zelos...@gmail.com schrieb am Freitag, 18. Februar 2022 um 06:31:27 UTC+1:
> torsdag 17 februari 2022 kl. 16:39:22 UTC+1 skrev WM:

> > Here is a sequence:
> > 1/1, 1/2, 2/1, 1/3, 2/2, ...
> Correct, a function from N to Q+
> > Is this also a sequence?
> > 1/1, 1/2, 2/1, 1/3, 2/2, ...
> > __, __, __, __, __, __, ...
> > __, __, __, __, __, __, ...
> > __, __, __, __, __, __, ...
> > __, __, __, __, __, __, ...
> > ...
> Nope because that is not a function from N to Q+

In the first line there is a function. The other places are not disturbing this fact.
> >
> > but this is not?
> > 1/1, __, __, __, ...
> > 1/2, __, __, __, ...
> > 2/1, __, __, __, ...
> > 1/3, __, __, __, ...
> > 2/2, __, __, __, ...
> > ... ?
> Nope because that is not a function from N to Q+
> > Please indicate the first deviation.
> The source set is not N, it is NxN and even fails to satisfy the basic criteria of a function, that any input has an output.

The first column is a sequence. The other places are not disturbing this fact.
> > > Nope, set theory works and has no known REAL internal consistency issues.
> > Small wonder that this opinion prevails in matheology when matheologians are too stupid to recognize a sequence in the first column of an infinite matrix.
> That is not a sequence,

It is a sequence writte in the first column.

> > It has been discarded by people who are intelligent enough to know that the first column is a sequence.

> > My question meanwhile has been "improved" to what you call math terminology.
> > The result remains the same.
> > cannot be reached by allowed transpositins
> > 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, ...
> > ... ... ... ...
> Irrelevant, again, not making a sequence.

It is a sequence of matrices.

Regards, WM

fredag 18 februari 2022 kl. 11:42:27 UTC+1 skrev WM:
> zelos...@gmail.com schrieb am Freitag, 18. Februar 2022 um 06:31:27 UTC+1:
> > torsdag 17 februari 2022 kl. 16:39:22 UTC+1 skrev WM:
>
> > > Here is a sequence:
> > > 1/1, 1/2, 2/1, 1/3, 2/2, ...
> > Correct, a function from N to Q+
> > > Is this also a sequence?
> > > 1/1, 1/2, 2/1, 1/3, 2/2, ...
> > > __, __, __, __, __, __, ...
> > > __, __, __, __, __, __, ...
> > > __, __, __, __, __, __, ...
> > > __, __, __, __, __, __, ...
> > > ...
> > Nope because that is not a function from N to Q+
> In the first line there is a function. The other places are not disturbing this fact.
> > >
> > > but this is not?
> > > 1/1, __, __, __, ...
> > > 1/2, __, __, __, ...
> > > 2/1, __, __, __, ...
> > > 1/3, __, __, __, ...
> > > 2/2, __, __, __, ...
> > > ... ?
> > Nope because that is not a function from N to Q+
> > > Please indicate the first deviation.
> > The source set is not N, it is NxN and even fails to satisfy the basic criteria of a function, that any input has an output.
> The first column is a sequence. The other places are not disturbing this fact.

It isn't a sequence, it is not a function from N to Q+

Your square isn't even a function.

> > > > Nope, set theory works and has no known REAL internal consistency issues.
> > > Small wonder that this opinion prevails in matheology when matheologians are too stupid to recognize a sequence in the first column of an infinite matrix.
> > That is not a sequence,
> It is a sequence writte in the first column.

It is not a function from N to Q+, ergo not a sequence.

> > > It has been discarded by people who are intelligent enough to know that the first column is a sequence.
> > > My question meanwhile has been "improved" to what you call math terminology.
> > > The result remains the same.
> > > cannot be reached by allowed transpositins
> > > 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, ...
> > > ... ... ... ...
> > Irrelevant, again, not making a sequence.
> It is a sequence of matrices.

A sequence of matrices has no relevance to cantors function from N to Q+, none of this has anything to do with it.

