On 11/8/2022 5:32 AM, WM wrote:
> zelos...@gmail.com schrieb am Montag, 7. November 2022 um 12:37:16 UTC+1:
>
>> None of that proves anythign "dark"
>
> Where are the O's?

they come in a box,

a box you get at the grocery store,

see https://www.cheerios.com/products

>
> Regards, WM

On 11/8/2022 6:47 AM, WM wrote:
> Jim Burns schrieb am Montag,
> 7. November 2022 um 21:16:05 UTC+1:

>> referring collectively to FISONs
>> will ALSO exhaust ℕ ?
>
> No.
> Dark means that *only*
> collectively mentioning is possible.

Here is what you (WM) mean by that:

> Referring individually to FISONs or natnumbers
> will never exhaust ℕ.
> Referring collectively to natnumbers
> will exhaust ℕ.

Your conditions for dark gizmos are
1.
No one gizmo equals (exhausts)
the Sea of Gizmocity.
2.
All gizmos collectively (the union of gizmos)
equals (exhausts) the Sea of Gizmocity.

Gizmos collectively exhaust _something_
which they cannot individually exhaust.
Therefore, dark gizmos exist.

Gizmos could be natural numbers,
and the Sea of Gizmocity could be ℕ

Gizmos could be FISONs,
and the Sea of Gizmocity could be ℕ_def

What you call ℕ_def is actually ℕ
That doesn't matter to my point:
All FISONs can only be *collectively* mentioned.

Therefore,
dark FISONs exist,
as well as dark natural numbers.

>> FISONs collectively exhaust the correct ℕ
>
> ℕ_def

FISONs collectively exhaust _something_
which they cannot individually exhaust.

Therefore,
dark FISONs exist,
as well as dark natural numbers.

>> the ℕ to which our theorems refer,
>> the ℕ which supersets each FISON

Corrected:
the ℕ to which our theorems refer,
the ℕ which supersets each FISON and
which subsets anything else which
supersets each FISON.

> That is the ℕ_def with only individually
> definable elements.
> But it is not the ℕ of Cantor's.

FISONs collectively exhaust _something_
which they cannot individually exhaust.

Therefore,
dark FISONs exist,
as well as dark natural numbers.

>> For each FISON, there is a unique FISON-end.
>> For each FISON-end, there is a unique FISON.
>>
>> Exhausting the FISONs exhausts the FISON-ends.
>
> Yes,

Therefore,
dark FISONs exist,
as well as dark natural numbers.

> but the natnumbers of Cantor's ℕ are more.

More than FISON-ends is equivalent to
induction being invalid.

Can you quote Cantor saying
induction is invalid?

I can't imagine such a quote existing.
I think you'd have a better chance finding
Cantor declaring Wilhelm II one of the Lizard People.

But, surely, if Cantor thought that,
he would mention it. It's rather important.

On Tuesday, November 8, 2022 at 8:06:00 AM UTC-8, Jim Burns wrote:
> On 11/8/2022 6:47 AM, WM wrote:
> > Jim Burns schrieb am Montag,
> > 7. November 2022 um 21:16:05 UTC+1:
> >> referring collectively to FISONs
> >> will ALSO exhaust ℕ ?
> >
> > No.
> > Dark means that *only*
> > collectively mentioning is possible.
> Here is what you (WM) mean by that:
> > Referring individually to FISONs or natnumbers
> > will never exhaust ℕ.
> > Referring collectively to natnumbers
> > will exhaust ℕ.
> Your conditions for dark gizmos are
> 1.
> No one gizmo equals (exhausts)
> the Sea of Gizmocity.
> 2.
> All gizmos collectively (the union of gizmos)
> equals (exhausts) the Sea of Gizmocity.
>
> Gizmos collectively exhaust _something_
> which they cannot individually exhaust.
> Therefore, dark gizmos exist.
>
> Gizmos could be natural numbers,
> and the Sea of Gizmocity could be ℕ
>
> Gizmos could be FISONs,
> and the Sea of Gizmocity could be ℕ_def
>
> What you call ℕ_def is actually ℕ
> That doesn't matter to my point:
> All FISONs can only be *collectively* mentioned.
>
> Therefore,
> dark FISONs exist,
> as well as dark natural numbers.
> >> FISONs collectively exhaust the correct ℕ
> >
> > ℕ_def
> FISONs collectively exhaust _something_
> which they cannot individually exhaust.
>
> Therefore,
> dark FISONs exist,
> as well as dark natural numbers.
> >> the ℕ to which our theorems refer,
> >> the ℕ which supersets each FISON
> Corrected:
> the ℕ to which our theorems refer,
> the ℕ which supersets each FISON and
> which subsets anything else which
> supersets each FISON.
> > That is the ℕ_def with only individually
> > definable elements.
> > But it is not the ℕ of Cantor's.
> FISONs collectively exhaust _something_
> which they cannot individually exhaust.
>
> Therefore,
> dark FISONs exist,
> as well as dark natural numbers.
> >> For each FISON, there is a unique FISON-end.
> >> For each FISON-end, there is a unique FISON.
> >>
> >> Exhausting the FISONs exhausts the FISON-ends.
> >
> > Yes,
> Therefore,
> dark FISONs exist,
> as well as dark natural numbers.
> > but the natnumbers of Cantor's ℕ are more.
> More than FISON-ends is equivalent to
> induction being invalid.
>
> Can you quote Cantor saying
> induction is invalid?
>
> I can't imagine such a quote existing.
> I think you'd have a better chance finding
> Cantor declaring Wilhelm II one of the Lizard People.
>
> But, surely, if Cantor thought that,
> he would mention it. It's rather important.

