 2/2, 5/2, 5/3, 5/4, ...
>> ... ... ... ...
>>
>> When all definable fractions of Cantor's sequence 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ... will have transferred into the first column, nevertheless all matrix places remain occupied by fractions which are undefinable, because all definable fractions have gone.
>>
>> If you have understood this, then we can proceed to understand, that even most places in the first column, all of which have been occupied by integer fractions or natural numbers, are undefinable too.
>>> No, your proof of
>>> An e N: n e [0,n]=F_n
>>> Aka, "all natural is in in a finite set" is instantly invalid as that applies to all natural numbers, thus one set is non-empty.
>> By induction we prove that every definable natural number, i.e., every natural number which is subject to induction, belongs to a finite set F_n but has ℵo successors which cannot be removed whatever n you consider. That means they cannot be used as individuals.
>>
>> Regards, WM
>
>
> The argument that I like to make is that mathematics has an important purpose, which is to provide a conceptual framework that facilitates reasoning about the real world (i.e. mathematics is the language of science). And Cantor's theory of infinite sets is simply irrelevant to that important purpose.

No, During his life Georg Cantor proved several concepts in mathematics that other mathematicians ahead of him were unable to prove. Cantor was
encouraged by his friend at Halle who was working on trigonometric series to work on the uniqueness of infinite series. In 1873 he was able to prove
that rational numbers are countable, he added that algebraic numbers that are roots, squares and square roots of polynomial equation with integer
coefficients are countable (Dauben, pp. 23-78). He published his first paper on theory of sets in 1874 where he proved that the set of integers had an
equal number of members.

He also came up with the argument that real numbers are not countable which he proved, he said that transcendental numbers are irrational numbers that
are not root, square or square root of any polynomial equation having integer coefficients (Ruker, pp. 27-79). Georg was able to show that the interval
between zero and one is uncountable. He is the only mathematician who was able to show that almost all numbers are transcendental by proving that real
numbers are not countable while proving that algebraic numbers were countable, he also showed that the set of all subsets of a given set are larger than
the original set. The introduction of the concept of the first derived set was his initiative (Dauben, pp. 23-78). Cantor also showed that union of two
countable sets should also be countable and brought across the existence of uncountable numbers.

Georg Cantor was the first person to discuss the continuum hypothesis which states that there exists a set of numbers whose power is greater than that
of the naturals and less than that of real, he tried it but all was in vain as he was able to prove and disprove it. Golden and Paul Cohen in 1963 said
that the hypothesis can be proved or disproved (Ruker, pp. 27-79).

>
> What I'm wondering is, how is your (Mueckenheim) argument relevant to the very important purpose of mathematics? Perhaps more importantly, why should people care about your argument? What's the point?

WM's pointless non mathematical post is to make himself feel important.

>
> Need I remind you that any theory of infinity is a fiction? Why is your fiction more important than Cantor's?

You write fiction too, finitely.

>
>
>
>

On 4/28/2022 8:45 AM, WM wrote:
> Jim Burns schrieb
> am Dienstag, 26. April 2022 um 19:51:50 UTC+2:
>> On 4/26/2022 7:10 AM, WM wrote:

>>> So it is. 1/1, 2/1, 3/1, ...
>>> By values this is same as 1, 2, 3, ...
>
>>> It is the set of indices.
>>
>> You haven't described an infinite sequence.
>> You've only given a name, "indices", as though
>> that name is the answer to the question.
>
> Liar.

'...' is not a description.

This is a description:
| | In discussion A, each collection
| is empty or contains a first element.
| | In discussion B, each _bounded-in-B_ collection
| is empty or contains a first _and a last_ element.
| | _omega_ is defined to be the first thing in
| discussion A which is not in discussion B.

But '...' is not a description.
'...' is _at best_ a way to say
"You don't need to be told the description here".

At best.
'...' can also be used to avoid giving a description.
That's the way you (wM) use "..."

> I have described the first column of the matrix:
>
> 1/1, 1/2, 1/3, 1/4, ...
> 2/1, 2/2, 2/3, 2/4, ...
> 3/1, 3/2, 3/3, 3/4, ...
> 4/1, 4/2, 4/3, 4/4, ...
> 5/1, 5/2, 5/3, 5/4, ...
> ...