>
> Regards, WM

fredag 18 februari 2022 kl. 11:37:33 UTC+1 skrev WM:
> horand....@gmail.com schrieb am Donnerstag, 17. Februar 2022 um 20:10:08 UTC+1:
> > On Thursday, 17 February 2022 at 11:39:22 UTC-4, WM wrote:
>
> > > > > The elements in the first column are an infinite sequence, just that what Cantor claimed the fractions could be.
> > > > It is a column, not a sequence. A sequence is a function from N to X, nothing else.
> > Well, it's a /little/ bit more than that. For instance, it must be clear how to obtain the image of *every* natural number from the function. (This could be a rule, or a partial enumeration, as below, or a great many other things.)
> Cantor specifies it, and I follow his specification neatly.

You follow nothing in mathematics.

> > > Here is a sequence:
> > > 1/1, 1/2, 2/1, 1/3, 2/2, ...
> > Here it is borderline acceptable to infer that 1 is mapped to 1/1, 2 is mapped to 1/2, 3 is mapped to 2/1, etc., since the formation rule is more or less obvious and would become clearer the more terms you supply.
> > > Is this also a sequence?
> > > 1/1, 1/2, 2/1, 1/3, 2/2, ...
> > > __, __, __, __, __, __, ...
> > > __, __, __, __, __, __, ...
> > > __, __, __, __, __, __, ...
> > > __, __, __, __, __, __, ...
> > > ...
> > No; this is gibberish. I think you are trying to imply that rows of this matrix beyond the first row are not part of the range of the function
> They are empty but do not disturb the function which is only in the first line.

Entries are not empty in a matrix, a sequence is a function from N to X. None of these things are mathematical objects you want them to be.

> >, but your intention is utterly unclear.
> It is clear, that the empty places are not hanging anything of the function. That is enough.

it is not a function, it isn't even a matrix.

> > And the same, of course, goes for transposing your glorious picture, as below.
> > > but this is not?
> > > 1/1, __, __, __, ...
> > > 1/2, __, __, __, ...
> > > 2/1, __, __, __, ...
> > > 1/3, __, __, __, ...
> > > 2/2, __, __, __, ...
> > > ... ?
> > > Please indicate the first deviation.
> > The "first deviation" occurs when you write down "1/1" without explaining what the hell you intend to do and think you have defined a function
> I need not define the function since Cantor did. It take his very function. Often we use use the serpent bringing the first column (1, 2, 3, ...) to the fractions, but if there is a bijection, we can also use the first column as it is and bring the fractions to the first column. Of course the elements residing there have to be removed but not forgotten.
>
> Regrads, WM

On 2/18/2022 4:37 AM, WM wrote:
> horand....@gmail.com schrieb am Donnerstag, 17. Februar 2022 um 20:10:08 UTC+1:
>> On Thursday, 17 February 2022 at 11:39:22 UTC-4, WM wrote:
>
>>>>> The elements in the first column are an infinite sequence, just that what Cantor claimed the fractions could be.
>>>> It is a column, not a sequence. A sequence is a function from N to X, nothing else.
>> Well, it's a /little/ bit more than that. For instance, it must be clear how to obtain the image of *every* natural number from the function. (This could be a rule, or a partial enumeration, as below, or a great many other things.)
>
> Cantor specifies it, and I follow his specification neatly.

Liar.

Now you resort to bold lies to try to disprove Cantor's simple and obvious proof. No more Schnapps for you!

>
>>> Here is a sequence:
>>> 1/1, 1/2, 2/1, 1/3, 2/2, ...
>> Here it is borderline acceptable to infer that 1 is mapped to 1/1, 2 is mapped to 1/2, 3 is mapped to 2/1, etc., since the formation rule is more or less obvious and would become clearer the more terms you supply.
>>> Is this also a sequence?
>>> 1/1, 1/2, 2/1, 1/3, 2/2, ...
>>> __, __, __, __, __, __, ...
>>> __, __, __, __, __, __, ...
>>> __, __, __, __, __, __, ...
>>> __, __, __, __, __, __, ...
>>> ...
>> No; this is gibberish. I think you are trying to imply that rows of this matrix beyond the first row are not part of the range of the function
>
> They are empty but do not disturb the function which is only in the first line.