Why not, "deduction is valid". ?

On 11/8/2022 11:33 AM, Ross A. Finlayson wrote:
> On Tuesday, November 8, 2022
> at 8:06:00 AM UTC-8, Jim Burns wrote:
>> On 11/8/2022 6:47 AM, WM wrote:

>>> but the natnumbers of Cantor's ℕ are more.
>>
>> More than FISON-ends is equivalent to
>> induction being invalid.
>>
>> Can you quote Cantor saying
>> induction is invalid?
>>
>> I can't imagine such a quote existing.
>> I think you'd have a better chance
>> finding Cantor declaring Wilhelm II
>> one of the Lizard People.
>>
>> But, surely, if Cantor thought that,
>> he would mention it. It's rather important.
>
> Why not, "deduction is valid". ?

Deduction is valid _for its subject matter_

The Pythagorean theorem is true of
any right triangle.
It might not be true of just any triangle.

Induction (below) is true of any FISON-end.
P(0) ∧ ∀j ∈ ⋃𝓕 : P(j) ⟹ P(j⁺⁺)
⟹ ∀k ∈ ⋃𝓕 : P(k)

It might not be true of just anything.

⋃𝓕 == FISON-ends

>>> but the natnumbers of Cantor's ℕ are more.

If the natnumbers of Cantor's ℕ are more,
then induction isn't valid for Cantor's ℕ
and Cantor didn't bother to mention that.

zelos...@gmail.com schrieb am Dienstag, 8. November 2022 um 13:54:14 UTC+1:
> tisdag 8 november 2022 kl. 12:32:32 UTC+1 skrev WM:
> > zelos...@gmail.com schrieb am Montag, 7. November 2022 um 12:37:16 UTC+1:
> >
> > > None of that proves anythign "dark"
> > Where are the O's?
> >
> Those do not matter because thati s not how the bijection is constructed!

But if a bijection existed, then it could be checked in this way.

Regards, WM

Gus Gassmann schrieb am Dienstag, 8. November 2022 um 14:31:55 UTC+1:
> On Tuesday, 8 November 2022 at 07:33:22 UTC-4, WM wrote:
> > Gus Gassmann schrieb am Montag, 7. November 2022 um 12:59:08 UTC+1:
> > > On Monday, 7 November 2022 at 07:37:16 UTC-4, zelos...@gmail.com wrote:
> > > > [...]
> > > > None of that proves anythign "dark"
> > > Oh, I'd say that this is ample proof for one dark thing:
> > Any limit desired?
> No, but it would help if you could read.

You limit claim is nonsense. That should be clear to everyone. Man beachte diese an Klarheit nichts zu wünschen übrig lassenden Formulierungen: sämtliche, und jede an einer bestimmten Stelle, an einen bestimmten Platz, wobei keine einzige vergessen ist.