No, you haven't.
'...' is not a description.

torsdag 28 april 2022 kl. 16:29:42 UTC+2 skrev david...@gmail.com:
> On Thursday, April 21, 2022 at 5:03:43 AM UTC-7, WM wrote:
> > zelos...@gmail.com schrieb am Donnerstag, 21. April 2022 um 12:34:25 UTC+2:
> > > Hey WM, let's start fresh. You keep claiming there are such things as "dark numbers"
> > >
> > > Define it in in terms of FOL and then prove that there exists two disjoint non-empty sets that has the union of natural numbers, where one set is your supposed claimed "dark" and the other is not, undark?
> > This task is more difficult than the proof that there are dark fractions. If you have understood that it is impossible to enumerate all fractions, because starting from
> >
> > 1/1, 1/2, 1/3, 1/4, ...
> > 2/1, 2/2, 2/3, 2/4, ...
> > 3/1, 3/2, 3/3, 3/4, ...
> > 4/1, 4/2, 4/3, 4/4, ...
> > 5/1, 5/2, 5/3, 5/4, ...
> > ...
> >
> > every attempt to collect all fractions in the first column will fail:
> >
> > 1/1, 2/1, 1/3, 1/4, ... 1/1, 3/1, 1/3, 1/4, ... 1/1, 3/1, 4/1, 1/4, ... 1/1, 3/1, 4/1, 1/4, ...
> > 1/2, 2/2, 2/3, 2/4, ... 1/2, 2/2, 2/3, 2/4, ... 1/2, 2/2, 2/3, 2/4, ... 1/2, 5/1, 2/3, 2/4, ...
> > 3/1, 3/2, 3/3, 3/4, ... 2/1, 3/2, 3/3, 3/4, ... 2/1, 3/2, 3/3, 3/4, ... 2/1, 3/2, 3/3, 3/4, ...
> > 4/1, 4/2, 4/3, 4/4, ... 4/1, 4/2, 4/3, 4/4, ... 1/3, 4/2, 4/3, 4/4, ... 1/3, 4/2, 4/3, 4/4, ...
> > 5/1, 5/2, 5/3, 5/4, ... 5/1, 5/2, 5/3, 5/4, ... 5/1, 5/2, 5/3, 5/4, ... 2/2, 5/2, 5/3, 5/4, ...
> > ... ... ... ...
> >
> > When all definable fractions of Cantor's sequence 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ... will have transferred into the first column, nevertheless all matrix places remain occupied by fractions which are undefinable, because all definable fractions have gone.
> >
> > If you have understood this, then we can proceed to understand, that even most places in the first column, all of which have been occupied by integer fractions or natural numbers, are undefinable too.
> > > No, your proof of
> > > An e N: n e [0,n]=F_n
> > > Aka, "all natural is in in a finite set" is instantly invalid as that applies to all natural numbers, thus one set is non-empty.
> > By induction we prove that every definable natural number, i.e., every natural number which is subject to induction, belongs to a finite set F_n but has ℵo successors which cannot be removed whatever n you consider. That means they cannot be used as individuals.
> >
> > Regards, WM
>
>
> The argument that I like to make is that mathematics has an important purpose, which is to provide a conceptual framework that facilitates reasoning about the real world (i.e. mathematics is the language of science). And Cantor's theory of infinite sets is simply irrelevant to that important purpose.
>
> What I'm wondering is, how is your (Mueckenheim) argument relevant to the very important purpose of mathematics? Perhaps more importantly, why should people care about your argument? What's the point?
>
> Need I remind you that any theory of infinity is a fiction? Why is your fiction more important than Cantor's?
You are however wrong, now GTFO

FromTheRafters schrieb am Donnerstag, 28. April 2022 um 17:20:19 UTC+2:
> WM formulated on Thursday :
> > FromTheRafters schrieb am Dienstag, 26. April 2022 um 22:05:48 UTC+2:
> >
> >> Then yes, it sort of describes WM's matrix's dimensions and that the
> >> cardinality of a single row or column can be the same as the
> >> cardinality of the whole thing. It is exactly this which he denies
> >> because it
> >
> > it can be disproved by the fact that every permutation of the X's fails to
> > cover the whole matrix
> >
> > XOOO...
> > XOOO...
> > XOOO...
> > XOOO...
> > ...
> How many permutations are there for an infinite set? Are you sure you
> have covered them all?