No, it is garbage, you have an entirely new matrix unrelated to the matrix of rationals

>
>> , but your intention is utterly unclear.
>
> It is clear, that the empty places are not hanging anything of the function. That is enough.

you intentionally make it unclear, it is what you have fun doing.

Empty places have no elements, and are not in a set.

>
>> And the same, of course, goes for transposing your glorious picture, as below.
>>> but this is not?
>>> 1/1, __, __, __, ...
>>> 1/2, __, __, __, ...
>>> 2/1, __, __, __, ...
>>> 1/3, __, __, __, ...
>>> 2/2, __, __, __, ...
>>> ... ?
>>> Please indicate the first deviation.
>> The "first deviation" occurs when you write down "1/1" without explaining what the hell you intend to do and think you have defined a function
>

agree, WM explains nothing.

> I need not define the function since Cantor did.

Wrong, and incompetent.

> It take his very function.

and you misapply it to something else. What you see as his formula, IS the one to one mapping from natural numbers to rationals, and back.
nothing else is needed.

Everything you added after his formula is bogus crap.

<snip crap>

>
> Regrads, WM

On 2/18/2022 4:42 AM, WM wrote:
> zelos...@gmail.com schrieb am Freitag, 18. Februar 2022 um 06:31:27 UTC+1:
>> torsdag 17 februari 2022 kl. 16:39:22 UTC+1 skrev WM:
>
>>> Here is a sequence:
>>> 1/1, 1/2, 2/1, 1/3, 2/2, ...
>> Correct, a function from N to Q+
>>> Is this also a sequence?
>>> 1/1, 1/2, 2/1, 1/3, 2/2, ...
>>> __, __, __, __, __, __, ...
>>> __, __, __, __, __, __, ...
>>> __, __, __, __, __, __, ...
>>> __, __, __, __, __, __, ...
>>> ...
>> Nope because that is not a function from N to Q+
>
> In the first line there is a function. The other places are not disturbing this fact.
>>>
>>> but this is not?
>>> 1/1, __, __, __, ...
>>> 1/2, __, __, __, ...
>>> 2/1, __, __, __, ...
>>> 1/3, __, __, __, ...
>>> 2/2, __, __, __, ...
>>> ... ?
>> Nope because that is not a function from N to Q+
>>> Please indicate the first deviation.
>> The source set is not N, it is NxN and even fails to satisfy the basic criteria of a function, that any input has an output.
>
> The first column is a sequence. The other places are not disturbing this fact.
>>>> Nope, set theory works and has no known REAL internal consistency issues.
>>> Small wonder that this opinion prevails in matheology when matheologians are too stupid to recognize a sequence in the first column of an infinite matrix.
>> That is not a sequence,
>
> It is a sequence writte in the first column.
>
>>> It has been discarded by people who are intelligent enough to know that the first column is a sequence.
>
>>> My question meanwhile has been "improved" to what you call math terminology.
>>> The result remains the same.
>>> cannot be reached by allowed transpositins
>>> 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, ...
>>> ... ... ... ...
>> Irrelevant, again, not making a sequence.
>
> It is a sequence of matrices.

WM you are out of Math, and in your imagination.

>
> Regards, WM

On Friday, February 18, 2022 at 4:14:46 PM UTC+1, sergio wrote:

> WM you are out of Math, and in your imagination.

Completely lost in his own (made up) "world".

On 2/18/2022 12:34 PM, Fritz Feldhase wrote:
> On Friday, February 18, 2022 at 4:14:46 PM UTC+1, sergio wrote:
>
>> WM you are out of Math, and in your imagination.
>
> Completely lost in his own (made up) "world".
>

he doesn't use equations, does not use proofs, does not follow the rules of Math

zelos...@gmail.com schrieb am Freitag, 18. Februar 2022 um 13:05:46 UTC+1:
> fredag 18 februari 2022 kl. 11:42:27 UTC+1 skrev WM:
> > The first column is a sequence. The other places are not disturbing this fact.
> It isn't a sequence, it is not a function from N to Q+

It is Cantor's funtion
1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...
defined by
k = (m + n - 1)(m + n - 2)/2 + m

> Your square isn't even a function.