Regards, WM

onsdag 9 november 2022 kl. 10:51:14 UTC+1 skrev WM:
> zelos...@gmail.com schrieb am Dienstag, 8. November 2022 um 13:54:14 UTC+1:
> > tisdag 8 november 2022 kl. 12:32:32 UTC+1 skrev WM:
> > > zelos...@gmail.com schrieb am Montag, 7. November 2022 um 12:37:16 UTC+1:
> > >
> > > > None of that proves anythign "dark"
> > > Where are the O's?
> > >
> > Those do not matter because thati s not how the bijection is constructed!
> But if a bijection existed, then it could be checked in this way.
>
> Regards, WM

No it can't! Because you are doing it in a step by step fashion, thati s not how you check a bijection! you check ALL OF THEM AT ONCE!

On Wednesday, 9 November 2022 at 05:54:33 UTC-4, WM wrote:
> Gus Gassmann schrieb am Dienstag, 8. November 2022 um 14:31:55 UTC+1:
> > On Tuesday, 8 November 2022 at 07:33:22 UTC-4, WM wrote:
> > > Gus Gassmann schrieb am Montag, 7. November 2022 um 12:59:08 UTC+1:
> > > > On Monday, 7 November 2022 at 07:37:16 UTC-4, zelos...@gmail.com wrote:
> > > > > [...]
> > > > > None of that proves anythign "dark"
> > > > Oh, I'd say that this is ample proof for one dark thing:
> > > Any limit desired?
> > No, but it would help if you could read.
> You limit claim is nonsense. That should be clear to everyone. Man beachte diese an Klarheit nichts zu wünschen übrig lassenden Formulierungen: sämtliche, und jede an einer bestimmten Stelle, an einen bestimmten Platz, wobei keine einzige vergessen ist.

Bullshit. You have no clue! An infinite process is not finite, and a mapping with an infinite domain does not have a finite one. How difficult can that be to comprehend? It is *YOUR* madness (Wahnidee) that thinks you can turn a finite process into an infinite one without taking limits. That is not how it works, and misinterpreting Cantor to suit your lunacy is not mathematics.

zelos...@gmail.com schrieb am Mittwoch, 9. November 2022 um 10:57:42 UTC+1:
> onsdag 9 november 2022 kl. 10:51:14 UTC+1 skrev WM:
> > zelos...@gmail.com schrieb am Dienstag, 8. November 2022 um 13:54:14 UTC+1:
> > > tisdag 8 november 2022 kl. 12:32:32 UTC+1 skrev WM:
> > > > zelos...@gmail.com schrieb am Montag, 7. November 2022 um 12:37:16 UTC+1:
> > > >
> > > > > None of that proves anythign "dark"
> > > > Where are the O's?
> > > >
> > > Those do not matter because thati s not how the bijection is constructed!
> > But if a bijection existed, then it could be checked in this way.
> >
> No it can't! Because you are doing it in a step by step fashion, thati s not how you check a bijection! you check ALL OF THEM AT ONCE!

That is cheating. Only fools will believe you. I prefer checking. "The infinite sequence thus defined has the peculiar property to contain all positive rational numbers and each of them only once at a determined place." [G. Cantor, letter to R. Lipschitz (19 Nov 1883)] Why not take it as Cantor calls it?

Regards, WM

On Wednesday, November 9, 2022 at 4:34:07 AM UTC-8, Gus Gassmann wrote:
> On Wednesday, 9 November 2022 at 05:54:33 UTC-4, WM wrote:
> > Gus Gassmann schrieb am Dienstag, 8. November 2022 um 14:31:55 UTC+1:
> > > On Tuesday, 8 November 2022 at 07:33:22 UTC-4, WM wrote:
> > > > Gus Gassmann schrieb am Montag, 7. November 2022 um 12:59:08 UTC+1:
> > > > > On Monday, 7 November 2022 at 07:37:16 UTC-4, zelos...@gmail.com wrote:
> > > > > > [...]
> > > > > > None of that proves anythign "dark"
> > > > > Oh, I'd say that this is ample proof for one dark thing:
> > > > Any limit desired?
> > > No, but it would help if you could read.
> > You limit claim is nonsense. That should be clear to everyone. Man beachte diese an Klarheit nichts zu wünschen übrig lassenden Formulierungen: sämtliche, und jede an einer bestimmten Stelle, an einen bestimmten Platz, wobei keine einzige vergessen ist.
> Bullshit. You have no clue! An infinite process is not finite, and a mapping with an infinite domain does not have a finite one. How difficult can that be to comprehend? It is *YOUR* madness (Wahnidee) that thinks you can turn a finite process into an infinite one without taking limits. That is not how it works, and misinterpreting Cantor to suit your lunacy is not mathematics.

