On Saturday, 16 April 2022 at 10:55:56 UTC-3, WM wrote:
[...]
> Although as many terms as you like of Cantor's sequence will be gathered in the first column, the desired result
> 1/1, __, __, __, ...
> 1/2, __, __, __, ...
> 1/3, __, __, __, ...
> 2/2, __, __, __, ...
> ...

Blah, blah, blah. That is the result *YOU* desire. That this is a hairbrained undertaking is clear to everyone who looks at it, but that in your single-minded stupidity you can't even *conceive* of a different result, namely the proper *LIMIT* of the sequence:

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

and still thinking you can call yourself a mathematician should be a source of shame and embarrassment to you. That it isn't marks you as a *FUCKING IMBECILE*. And now spare us all more of this same *BULLSHIT* and piss off.

On Saturday, April 16, 2022 at 10:55:56 AM UTC-3, WM wrote:
> William schrieb am Freitag, 15. April 2022 um 23:34:09 UTC+2:
> > On Friday, April 15, 2022 at 5:45:58 PM UTC-3, WM wrote:
>
> > > Cardinality would require a mapping of all elements. That is impossible for infinite sets.
> > Piffle. The identity function (which exists of any set that exist, e.g. the Peano set of natural numbers) is a bijection
> It appears so to simple minds, but there is always a dark part that cannot be mapped.

Piffle. A Peano set cannon contain "dark" elements (trivial induction)

-William Hughes

horand....@gmail.com schrieb am Samstag, 16. April 2022 um 16:58:52 UTC+2:
> On Saturday, 16 April 2022 at 10:55:56 UTC-3, WM wrote:
> [...]
> > Although as many terms as you like of Cantor's sequence will be gathered in the first column, the desired result
> > 1/1, __, __, __, ...
> > 1/2, __, __, __, ...
> > 1/3, __, __, __, ...
> > 2/2, __, __, __, ...
> > ...
> That is the result *YOU* desire.

No it is claimed by Cantor that all positive fractions will be collected in the first column.

> That this is a hairbrained undertaking is clear to everyone who looks at it,

It should be so, but many believe in this trash.

> the proper *LIMIT* of the sequence:
>
> 1/1, oo, oo, oo, ...
> 1/2, oo, oo, oo, ...
> 1/3, oo, oo, oo, ...
> 2/2, oo, oo, oo, ...
> ...

which oo is the first one reached. Note that if you want to establish a second oo, then the first one must be realized or finished. But then all natural numbers have been exhausted.

Regards, WM

William schrieb am Samstag, 16. April 2022 um 18:01:52 UTC+2:
> On Saturday, April 16, 2022 at 10:55:56 AM UTC-3, WM wrote:
> > William schrieb am Freitag, 15. April 2022 um 23:34:09 UTC+2:
> > > On Friday, April 15, 2022 at 5:45:58 PM UTC-3, WM wrote:
> >
> > > > Cardinality would require a mapping of all elements. That is impossible for infinite sets.
> > > Piffle. The identity function (which exists of any set that exist, e.g. the Peano set of natural numbers) is a bijection
> > It appears so to simple minds, but there is always a dark part that cannot be mapped.
> A Peano set cannon contain "dark" elements (trivial induction)

Induction cannot reach omega. Induction cannot remove ℵo dark numbers before omega. Does every defined term have ℵo successors, ℵo of which are undefined, or not?

Regards, WM

On Sunday, 17 April 2022 at 05:59:27 UTC-3, WM wrote:
[...]
> > 1/1, oo, oo, oo, ...
> > 1/2, oo, oo, oo, ...
> > 1/3, oo, oo, oo, ...
> > 2/2, oo, oo, oo, ...
> > ...
> which oo is the first one reached. Note that if you want to establish a second oo, then the first one must be realized or finished. But then all natural numbers have been exhausted.

*NO* oo is "reached", any more than 0 is "reached" when you step through the sequence 1/1, 1/2, 1/3, 1/4, ... Nonetheless 0 is the *LIMIT*, and

> > 1/1, oo, oo, oo, ...
> > 1/2, oo, oo, oo, ...
> > 1/3, oo, oo, oo, ...
> > 2/2, oo, oo, oo, ...
> > ...

is the limit of your sequence of matrices.