If Cantor was right, then the infinite matrix could be covered by the O's of the first coulmn

OXXX...
OXXX...
OXXX...
OXXX...
....

That is nonsense.

If Cantor was right, then all fractions of the matrix representing the set Q+

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, ...
....

could be housed in the first column of any infinite matrix inclusing the above one, yielding:

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

That is independent of your whining about functions. But when considering the fractions residing there, it becomes clear that Cantor fails.

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, ...
.... ... ... ...

> > It is a sequence of matrices.
> A sequence of matrices has no relevance to cantors function from N to Q+, none of this has anything to do with it.

You are too stupid to understand it. You may be happy that you have many comrades as stupid as you:
https://math.stackexchange.com/questions/4377025/countability-and-coordinate-representations
But in mathematics not the stupid majority but logic is revealing the truth.

Regards, WM

horand....@gmail.com schrieb am Freitag, 18. Februar 2022 um 13:58:19 UTC+1:

> The fact that there is a bijection between N and the first row (or column) of your matrix does *NOT* preclude another bijection between N and the entire matrix.

The bijection between Nℕ and the matrix would imply the bijection between the matrix and the first column. This has been disproved.

> The whole point of infinite sets is that they can be put in bijection with proper subsets.

Here the contrary is shown:

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, ...
.... ... ... ...

> You can of course deny that

It has not been denied but it has been proved that never any transposition will empty the matrix.
>
> However, as I reflect a little more, the conclusion forces itself upon me that you actually concede that there *IS* a bijection between N and the first row of your matrix.

No, I do not concede that. However it is easier to assume it and then to disprove the bijection. It is so easy that even a completely independent editor has understood the problematic aspect
https://math.stackexchange.com/questions/4377025/countability-and-coordinate-representations

There are three proofs against matheology in my work
https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf

(1) There is no actual infinity. For instance there is no complete infinite set ℕ with ℵo identifiable natural numbers.

(2) Assuming that ℵo exists and is consistent, countability turns out to be a self-contradictory notion. For instance, there is no bijection between ℕ and Q.

(3) Even if ℵo and countability are assumed to exist free of self-contradictions and to make sense, there are no uncountable sets.

Regards, WM

WM brought next idea :
> zelos...@gmail.com schrieb am Freitag, 18. Februar 2022 um 13:05:46 UTC+1:
>> fredag 18 februari 2022 kl. 11:42:27 UTC+1 skrev WM:
>>> The first column is a sequence. The other places are not disturbing this
>>> fact.
>> It isn't a sequence, it is not a function from N to Q+
>
> It is Cantor's funtion
> 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...
> defined by
> k = (m + n - 1)(m + n - 2)/2 + m
>
>> Your square isn't even a function.
>
> If Cantor was right, then the infinite matrix could be covered by the O's of
> the first coulmn
>
> OXXX...
> OXXX...
> OXXX...
> OXXX...
> ...
>
> That is nonsense.
>
> If Cantor was right, then all fractions of the matrix representing the set Q+
>
> 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, ...
> ...
>
> could be housed in the first column of any infinite matrix inclusing the
> above one, yielding:
>
> 1/1, __, __, __, ...
> 1/2, __, __, __, ...
> 2/1, __, __, __, ...
> 1/3, __, __, __, ...
> 2/2, __, __, __, ...
> ...
>
> That is independent of your whining about functions. But when considering the
> fractions residing there, it becomes clear that Cantor fails.
>
> 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, ... ... ... ... ...
>
>>> It is a sequence of matrices.
>> A sequence of matrices has no relevance to cantors function from N to Q+,
>> none of this has anything to do with it.
>
> You are too stupid to understand it. You may be happy that you have many
> comrades as stupid as you:
> https://math.stackexchange.com/questions/4377025/countability-and-coordinate-representations
> But in mathematics not the stupid majority but logic is revealing the truth.