Cantor proves the line is drawn.

So..., heal thyself?

Fritz Feldhase schrieb am Dienstag, 8. November 2022 um 14:18:00 UTC+1:

> IN_def := {n e IN : |IN \ {1, 2, 3, ..., n}| = ℵo}.
>
> From this we get: IN_def = IN.
>
> This means: |ℕ \ ℕ_def| = ℵo does not hold.

Define a number with less than ℵo natural successors. Fail.
ℕ collectively defined has no natural successors.

Regards, WM

zelos...@gmail.com schrieb am Dienstag, 8. November 2022 um 13:55:26 UTC+1:
> tisdag 8 november 2022 kl. 12:47:14 UTC+1 skrev WM:

> > That is the ℕ_def with only individually definable elements. But it is not the ℕ of Cantor's.
> > > For each FISON, there is a unique FISON-end.
> > > For each FISON-end, there is a unique FISON.
> > >
> > > Exhausting the FISONs exhausts the FISON-ends.
> > Yes, but the natnumbers of Cantor's ℕ are more.

Every FISON misses almost all.

Regards, WM

onsdag 9 november 2022 kl. 13:57:38 UTC+1 skrev WM:
> zelos...@gmail.com schrieb am Mittwoch, 9. November 2022 um 10:57:42 UTC+1:
> > onsdag 9 november 2022 kl. 10:51:14 UTC+1 skrev WM:
> > > zelos...@gmail.com schrieb am Dienstag, 8. November 2022 um 13:54:14 UTC+1:
> > > > tisdag 8 november 2022 kl. 12:32:32 UTC+1 skrev WM:
> > > > > zelos...@gmail.com schrieb am Montag, 7. November 2022 um 12:37:16 UTC+1:
> > > > >
> > > > > > None of that proves anythign "dark"
> > > > > Where are the O's?
> > > > >
> > > > Those do not matter because thati s not how the bijection is constructed!
> > > But if a bijection existed, then it could be checked in this way.
> > >
> > No it can't! Because you are doing it in a step by step fashion, thati s not how you check a bijection! you check ALL OF THEM AT ONCE!
> That is cheating.

No it isn't, it is how you fucking do mathematics!

>Only fools will believe you.

Mathematicians accept it, you're a crank.

>I prefer checking.

You prefer "checking" through a flawed mean that proves nothing? That is exactly why you're a fucking crank.

>"The infinite sequence thus defined has the peculiar property to contain all positive rational numbers and each of them only once at a determined place." [G. Cantor, letter to R. Lipschitz (19 Nov 1883)] Why not take it as Cantor calls it?

Notice he says nothing about "checking" like you imagine it!

>
> Regards, WM

onsdag 9 november 2022 kl. 13:59:13 UTC+1 skrev WM:
> Fritz Feldhase schrieb am Dienstag, 8. November 2022 um 14:18:00 UTC+1:
>
> > IN_def := {n e IN : |IN \ {1, 2, 3, ..., n}| = ℵo}.
> >
> > From this we get: IN_def = IN.
> >
> > This means: |ℕ \ ℕ_def| = ℵo does not hold.
> Define a number with less than ℵo natural successors. Fail.
> ℕ collectively defined has no natural successors.
>
> Regards, WM

That doesn't prove that your N_def is not equal to N

Gus Gassmann schrieb am Mittwoch, 9. November 2022 um 13:34:07 UTC+1:
> On Wednesday, 9 November 2022 at 05:54:33 UTC-4, WM wrote:

> > You limit claim is nonsense. That should be clear to everyone. Man beachte diese an Klarheit nichts zu wünschen übrig lassenden Formulierungen: sämtliche, und jede an einer bestimmten Stelle, an einen bestimmten Platz, wobei keine einzige vergessen ist.

> An infinite process is not finite,

Therefore FISONs will always stay in tiny finite initial segments of ℕ.

> and a mapping with an infinite domain does not have a finite one.