On Sunday, April 17, 2022 at 6:02:25 AM UTC-3, WM wrote:
> William schrieb am Samstag, 16. April 2022 um 18:01:52 UTC+2:
> > On Saturday, April 16, 2022 at 10:55:56 AM UTC-3, WM wrote:
> > > William schrieb am Freitag, 15. April 2022 um 23:34:09 UTC+2:
> > > > On Friday, April 15, 2022 at 5:45:58 PM UTC-3, WM wrote:
> > >
> > > > > Cardinality would require a mapping of all elements. That is impossible for infinite sets.
> > > > Piffle. The identity function (which exists of any set that exist, e.g. the Peano set of natural numbers) is a bijection
> > > It appears so to simple minds, but there is always a dark part that cannot be mapped.
> > Piffle. A Peano set cannon contain "dark" elements (trivial induction)
> Induction cannot reach omega.

Piffle. Omega is not an element of N_p. Induction shows something about every "element" of N_p. In particular, one of the things is shows is that if n is an element of N_p then n is not "dark"

> ... every defined term have ℵo successors, ℵo of which are undefined

Piffle, "definied" us just another one of you many many ways of saying "will be written down": Every term of N_p that "will be written down" has a ℵo successors, none of which are "dark" and ℵo of which "will not be written down".

--
William Hughes

On 4/17/2022 3:59 AM, WM wrote:
>
> horand....@gmail.com schrieb am Samstag, 16. April 2022 um 16:58:52 UTC+2:
>> On Saturday, 16 April 2022 at 10:55:56 UTC-3, WM wrote:
>> [...]
>>> Although as many terms as you like of Cantor's sequence will be gathered in the first column, the desired result
>>> 1/1, __, __, __, ...
>>> 1/2, __, __, __, ...
>>> 1/3, __, __, __, ...
>>> 2/2, __, __, __, ...
>>> ...
>> That is the result *YOU* desire.
>
> No it is claimed by Cantor that all positive fractions will be collected in the first column.
>
>> That this is a hairbrained undertaking is clear to everyone who looks at it,
>
> It should be so, but many believe in this trash.
>
>> the proper *LIMIT* of the sequence:
>>
>> 1/1, oo, oo, oo, ...
>> 1/2, oo, oo, oo, ...
>> 1/3, oo, oo, oo, ...
>> 2/2, oo, oo, oo, ...
>> ...
>
> which oo is the first one reached. Note that if you want to establish a second oo, then the first one must be realized or finished. But then all natural numbers have been exhausted.
>
> Regards, WM

no one believes you, nor your intentional mess above, which does not make any sense, and you cant explain it.

Face it:

WM's switcharoo is obviously wrong, and WM has proved Cantor is correct.

On 4/17/2022 4:02 AM, WM wrote:
> William schrieb am Samstag, 16. April 2022 um 18:01:52 UTC+2:
>> On Saturday, April 16, 2022 at 10:55:56 AM UTC-3, WM wrote:
>>> William schrieb am Freitag, 15. April 2022 um 23:34:09 UTC+2:
>>>> On Friday, April 15, 2022 at 5:45:58 PM UTC-3, WM wrote:
>>>
>>>>> Cardinality would require a mapping of all elements. That is impossible for infinite sets.
>>>> Piffle. The identity function (which exists of any set that exist, e.g. the Peano set of natural numbers) is a bijection
>>> It appears so to simple minds, but there is always a dark part that cannot be mapped.
>> A Peano set cannon contain "dark" elements (trivial induction)
>
> Induction cannot reach omega.

only if you stop!

> Induction cannot remove ℵo dark numbers before omega.

All numbers are included by induction. (unless you stop at k).

> Does every defined term have ℵo successors, ℵo of which are undefined, or not?

did you define every term using your beeps, raps, taps, lights flashing ?