You are a liar WM. I notice they caught onto your game and closed the
question.

On 2/19/2022 4:07 AM, WM wrote:
> horand....@gmail.com schrieb am Freitag, 18. Februar 2022 um 13:58:19 UTC+1:
>
>> The fact that there is a bijection between N and the first row (or column) of your matrix does *NOT* preclude another bijection between N and the entire matrix.
>
> The bijection between Nℕ and the matrix would imply the bijection between the matrix and the first column. This has been disproved.
>
>> The whole point of infinite sets is that they can be put in bijection with proper subsets.
>
> Here the contrary is shown:
>

distraction, monkey-math

>> You can of course deny that
>
> It has not been denied but it has been proved that never any transposition will empty the matrix.

No, you offer no Proof, only what you imagine, tic-tac-toe games

>>
>> However, as I reflect a little more, the conclusion forces itself upon me that you actually concede that there *IS* a bijection between N and the first row of your matrix.

> No, I do not concede that. However it is easier to assume it and then to disprove the bijection.

Which you failed to do in all your tries.

>
> There are three proofs against matheology in my work
> https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf

a self published troll book

>
> (1) There is no actual infinity. For instance there is no complete infinite set ℕ with ℵo identifiable natural numbers.

nonsense

>
> (2) Assuming that ℵo exists and is consistent, countability turns out to be a self-contradictory notion.

So you fail to understand Math concepts too

>
> (3) Even if ℵo and countability are assumed to exist free of self-contradictions and to make sense, there are no uncountable sets.

another lie.

>
> Regards, WM

horand....@gmail.com schrieb am Samstag, 19. Februar 2022 um 15:42:22 UTC+1:
> The function f:ℕxℕ --> ℕ defined by f(n,m) = (m + n - 1)(m + n - 2)/2 + m is a bijection from ℕxℕ onto ℕ. You can dance around this as long and often as you like, you can obfuscate till the cows come home, and you will still not have found a contradictory result.

Which fraction is missing in the first row of the matrix that shows no empty position? Which fraction is remaining in the rest of the matrix? Can you name any? Can you deny that there is never an empty position?

> (There may well be an inconsistency in ZFC, but in 150 years nobody --

Wrong. See chapter V of https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf. For instance Borel, having written 50 books on math, knew that ZFC is inconsistent.
Matheology is based on the contradiciton: If a bijection exists then not every injection must be a bijection. But as just a friend wrote: Es wird uns zwar nicht gelingen, die Anstalt von den Insassen zurückzuerobern, aber man sollte wohl so weit wie möglich den Zugang zu Tatsachen verteidigen und fördern.

Regards, WM

FromTheRafters schrieb am Samstag, 19. Februar 2022 um 12:49:02 UTC+1:
> WM brought next idea :
> >> A sequence of matrices has no relevance to cantors function from N to Q+,
> >> none of this has anything to do with it.
> >
> > You are too stupid to understand it. You may be happy that you have many
> > comrades as stupid as you:
> > https://math.stackexchange.com/questions/4377025/countability-and-coordinate-representations
> > But in mathematics not the stupid majority but logic is revealing the truth.
> I notice they caught onto your game and closed the question.

Without having an answer! Do you know where my model dissents from Cantor's?

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, ...
.... ... ... ...

Can you name a fraction not appearing in the first colum? Can you name a fraction remaining in the rest of the matrix?

But you cannot find any empty place in the matrix. That proves dark fractions.

Regards, WM

On Sunday, February 20, 2022 at 9:20:52 AM UTC+1, WM wrote:
> horand....@gmail.com schrieb am Samstag, 19. Februar 2022 um 15:42:22 UTC+1:
> > The function f:ℕxℕ --> ℕ defined by f(n,m) = (m + n - 1)(m + n - 2)/2 + m is a bijection from ℕxℕ onto ℕ. You can dance around this as long and often as you like, you can obfuscate till the cows come home, and you will still not have found a contradictory result.
> Which fraction is missing in the first row of the matrix that shows no empty position? Which fraction is remaining in the rest of the matrix? Can you name any? Can you deny that there is never an empty position?
> > (There may well be an inconsistency in ZFC, but in 150 years nobody --
> Wrong. See chapter V of https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf. For instance Borel, having written 50 books on math, knew that ZFC is inconsistent.
> Matheology is based on the contradiciton: If a bijection exists then not every injection must be a bijection. But as just a friend wrote: Es wird uns zwar nicht gelingen, die Anstalt von den Insassen zurückzuerobern, aber man sollte wohl so weit wie möglich den Zugang zu Tatsachen verteidigen und fördern.
>
> Regards, WM