That has been provede by me.

> It is *YOUR* madness (Wahnidee) that thinks you can turn a finite process into an infinite one without taking limits.

No, it is Cantor's.

> That is not how it works,

Yes!

> and misinterpreting Cantor

Some proponents of set theory claim that the set theoretical limit has to be applied. But also if doing so, we come to the conclusion that all the O remain present in all definable matrices until "in the limit" these infinitely many O have to leave in trouble such that no individual leaves in a definable way. This implies that "in the limit" infinitely many fractions have to become indexed such that none of them can be checked.

Regards, WM

Jim Burns schrieb am Dienstag, 8. November 2022 um 17:06:00 UTC+1:
> On 11/8/2022 6:47 AM, WM wrote:

> Gizmos could be natural numbers,
> and the Sea of Gizmocity could be ℕ
>
> Gizmos could be FISONs,
> and the Sea of Gizmocity could be ℕ_def

ℕ_def is a direction, nothing that could be exhausted.
>
> What you call ℕ_def is actually ℕ
> That doesn't matter to my point:
> All FISONs can only be *collectively* mentioned.

There is no "all" in potential imfinity.
>
> >> FISONs collectively exhaust the correct ℕ
> >
> > ℕ_def
> FISONs collectively exhaust _something_
> which they cannot individually exhaust.

It is not quite right to talk of exhausting with respect to ℕ_def because potential infinity is a direction, not a quantity.
>
> Corrected:
> the ℕ to which our theorems refer,
> the ℕ which supersets each FISON and
> which subsets anything else which
> supersets each FISON.

The reason is that the dark numbers existing between ℕ_def and ℕ cannot be defined and cannot serve as marks or endpoints of supersets of all FISONs.

> >> For each FISON, there is a unique FISON-end.
> >> For each FISON-end, there is a unique FISON.
> >>
> >> Exhausting the FISONs exhausts the FISON-ends.
> >
> > Yes,
But see the remark above concerning exhausting.

> Therefore,
> dark FISONs exist,
> as well as dark natural numbers.

A FISON is by definition defined.

> > but the natnumbers of Cantor's ℕ are more.
> More than FISON-ends is equivalent to
> induction being invalid.
>
> Can you quote Cantor saying
> induction is invalid?

No, he usese induction frequently to prove properties of infinite sets. I use it to prove that no FISON is necessary or sufficient to produce ℕ. Every FISON that is shorter is not required. A FISON that is infinite is not available.

Regards, WM

zelos...@gmail.com schrieb am Mittwoch, 9. November 2022 um 14:41:02 UTC+1:
> onsdag 9 november 2022 kl. 13:57:38 UTC+1 skrev WM:
>
> >I prefer checking.
>
> You prefer "checking" through a flawed mean that proves nothing? That is exactly why

I have recognized that matheology is less useful than scientology or astrology.

> >"The infinite sequence thus defined has the peculiar property to contain all positive rational numbers and each of them only once at a determined place." [G. Cantor, letter to R. Lipschitz (19 Nov 1883)] Why not take it as Cantor calls it?
> Notice he says nothing about "checking" like you imagine it!

But I require only to find "each of them only once at a determined place".

Regards, WM

On Wednesday, 9 November 2022 at 10:59:58 UTC-4, WM wrote:
> Gus Gassmann schrieb am Mittwoch, 9. November 2022 um 13:34:07 UTC+1:
> > On Wednesday, 9 November 2022 at 05:54:33 UTC-4, WM wrote:
>
> > > You limit claim is nonsense. That should be clear to everyone. Man beachte diese an Klarheit nichts zu wünschen übrig lassenden Formulierungen: sämtliche, und jede an einer bestimmten Stelle, an einen bestimmten Platz, wobei keine einzige vergessen ist.
> > An infinite process is not finite,
> Therefore FISONs will always stay in tiny finite initial segments of ℕ.

No, you fucking imbecile. Every natural number, that is, every element of N, defines a FISON, whether you like it or not.

[...]

> Some proponents of set theory claim that the set theoretical limit has to be applied. But also if doing so, we come to the conclusion that all the O remain present in all definable matrices until "in the limit" these infinitely many O have to leave in trouble such that no individual leaves in a definable way. This implies that "in the limit" infinitely many fractions have to become indexed such that none of them can be checked.