I am sure that none will change the sets of O's and X's. That is all I need.

Regards, WM

david...@gmail.com schrieb am Donnerstag, 28. April 2022 um 16:29:42 UTC+2:
> On Thursday, April 21, 2022 at 5:03:43 AM UTC-7, WM wrote:
> > zelos...@gmail.com schrieb am Donnerstag, 21. April 2022 um 12:34:25 UTC+2:
> > > Hey WM, let's start fresh. You keep claiming there are such things as "dark numbers"
> > >
> > > Define it in in terms of FOL and then prove that there exists two disjoint non-empty sets that has the union of natural numbers, where one set is your supposed claimed "dark" and the other is not, undark?
> > This task is more difficult than the proof that there are dark fractions. If you have understood that it is impossible to enumerate all fractions, because starting from
> >
> > 1/1, 1/2, 1/3, 1/4, ...
> > 2/1, 2/2, 2/3, 2/4, ...
> > 3/1, 3/2, 3/3, 3/4, ...
> > 4/1, 4/2, 4/3, 4/4, ...
> > 5/1, 5/2, 5/3, 5/4, ...
> > ...
> >
> > every attempt to collect all fractions in the first column will fail:
> >
> > 1/1, 2/1, 1/3, 1/4, ... 1/1, 3/1, 1/3, 1/4, ... 1/1, 3/1, 4/1, 1/4, ... 1/1, 3/1, 4/1, 1/4, ...
> > 1/2, 2/2, 2/3, 2/4, ... 1/2, 2/2, 2/3, 2/4, ... 1/2, 2/2, 2/3, 2/4, ... 1/2, 5/1, 2/3, 2/4, ...
> > 3/1, 3/2, 3/3, 3/4, ... 2/1, 3/2, 3/3, 3/4, ... 2/1, 3/2, 3/3, 3/4, ... 2/1, 3/2, 3/3, 3/4, ...
> > 4/1, 4/2, 4/3, 4/4, ... 4/1, 4/2, 4/3, 4/4, ... 1/3, 4/2, 4/3, 4/4, ... 1/3, 4/2, 4/3, 4/4, ...
> > 5/1, 5/2, 5/3, 5/4, ... 5/1, 5/2, 5/3, 5/4, ... 5/1, 5/2, 5/3, 5/4, ... 2/2, 5/2, 5/3, 5/4, ...
> > ... ... ... ...
> >
> > When all definable fractions of Cantor's sequence 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ... will have transferred into the first column, nevertheless all matrix places remain occupied by fractions which are undefinable, because all definable fractions have gone.
> >
> > If you have understood this, then we can proceed to understand, that even most places in the first column, all of which have been occupied by integer fractions or natural numbers, are undefinable too.
> > > No, your proof of
> > > An e N: n e [0,n]=F_n
> > > Aka, "all natural is in in a finite set" is instantly invalid as that applies to all natural numbers, thus one set is non-empty.
> > By induction we prove that every definable natural number, i.e., every natural number which is subject to induction, belongs to a finite set F_n but has ℵo successors which cannot be removed whatever n you consider. That means they cannot be used as individuals.
>
> The argument that I like to make is that mathematics has an important purpose, which is to provide a conceptual framework that facilitates reasoning about the real world (i.e. mathematics is the language of science). And Cantor's theory of infinite sets is simply irrelevant to that important purpose.
>
> What I'm wondering is, how is your (Mueckenheim) argument relevant to the very important purpose of mathematics? Perhaps more importantly, why should people care about your argument? What's the point?

The point is to show that Cantor's theory is ninsense and should be dropped..
>
> Need I remind you that any theory of infinity is a fiction? Why is your fiction more important than Cantor's?

I am not improving mathematics. That would go beyond my power. I am only proving, that Cantor's countability and uncountability are ill concepts.

Regards, WM

Jim Burns schrieb am Freitag, 29. April 2022 um 04:16:56 UTC+2:
> On 4/28/2022 8:45 AM, WM wrote:

> '...' is not a description.