Na dann verteidigen Sie und fördern Sie den Zugang mal schön. Aber aufgepasst,
denn manche Tatsachen haben scharfe Krallen:
https://i0.wp.com/uploads7.wikipaintings.org/images/gustave-dore/don-quixote-118.jpg

O wehe! wir sind verloren,
Sie sind schon vor den Toren!
Der Bürgermeister und Senat,
Sie schütteln die Köpfe, und keiner weiß Rat.

Die Bürgerschaft greift zu den Waffen,
Die Glocken läuten die Pfaffen.
Gefährdet ist das Palladium
Des sittlichen Staats, das Eigentum.

Nicht Glockengeläute, nicht Pfaffengebete,
Nicht hochwohlweise Senatsdekrete,
Auch nicht Kanonen, viel Hundertpfünder,
Sie helfen Euch heute, Ihr lieben Kinder!

Heut helfen Euch nicht die Wortgespinste
Der abgelebten Redekünste.
Man fängt nicht Ratten mit Syllogismen,
Sie springen über die feinsten Sophismen.
-- Heine: Die Wanderratten

WM presented the following explanation :
> horand....@gmail.com schrieb am Samstag, 19. Februar 2022 um 15:42:22 UTC+1:
>> The function f:ℕxℕ --> ℕ defined by f(n,m) = (m + n - 1)(m + n - 2)/2 + m is
>> a bijection from ℕxℕ onto ℕ. You can dance around this as long and often as
>> you like, you can obfuscate till the cows come home, and you will still not
>> have found a contradictory result.
>
> Which fraction is missing in the first row of the matrix that shows no empty
> position?

Infinitely many fractions are missing. For instance C/D is missing.

It happens that WM formulated :
> FromTheRafters schrieb am Samstag, 19. Februar 2022 um 12:49:02 UTC+1:
>> WM brought next idea :
>
>>>> A sequence of matrices has no relevance to cantors function from N to Q+,
>>>> none of this has anything to do with it.
>>>
>>> You are too stupid to understand it. You may be happy that you have many
>>> comrades as stupid as you:
>>> https://math.stackexchange.com/questions/4377025/countability-and-coordinate-representations
>>> But in mathematics not the stupid majority but logic is revealing the
>>> truth.
>> I notice they caught onto your game and closed the question.
>
> Without having an answer! Do you know where my model dissents from Cantor's?

Yes, almost immediately.

On 2/20/2022 2:20 AM, WM wrote:
> horand....@gmail.com schrieb am Samstag, 19. Februar 2022 um 15:42:22 UTC+1:
>> The function f:ℕxℕ --> ℕ defined by f(n,m) = (m + n - 1)(m + n - 2)/2 + m is a bijection from ℕxℕ onto ℕ. You can dance around this as long and often as you like, you can obfuscate till the cows come home, and you will still not have found a contradictory result.
>
> Which fraction is missing in the first row of the matrix that shows no empty position? Which fraction is remaining in the rest of the matrix? Can you name any? Can you deny that there is never an empty position?

use the bijection mapping directly.

(You only confuse yourself by your matrix and your movable tiles, it is diversion, no math there)

> Regards, WM

On 2/20/2022 2:25 AM, WM wrote:
> FromTheRafters schrieb am Samstag, 19. Februar 2022 um 12:49:02 UTC+1:
>> WM brought next idea :
>
>>>> A sequence of matrices has no relevance to cantors function from N to Q+,
>>>> none of this has anything to do with it.
>>>
>>> You are too stupid to understand it. You may be happy that you have many
>>> comrades as stupid as you:
>>> https://math.stackexchange.com/questions/4377025/countability-and-coordinate-representations
>>> But in mathematics not the stupid majority but logic is revealing the truth.
>> I notice they caught onto your game and closed the question.
>
> Without having an answer! Do you know where my model dissents from Cantor's?