I showed you exactly how the limit is to be applied: Pointwise to every element of the matrix. For every location (n, m) in row n and column m there is a smallest index k(n,m) (which actually comes from the Cantor mapping) when the 'O' in that location is changed to an 'X' --- and remains an 'X' forever after. So in every location you have a sequence that looks like (O, O , O..., O, X, X, ..., X). For the whole matrix you therefore get pointwise (or element-wise) convergence to M(oo)
X X X,...
X X X,...
X X X,...
....

Nothing mysterious about it at all, but it requires firing neurons.

Gus Gassmann schrieb am Mittwoch, 9. November 2022 um 16:58:23 UTC+1:
> On Wednesday, 9 November 2022 at 10:59:58 UTC-4, WM wrote:

> > Some proponents of set theory claim that the set theoretical limit has to be applied. But also if doing so, we come to the conclusion that all the O remain present in all definable matrices until "in the limit" these infinitely many O have to leave in trouble such that no individual leaves in a definable way. This implies that "in the limit" infinitely many fractions have to become indexed such that none of them can be checked.
> I showed you exactly how the limit is to be applied: Pointwise to every element of the matrix. For every location (n, m) in row n and column m there is a smallest index k(n,m) (which actually comes from the Cantor mapping) when the 'O' in that location is changed to an 'X' --- and remains an 'X' forever after. So in every location you have a sequence that looks like (O, O , O..., O, X, X, ..., X).

At every finite step k no O has been removed from the visible part of the matrix.

> For the whole matrix you therefore get pointwise (or element-wise) convergence to M(oo) =
>
> X X X,...
> X X X,...
> X X X,...
> ...
>
> Nothing mysterious about it at all, but it requires firing neurons.

Fact is: At every finite step k no O has been removed from the matrix. In your "limit" all O's have been removed from the visible part of the matrix. That means ℵo fractions have not been indexed at finite steps k.

Regards, WM

On 11/9/2022 3:51 AM, WM wrote:
> zelos...@gmail.com schrieb am Dienstag, 8. November 2022 um 13:54:14 UTC+1:
>> tisdag 8 november 2022 kl. 12:32:32 UTC+1 skrev WM:
>>> zelos...@gmail.com schrieb am Montag, 7. November 2022 um 12:37:16 UTC+1:
>>>
>>>> None of that proves anythign "dark"
>>> Where are the O's?
>>>
>> Those do not matter because thati s not how the bijection is constructed!
>
> But if a bijection existed, then it could be checked in this way.

you're "checking" with masking stickies Os and pasties Xs, shows a complete lack of Math skills.

your "checking" is a Swaparoodoodlefest, and destroys the matrix of rationals.

>
> Regards, WM

On Wednesday, 9 November 2022 at 12:31:11 UTC-4, WM wrote:
> Gus Gassmann schrieb am Mittwoch, 9. November 2022 um 16:58:23 UTC+1:
> > On Wednesday, 9 November 2022 at 10:59:58 UTC-4, WM wrote:
>
> > > Some proponents of set theory claim that the set theoretical limit has to be applied. But also if doing so, we come to the conclusion that all the O remain present in all definable matrices until "in the limit" these infinitely many O have to leave in trouble such that no individual leaves in a definable way. This implies that "in the limit" infinitely many fractions have to become indexed such that none of them can be checked.
> > I showed you exactly how the limit is to be applied: Pointwise to every element of the matrix. For every location (n, m) in row n and column m there is a smallest index k(n,m) (which actually comes from the Cantor mapping) when the 'O' in that location is changed to an 'X' --- and remains an 'X' forever after. So in every location you have a sequence that looks like (O, O , O..., O, X, X, ..., X).
> At every finite step k no O has been removed from the visible part of the matrix.
> > For the whole matrix you therefore get pointwise (or element-wise) convergence to M(oo) =
> >
> > X X X,...
> > X X X,...
> > X X X,...
> > ...
> >
> > Nothing mysterious about it at all, but it requires firing neurons.
> Fact is: At every finite step k no O has been removed from the matrix. In your "limit" all O's have been removed from the visible part of the matrix.. That means ℵo fractions have not been indexed at finite steps k.

Did I claim otherwise? You are too stupid to understand that lim(card{...}) =/= card(lim{...}). That is *YOUR* defect, not mine. Please FUCK OFF!