1/1, 2/1, 3/1, ...

is a description.
>

> > I have described the first column of the matrix:
> >
> > 1/1, 1/2, 1/3, 1/4, ...
> > 2/1, 2/2, 2/3, 2/4, ...
> > 3/1, 3/2, 3/3, 3/4, ...
> > 4/1, 4/2, 4/3, 4/4, ...
> > 5/1, 5/2, 5/3, 5/4, ...
> > ...
> No, you haven't.
> '...' is not a description.

Liar. As anybody if he knows the next terms.

Regards, WM

WM has brought this to us :
> Jim Burns schrieb am Freitag, 29. April 2022 um 04:16:56 UTC+2:
>> On 4/28/2022 8:45 AM, WM wrote:
>
>> '...' is not a description.
>
> 1/1, 2/1, 3/1, ...
>
> is a description.
>>
>
>>> I have described the first column of the matrix:
>>>
>>> 1/1, 1/2, 1/3, 1/4, ...
>>> 2/1, 2/2, 2/3, 2/4, ...
>>> 3/1, 3/2, 3/3, 3/4, ...
>>> 4/1, 4/2, 4/3, 4/4, ...
>>> 5/1, 5/2, 5/3, 5/4, ...
>>> ...
>> No, you haven't.
>> '...' is not a description.
>
> Liar. As anybody if he knows the next terms.

That's easy because each row is countable and each column is countable
and they exhibit an easy to follow pattern.

On 4/29/2022 12:07 PM, FromTheRafters wrote:
> WM has brought this to us :
>> Jim Burns schrieb
>> am Freitag, 29. April 2022 um 04:16:56 UTC+2:

>>> '...' is not a description.
>>
>> 1/1, 2/1, 3/1, ...
>> is a description.
>>
>>>> I have described the first column of the matrix:
>>>> 1/1, 1/2, 1/3, 1/4, ...
>>>> 2/1, 2/2, 2/3, 2/4, ...
>>>> 3/1, 3/2, 3/3, 3/4, ...
>>>> 4/1, 4/2, 4/3, 4/4, ...
>>>> 5/1, 5/2, 5/3, 5/4, ...
>>>> ...
>>>
>>> No, you haven't. '...' is not a description.
>>
>> Liar. As anybody if he knows the next terms.
>
> That's easy because
> each row is countable and each column is countable
> and they exhibit an easy to follow pattern.

Yes.
Everyone knows the next terms, but
knowing the next terms is not having a description.

WM deletes my description.
Not-having a description is clearly central to
his "argument" == bait-and-switch.

This is a description:
| | In discussion A, each collection
| is empty or contains a first element.
| | In discussion B, each _bounded-in-B_ collection
| is empty or contains a first _and a last_ element.
| | _omega_ is defined to be the first thing in
| discussion A which is not in discussion B.

Discussion B is of the natural numbers.
Discussion A is of the finite and transfinite ordinals.

Jim Burns schrieb am Freitag, 29. April 2022 um 19:38:47 UTC+2:
> On 4/29/2022 12:07 PM, FromTheRafters wrote:
> > WM has brought this to us :
> >> Jim Burns schrieb
> >> am Freitag, 29. April 2022 um 04:16:56 UTC+2:
> >>> '...' is not a description.
> >>
> >> 1/1, 2/1, 3/1, ...
> >> is a description.
> >>
> >>>> I have described the first column of the matrix:
> >>>> 1/1, 1/2, 1/3, 1/4, ...
> >>>> 2/1, 2/2, 2/3, 2/4, ...
> >>>> 3/1, 3/2, 3/3, 3/4, ...
> >>>> 4/1, 4/2, 4/3, 4/4, ...
> >>>> 5/1, 5/2, 5/3, 5/4, ...
> >>>> ...
> >>>
> >>> No, you haven't. '...' is not a description.
> >>
> >> Liar. Ask anybody if he knows the next terms.
> >
> > That's easy because
> > each row is countable and each column is countable
> > and they exhibit an easy to follow pattern.
> Yes.
> Everyone knows the next terms, but
> knowing the next terms is not having a description.

Wrong. You try to blur the discussion by nonensical words.