You have not described a model. What you post here is unrelated to Cantor.

>
> 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, ...
> ... ... ... ...
>
> Can you name a fraction not appearing in the first colum?

which first column ? and where is 19863/84736177 ?

> Can you name a fraction remaining in the rest of the matrix?

yes, 19863/84736177

>
> But you cannot find any empty place in the matrix. That proves dark fractions.

no, it proves your model sucks and is no good at all, just imagination.

>
> Regards, WM

lördag 19 februari 2022 kl. 10:54:29 UTC+1 skrev WM:
> zelos...@gmail.com schrieb am Freitag, 18. Februar 2022 um 13:05:46 UTC+1:
> > fredag 18 februari 2022 kl. 11:42:27 UTC+1 skrev WM:
> > > The first column is a sequence. The other places are not disturbing this fact.
> > It isn't a sequence, it is not a function from N to Q+
> It is Cantor's funtion
> 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...
> defined by
> k = (m + n - 1)(m + n - 2)/2 + m

That is a function, yours is not.

> > Your square isn't even a function.
> If Cantor was right, then the infinite matrix could be covered by the O's of the first coulmn
> OXXX...
> OXXX...
> OXXX...
> OXXX...
> ...
> That is nonsense.

It implies nothing of the sort.

>
> If Cantor was right, then all fractions of the matrix representing the set Q+
> 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, ...
> ...
>
> could be housed in the first column of any infinite matrix inclusing the above one, yielding:
> 1/1, __, __, __, ...
> 1/2, __, __, __, ...
> 2/1, __, __, __, ...
> 1/3, __, __, __, ...
> 2/2, __, __, __, ...

It says nothing of the sort, it implies nothing of the sort. This is not even a function so it is entirely irrelevant.

> ...
> That is independent of your whining about functions. But when considering the fractions residing there, it becomes clear that Cantor fails.
> 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, ...
> ... ... ... ...
> > > It is a sequence of matrices.
> > A sequence of matrices has no relevance to cantors function from N to Q+, none of this has anything to do with it.
> You are too stupid to understand it. You may be happy that you have many comrades as stupid as you:
> https://math.stackexchange.com/questions/4377025/countability-and-coordinate-representations
> But in mathematics not the stupid majority but logic is revealing the truth.

And logic reveals you are wrong. You cannot even unederstand thhat what you are trying to do is not a valid function.

>
> Regards, WM

zelos...@gmail.com schrieb am Montag, 21. Februar 2022 um 06:57:26 UTC+1:

> And logic reveals you are wrong.

Not logic! Every fraction that can be found in Cantor's sequence can be found in the first column. No fraction can be found in the remaining columns. That shows identity of my sequence with Cantor's sequence. But never an empty place can be found either. That shows the existence of dark fractions.

Regards, WM

FromTheRafters schrieb am Sonntag, 20. Februar 2022 um 13:59:28 UTC+1:
> WM presented the following explanation :
> > horand....@gmail.com schrieb am Samstag, 19. Februar 2022 um 15:42:22 UTC+1:
> >> The function f:ℕxℕ --> ℕ defined by f(n,m) = (m + n - 1)(m + n - 2)/2 + m is
> >> a bijection from ℕxℕ onto ℕ. You can dance around this as long and often as
> >> you like, you can obfuscate till the cows come home, and you will still not
> >> have found a contradictory result.
> >
> > Which fraction is missing in the first row of the matrix that shows no empty
> > position?
> Infinitely many fractions are missing. For instance C/D is missing.

Every fraction that can be found in Cantor's sequence can be found in the first column. No fraction can be found in the remaining columns. That shows identity of my sequence with Cantor's sequence. But never an empty place can be found either. That shows the existence of dark fractions.