Gus Gassmann schrieb am Mittwoch, 9. November 2022 um 17:34:55 UTC+1:
> On Wednesday, 9 November 2022 at 12:31:11 UTC-4, WM wrote:
> >
> > Fact is: At every finite step k no O has been removed from the matrix. In your "limit" all O's have been removed from the visible part of the matrix. That means ℵo fractions have not been indexed at finite steps k..
> Did I claim otherwise?

Cantor does. A bijection requires it.

Regards, WM

On 11/9/2022 9:26 AM, WM wrote:
> zelos...@gmail.com schrieb am Mittwoch, 9. November 2022 um 14:41:02 UTC+1:
>> onsdag 9 november 2022 kl. 13:57:38 UTC+1 skrev WM:
>>
>>> I prefer checking.
>>
>> You prefer "checking" through a flawed mean that proves nothing? That is exactly why
>
> I have recognized that matheology is less useful than scientology or astrology.
>
>>> "The infinite sequence thus defined has the peculiar property to contain all positive rational numbers and each of them only once at a determined place." [G. Cantor, letter to R. Lipschitz (19 Nov 1883)] Why not take it as Cantor calls it?
>> Notice he says nothing about "checking" like you imagine it!
>
> But I require only to find "each of them only once at a determined place".
>
> Regards, WM

which Cantor already did.

You failed when you tried to HIDE each number in the matrix of rationals with O stickies, and X pasties, trying to COVER UP and HIDE numerical
relationships, then you mutilated and overwrote the matrix of rationals, in your efforts to deceive.

On Wednesday, 9 November 2022 at 12:37:37 UTC-4, WM wrote:
> Gus Gassmann schrieb am Mittwoch, 9. November 2022 um 17:34:55 UTC+1:
> > On Wednesday, 9 November 2022 at 12:31:11 UTC-4, WM wrote:
> > >
> > > Fact is: At every finite step k no O has been removed from the matrix.. In your "limit" all O's have been removed from the visible part of the matrix. That means ℵo fractions have not been indexed at finite steps k.
> > Did I claim otherwise?
> Cantor does. A bijection requires it.

You are a fucking liar and a moronic imbecile to boot.

An infinite set is not finite, and a finite set is not infinite. More is not claimed, and more is not required.

Gus Gassmann schrieb am Mittwoch, 9. November 2022 um 18:33:38 UTC+1:
> On Wednesday, 9 November 2022 at 12:37:37 UTC-4, WM wrote:
> > Gus Gassmann schrieb am Mittwoch, 9. November 2022 um 17:34:55 UTC+1:
> > > On Wednesday, 9 November 2022 at 12:31:11 UTC-4, WM wrote:
> > > >
> > > > Fact is: At every finite step k no O has been removed from the matrix. In your "limit" all O's have been removed from the visible part of the matrix. That means ℵo fractions have not been indexed at finite steps k.
> > > Did I claim otherwise?
> > Cantor does. A bijection requires it.

> An infinite set is not finite, and a finite set is not infinite. More is not claimed, and more is not required.

Limits are not accepted but every step for one item.

"If we think the numbers p/q in such an order [...] then every number p/q comes at an absolutely fixed place of a simple infinite sequence" [E. Zermelo: "Georg Cantor – Gesammelte Abhandlungen mathematischen und philosophischen Inhalts", Springer, Berlin (1932), S. 126]

"The infinite sequence thus defined has the peculiar property to contain all positiv rational numbers and each one of them only once at a determined place." [Cantor an Lipschitz (19 Nov 1883)]

"thus we get the epitome (ω) of all real algebraic numbers [...] and with respect to this order we can talk about the th algebraic number where not a single one from this epitome () has been forgotten. [E. Zermelo: "Georg Cantor – Gesammelte Abhandlungen mathematischen und philosophischen Inhalts", Springer, Berlin (1932) S. 116]

"such that every element of the set stands at a definite position of this sequence" [E. Zermelo: "Georg Cantor – Gesammelte Abhandlungen mathematischen und philosophischen Inhalts", Springer, Berlin (1932) S. 152]

The clearness of these expression is noteworthy: all and every, at an absolutely fixed place, at a definite position, not a single one has been forgotten. In particular no limits.

Regards, WM