Regards, WM

On 4/29/2022 3:25 PM, WM wrote:
> Jim Burns schrieb am Freitag, 29. April 2022 um 19:38:47 UTC+2:
>> On 4/29/2022 12:07 PM, FromTheRafters wrote:
>>> WM has brought this to us :
>>>> Jim Burns schrieb
>>>> am Freitag, 29. April 2022 um 04:16:56 UTC+2:
>>>>> '...' is not a description.
>>>>
>>>> 1/1, 2/1, 3/1, ...
>>>> is a description.
>>>>
>>>>>> I have described the first column of the matrix:
>>>>>> 1/1, 1/2, 1/3, 1/4, ...
>>>>>> 2/1, 2/2, 2/3, 2/4, ...
>>>>>> 3/1, 3/2, 3/3, 3/4, ...
>>>>>> 4/1, 4/2, 4/3, 4/4, ...
>>>>>> 5/1, 5/2, 5/3, 5/4, ...
>>>>>> ...
>>>>>
>>>>> No, you haven't. '...' is not a description.
>>>>
>>>> Liar. Ask anybody if he knows the next terms.
>>>
>>> That's easy because
>>> each row is countable and each column is countable
>>> and they exhibit an easy to follow pattern.
>> Yes.
>> Everyone knows the next terms, but
>> knowing the next terms is not having a description.
>
> Wrong. You try to blur the discussion by nonensical words.

I am sure he did not intentionally step into your area of expertise.

>
> Regards, WM

On 4/29/2022 4:25 PM, WM wrote:
> Jim Burns schrieb
> am Freitag, 29. April 2022 um 19:38:47 UTC+2:
>> On 4/29/2022 12:07 PM, FromTheRafters wrote:
>>> WM has brought this to us :
>>>> Jim Burns schrieb
>>>> am Freitag, 29. April 2022 um 04:16:56 UTC+2:

>>>>>> I have described the first column of the matrix:
>>>>>> 1/1, 1/2, 1/3, 1/4, ...
>>>>>> 2/1, 2/2, 2/3, 2/4, ...
>>>>>> 3/1, 3/2, 3/3, 3/4, ...
>>>>>> 4/1, 4/2, 4/3, 4/4, ...
>>>>>> 5/1, 5/2, 5/3, 5/4, ...
>>>>>> ...
>>>>>
>>>>> No, you haven't. '...' is not a description.
>>>>
>>>> Liar. Ask anybody if he knows the next terms.
>>>
>>> That's easy because
>>> each row is countable and each column is countable
>>> and they exhibit an easy to follow pattern.
>>
>> Yes.
>> Everyone knows the next terms, but
>> knowing the next terms is not having a description.
>
> Wrong.
> You try to blur the discussion by nonensical words.

Ask.

In discussion A, each collection
is empty or contains a first element.

In discussion B, each _bounded-in-B_ collection
is empty or contains a first _and a last_ element.

_omega_ is defined to be the first thing in
discussion A which is not in discussion B.

B is the discussion of the natural numbers.
A is the discussion of the finite and transfinite ordinals.

WM brought next idea :
> Jim Burns schrieb am Freitag, 29. April 2022 um 19:38:47 UTC+2:
>> On 4/29/2022 12:07 PM, FromTheRafters wrote:
>>> WM has brought this to us :
>>>> Jim Burns schrieb
>>>> am Freitag, 29. April 2022 um 04:16:56 UTC+2:
>>>>> '...' is not a description.
>>>>
>>>> 1/1, 2/1, 3/1, ...
>>>> is a description.
>>>>
>>>>>> I have described the first column of the matrix:
>>>>>> 1/1, 1/2, 1/3, 1/4, ...
>>>>>> 2/1, 2/2, 2/3, 2/4, ...
>>>>>> 3/1, 3/2, 3/3, 3/4, ...
>>>>>> 4/1, 4/2, 4/3, 4/4, ...
>>>>>> 5/1, 5/2, 5/3, 5/4, ...
>>>>>> ...
>>>>>
>>>>> No, you haven't. '...' is not a description.
>>>>
>>>> Liar. Ask anybody if he knows the next terms.
>>>
>>> That's easy because
>>> each row is countable and each column is countable
>>> and they exhibit an easy to follow pattern.
>> Yes.
>> Everyone knows the next terms, but
>> knowing the next terms is not having a description.
>
> Wrong. You try to blur the discussion by nonensical words.