Regards, WM

horand....@gmail.com schrieb am Sonntag, 20. Februar 2022 um 16:25:33 UTC+1:
> On Sunday, 20 February 2022 at 04:20:52 UTC-4, WM wrote:
> > horand....@gmail.com schrieb am Samstag, 19. Februar 2022 um 15:42:22 UTC+1:
> > > The function f:ℕxℕ --> ℕ defined by f(n,m) = (m + n - 1)(m + n - 2)/2 + m is a bijection from ℕxℕ onto ℕ. You can dance around this as long and often as you like, you can obfuscate till the cows come home, and you will still not have found a contradictory result.
> > Which fraction is missing in the first row of the matrix that shows no empty position? Which fraction is remaining in the rest of the matrix? Can you name any? Can you deny that there is never an empty position?
> For every fraction you care to give me, I can tell you the finite step at which it moves from the bottom part of the matrix (or the right or whatever part corresponds to your arrangement of the day) to the row or column where you gather them.

Of course! Every fraction that can be found in Cantor's sequence can be found in the first column. No fraction can be found staying in the remaining columns. That shows identity of my sequence with Cantor's sequence. But never an empty place can be found either. That shows the existence of dark fractions.

> Once in position it will not move any more. Ultimately (but, as you know, this is an infinite process so it will never stop) *EVERY* fraction has been moved to its final position.

Every fraction that you can ask for will appear in the first column. Nevertheless all places of the matrix remain occupied. Na dämmert's?

> infinite processes require limits and/or careful arguments,

If never an empty place occurs then the limit has no empty place(s).

> > > (There may well be an inconsistency in ZFC, but in 150 years nobody --
> > Wrong. See chapter V of https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf. For instance Borel, having written 50 books on math, knew that ZFC is inconsistent.
> If, in those 50 books you could actually point at a proper quote, where he says and proves that, you'd be doing your case a lot of good.

My case has been settled above. No further quotes or proofs are required.

> > Matheology is based on the contradiciton: If a bijection exists then not every injection must be a bijection.
> How is that a contradiction????

Because bijection proves equinumerosity, not only equicardinality.

Regards, WM

WM presented the following explanation :
> FromTheRafters schrieb am Sonntag, 20. Februar 2022 um 13:59:28 UTC+1:
>> WM presented the following explanation :
>>> horand....@gmail.com schrieb am Samstag, 19. Februar 2022 um 15:42:22
>>> UTC+1:
>>>> The function f:ℕxℕ --> ℕ defined by f(n,m) = (m + n - 1)(m + n - 2)/2 + m
>>>> is a bijection from ℕxℕ onto ℕ. You can dance around this as long and
>>>> often as you like, you can obfuscate till the cows come home, and you
>>>> will still not have found a contradictory result.
>>>
>>> Which fraction is missing in the first row of the matrix that shows no
>>> empty position?
>> Infinitely many fractions are missing. For instance C/D is missing.
>
> Every fraction that can be found in Cantor's sequence can be found in the
> first column.

Good, because Cantor was counting rational numbers, not fractions.

> No fraction can be found in the remaining columns. That shows
> identity of my sequence with Cantor's sequence. But never an empty place can
> be found either. That shows the existence of dark fractions.

No it doesn't, what set represents the permutations of a countably
infinite set?

FromTheRafters schrieb am Montag, 21. Februar 2022 um 09:41:09 UTC+1:
> WM presented the following explanation :

> > Every fraction that can be found in Cantor's sequence can be found in the
> > first column.
> Good, because Cantor was counting rational numbers, not fractions.

Wrong. k = (m + n - 1)(m + n - 2)/2 + m counts
1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...

> > No fraction can be found in the remaining columns. That shows
> > identity of my sequence with Cantor's sequence. But never an empty place can
> > be found either. That shows the existence of dark fractions.
> No it doesn't, what set represents the permutations of a countably
> infinite set?

My proof shows that all definable fractions appear in the first column. All other fractions are dark and have no permutations. Try it.

Regards, WM

On Monday, February 21, 2022 at 9:53:46 AM UTC+1, WM wrote:
>
> My proof

Your WHAT?!