Slogging through some thick irony here, but it all makes ense.

fredag 29 april 2022 kl. 14:41:13 UTC+2 skrev WM:
> david...@gmail.com schrieb am Donnerstag, 28. April 2022 um 16:29:42 UTC+2:
> > On Thursday, April 21, 2022 at 5:03:43 AM UTC-7, WM wrote:
> > > zelos...@gmail.com schrieb am Donnerstag, 21. April 2022 um 12:34:25 UTC+2:
> > > > Hey WM, let's start fresh. You keep claiming there are such things as "dark numbers"
> > > >
> > > > Define it in in terms of FOL and then prove that there exists two disjoint non-empty sets that has the union of natural numbers, where one set is your supposed claimed "dark" and the other is not, undark?
> > > This task is more difficult than the proof that there are dark fractions. If you have understood that it is impossible to enumerate all fractions, because starting from
> > >
> > > 1/1, 1/2, 1/3, 1/4, ...
> > > 2/1, 2/2, 2/3, 2/4, ...
> > > 3/1, 3/2, 3/3, 3/4, ...
> > > 4/1, 4/2, 4/3, 4/4, ...
> > > 5/1, 5/2, 5/3, 5/4, ...
> > > ...
> > >
> > > every attempt to collect all fractions in the first column will fail:
> > >
> > > 1/1, 2/1, 1/3, 1/4, ... 1/1, 3/1, 1/3, 1/4, ... 1/1, 3/1, 4/1, 1/4, .... 1/1, 3/1, 4/1, 1/4, ...
> > > 1/2, 2/2, 2/3, 2/4, ... 1/2, 2/2, 2/3, 2/4, ... 1/2, 2/2, 2/3, 2/4, .... 1/2, 5/1, 2/3, 2/4, ...
> > > 3/1, 3/2, 3/3, 3/4, ... 2/1, 3/2, 3/3, 3/4, ... 2/1, 3/2, 3/3, 3/4, .... 2/1, 3/2, 3/3, 3/4, ...
> > > 4/1, 4/2, 4/3, 4/4, ... 4/1, 4/2, 4/3, 4/4, ... 1/3, 4/2, 4/3, 4/4, .... 1/3, 4/2, 4/3, 4/4, ...
> > > 5/1, 5/2, 5/3, 5/4, ... 5/1, 5/2, 5/3, 5/4, ... 5/1, 5/2, 5/3, 5/4, .... 2/2, 5/2, 5/3, 5/4, ...
> > > ... ... ... ...
> > >
> > > When all definable fractions of Cantor's sequence 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ... will have transferred into the first column, nevertheless all matrix places remain occupied by fractions which are undefinable, because all definable fractions have gone.
> > >
> > > If you have understood this, then we can proceed to understand, that even most places in the first column, all of which have been occupied by integer fractions or natural numbers, are undefinable too.
> > > > No, your proof of
> > > > An e N: n e [0,n]=F_n
> > > > Aka, "all natural is in in a finite set" is instantly invalid as that applies to all natural numbers, thus one set is non-empty.
> > > By induction we prove that every definable natural number, i.e., every natural number which is subject to induction, belongs to a finite set F_n but has ℵo successors which cannot be removed whatever n you consider. That means they cannot be used as individuals.
> >
> > The argument that I like to make is that mathematics has an important purpose, which is to provide a conceptual framework that facilitates reasoning about the real world (i.e. mathematics is the language of science). And Cantor's theory of infinite sets is simply irrelevant to that important purpose.
> >
> > What I'm wondering is, how is your (Mueckenheim) argument relevant to the very important purpose of mathematics? Perhaps more importantly, why should people care about your argument? What's the point?
> The point is to show that Cantor's theory is ninsense and should be dropped.

All you manage ot show is that you are an idiot.

> >
> > Need I remind you that any theory of infinity is a fiction? Why is your fiction more important than Cantor's?
> I am not improving mathematics. That would go beyond my power. I am only proving, that Cantor's countability and uncountability are ill concepts.
>
> Regards, WM

Those concepts work very fine, the issue is you are an idiot

On Sunday, 1 May 2022 at 12:11:27 UTC-3, zelos...@gmail.com wrote:
> fredag 29 april 2022 kl. 14:41:13 UTC+2 skrev WM:

> > I am not improving mathematics. That would go beyond my power. I am only proving, that [...]

Proving *anything* goes well beyond your powers (other than that you are an idiot, at which you are very good).

On 4/29/2022 7:41 AM, WM wrote:
> david...@gmail.com schrieb am Donnerstag, 28. April 2022 um 16:29:42 UTC+2:

>
> I am not improving mathematics. That would go beyond my power.

totally agree, in fact you are trying to destroy vast areas of math with your Dark Army.

> I am only proving, that Cantor's countability and uncountability are ill concepts.

so where is your proof ? and what type of proof is it ?

https://en.wikipedia.org/wiki/Mathematical_proof

>
> Regards, WM

On Thursday, April 21, 2022 at 3:34:25 AM UTC-7, zelos...@gmail.com wrote:
> Hey WM, let's start fresh. You keep claiming there are such things as "dark numbers"
>

They are below the finite.

tisdag 3 maj 2022 kl. 23:57:45 UTC+2 skrev mitchr...@gmail.com:
> On Thursday, April 21, 2022 at 3:34:25 AM UTC-7, zelos...@gmail.com wrote:
> > Hey WM, let's start fresh. You keep claiming there are such things as "dark numbers"
> >
> They are below the finite.
Stay out of this, you are too stupid to understand even basic negatives

onsdag 4 maj 2022 kl. 06:55:07 UTC+2 skrev zelos...@gmail.com:
> tisdag 3 maj 2022 kl. 23:57:45 UTC+2 skrev mitchr...@gmail.com:
> > On Thursday, April 21, 2022 at 3:34:25 AM UTC-7, zelos...@gmail.com wrote:
> > > Hey WM, let's start fresh. You keep claiming there are such things as "dark numbers"
> > >
> > They are below the finite.
> Stay out of this, you are too stupid to understand even basic negatives
Notice WM, how you failed defining your "dark numbers"

zelos...@gmail.com schrieb am Montag, 9. Mai 2022 um 06:53:40 UTC+2:

> Notice WM, how you failed defining your "dark numbers"

No, you have failed to understand. That's a difference.

1/1, 1/2, 1/3, 1/4, ...
2/1, 2/2, 2/3, 2/4, ...
3/1, 3/2, 3/3, 3/4, ...
4/1, 4/2, 4/3, 4/4, ...
5/1, 5/2, 5/3, 5/4, ...
....

Every attempt to collect all fractions in the first column of this matrix will fail. But all definable fractions of Cantor's sequence
1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...
will be transferred into the first column. Nevertheless all matrix places remain occupied by fractions which are undefinable, because all definable fractions have gone. That means dark.

Regards, WM

On Monday, 9 May 2022 at 09:58:49 UTC-3, WM wrote:
[...]
> No, you have failed to understand. That's a difference.
> 1/1, 1/2, 1/3, 1/4, ...
> 2/1, 2/2, 2/3, 2/4, ...
> 3/1, 3/2, 3/3, 3/4, ...
> 4/1, 4/2, 4/3, 4/4, ...
> 5/1, 5/2, 5/3, 5/4, ...
> ...
> Every attempt to collect all fractions in the first column of this matrix will fail.

That brain-dead garbage again? Please take your dump elsewhere.

On 5/9/2022 7:58 AM, WM wrote:
> zelos...@gmail.com schrieb am Montag, 9. Mai 2022 um 06:53:40 UTC+2:
>
>> Notice WM, how you failed defining your "dark numbers"
>
> No, you have failed to understand. That's a difference.
>
> 1/1, 1/2, 1/3, 1/4, ...
> 2/1, 2/2, 2/3, 2/4, ...
> 3/1, 3/2, 3/3, 3/4, ...
> 4/1, 4/2, 4/3, 4/4, ...
> 5/1, 5/2, 5/3, 5/4, ...
> ...
>

OK, a matrix of the rationals

> Every attempt to collect all fractions in the first column of this matrix will fail.

Wrong on 2 counts.

Mistake 1. Overwrite the first column, you destroy the matrix of rationals, just write out a new sequence as its own set.
Mistake 2. You say you fail doing this.

remember you are only doing a simple re-indexing.

Google "Cantor's Enumeration" for further help and guidance.

> But all definable fractions of Cantor's sequence
> 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...

no need for "definable", your failed daffynitions of "defined,definable" are the silly sand your math is based upon, and floundering.

you leave no room for you to be correct.

> will be transferred into the first column.

that is the wrong way to do it, so you fail again. no need to transfer, "swapparoobees" that is diversion.

> Nevertheless all matrix places remain occupied by fractions which are undefinable, because all definable fractions have gone. That means dark.

wrong, your math degenerates on its own.

>
> Regards, WM

Use equations and math to prove your dark ones exist, can you do that ?

On 4/21/2022 7:05 AM, WM wrote:
> horand....@gmail.com schrieb am Donnerstag, 21. April 2022 um 13:22:54 UTC+2:
>
>> A number is called "instantiated" if it has been used by someone, somewhere.
>
> A number is called instantiatable if it can be instantiated.

A Post is called Bullshit if it has bullshit in it.

>By induction

where is your induction ?

> we prove

no, you have never proved anything.

that every instantiatable

what does that mean, you make them magically appear ?

> natural number, i.e., every natural number which is subject to induction

which is all of N

>, belongs to a finite set F_n

no. infinite cannot fit in finite. Go get a bucket, and put it under the tap for 12 hours and report back.

>but has ℵo successors which cannot be removed

you need the removal squad to do that

> whatever n you consider. That means they cannot be instantiated

hocus pocus, you a circus dude! make that rabbit appear !

>or used as individuals.

no one wants "Used individuals", that is sick, dude.

>
> Regards, WM

måndag 9 maj 2022 kl. 14:58:49 UTC+2 skrev WM:
> zelos...@gmail.com schrieb am Montag, 9. Mai 2022 um 06:53:40 UTC+2:
>
> > Notice WM, how you failed defining your "dark numbers"
> No, you have failed to understand. That's a difference.

You are the one failing to define it.

> 1/1, 1/2, 1/3, 1/4, ...
> 2/1, 2/2, 2/3, 2/4, ...
> 3/1, 3/2, 3/3, 3/4, ...
> 4/1, 4/2, 4/3, 4/4, ...
> 5/1, 5/2, 5/3, 5/4, ...
> ...
> Every attempt to collect all fractions in the first column of this matrix will fail.

No one is "collecting" them in the first column
>But all definable fractions of Cantor's sequence
> 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...
> will be transferred into the first column. Nevertheless all matrix places remain occupied by fractions which are undefinable, because all definable fractions have gone. That means dark.
>
> Regards, WM

You have not defined "definable" or "dark", you just say "they exist" based on misunderstandings by you. This is not a fucking definition

zelos...@gmail.com schrieb am Dienstag, 10. Mai 2022 um 07:02:43 UTC+2:
> måndag 9 maj 2022 kl. 14:58:49 UTC+2 skrev WM:

> > 1/1, 1/2, 1/3, 1/4, ...
> > 2/1, 2/2, 2/3, 2/4, ...
> > 3/1, 3/2, 3/3, 3/4, ...
> > 4/1, 4/2, 4/3, 4/4, ...
> > 5/1, 5/2, 5/3, 5/4, ...
> > ...
> > Every attempt to collect all fractions in the first column of this matrix will fail.
> No one is "collecting" them in the first column.

That is the way to index them because by definition the indices are the positions in the first column.

> >But all definable fractions of Cantor's sequence
> > 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...
> > will be transferred into the first column. Nevertheless all matrix places remain occupied by fractions which are undefinable, because all definable fractions have gone. That means dark.

> You have not defined "definable" or "dark", you just say "they exist" based on

the fact that most cannot be indexed by tranferring them into the first column.

Regards, WM

On Tuesday, 10 May 2022 at 10:26:20 UTC-3, WM wrote:
> zelos...@gmail.com schrieb am Dienstag, 10. Mai 2022 um 07:02:43 UTC+2:
[...]
> > You have not defined "definable" or "dark", you just say "they exist" based on
> the fact that
the great perfosser desperately wishes them to exist, against reason, and without any shred of evidence. Piss off, moron.