>
> Regards, WM

horand....@gmail.com schrieb am Sonntag, 17. April 2022 um 16:07:40 UTC+2:
> On Sunday, 17 April 2022 at 05:59:27 UTC-3, WM wrote:
> [...]
> > > 1/1, oo, oo, oo, ...
> > > 1/2, oo, oo, oo, ...
> > > 1/3, oo, oo, oo, ...
> > > 2/2, oo, oo, oo, ...
> > > ...
> > which oo is the first one reached. Note that if you want to establish a second oo, then the first one must be realized or finished. But then all natural numbers have been exhausted.
> *NO* oo is "reached", any more than 0 is "reached" when you step through the sequence 1/1, 1/2, 1/3, 1/4, ... Nonetheless 0 is the *LIMIT*, and
> > > 1/1, oo, oo, oo, ...
> > > 1/2, oo, oo, oo, ...
> > > 1/3, oo, oo, oo, ...
> > > 2/2, oo, oo, oo, ...
> > > ...
> is the limit of your sequence of matrices.

Nonsense. There is no limit in enumerating the rationals but uniqueness and completeness:

"Wenn zwei wohldefinierte Mannigfaltigkeiten M und N sich eindeutig und vollständig, Element für Element, einander zuordnen lassen (was, wenn es auf eine Art möglich ist, immer auch noch auf viele andere Weisen geschehen kann), so möge für das Folgende die Ausdrucksweise gestattet sein, daß diese Mannigfaltigkeiten gleiche Mächtigkeit haben, oder auch, daß sie äquivalent sind." [Cantor, p. 119]

Who has confused your brain with wischi-waschi limits?

Regards, WM

William schrieb am Sonntag, 17. April 2022 um 16:07:55 UTC+2:
> On Sunday, April 17, 2022 at 6:02:25 AM UTC-3, WM wrote:
> > William schrieb am Samstag, 16. April 2022 um 18:01:52 UTC+2:
> > > On Saturday, April 16, 2022 at 10:55:56 AM UTC-3, WM wrote:
> > > > William schrieb am Freitag, 15. April 2022 um 23:34:09 UTC+2:
> > > > > On Friday, April 15, 2022 at 5:45:58 PM UTC-3, WM wrote:
> > > >
> > > > > > Cardinality would require a mapping of all elements. That is impossible for infinite sets.
> > > > > Piffle. The identity function (which exists of any set that exist, e.g. the Peano set of natural numbers) is a bijection
> > > > It appears so to simple minds, but there is always a dark part that cannot be mapped.
> > > Piffle. A Peano set cannon contain "dark" elements (trivial induction)
> > Induction cannot reach omega.
>
> Piffle. Omega is not an element of N_p.

But its ℵo predecessors are natural numbers.

> Induction shows something about every "element" of N_p. In particular, one of the things is shows is that if n is an element of N_p then n is not "dark"
>
> > ... every defined term have ℵo successors, ℵo of which are undefined
>
> "definied" us just another one of you many many ways of saying "will be written down":

No, it is a way to name natural numbers according to Peano.

> Every term of N_p that "will be written down" has a ℵo successors, none of which are "dark"

Why can you not remove them? All natural numbers which are not dark, can be named. But ℵo successors cannot be named because they remain to be undefined, not named numbers forever.

Regards, WM

On Sunday, 17 April 2022 at 13:59:58 UTC-3, WM wrote:
> horand....@gmail.com schrieb am Sonntag, 17. April 2022 um 16:07:40 UTC+2:
> > On Sunday, 17 April 2022 at 05:59:27 UTC-3, WM wrote:
> > [...]
> > > > 1/1, oo, oo, oo, ...
> > > > 1/2, oo, oo, oo, ...
> > > > 1/3, oo, oo, oo, ...
> > > > 2/2, oo, oo, oo, ...
> > > > ...
> > > which oo is the first one reached. Note that if you want to establish a second oo, then the first one must be realized or finished. But then all natural numbers have been exhausted.
> > *NO* oo is "reached", any more than 0 is "reached" when you step through the sequence 1/1, 1/2, 1/3, 1/4, ... Nonetheless 0 is the *LIMIT*, and
> > > > 1/1, oo, oo, oo, ...
> > > > 1/2, oo, oo, oo, ...
> > > > 1/3, oo, oo, oo, ...
> > > > 2/2, oo, oo, oo, ...
> > > > ...
> > is the limit of your sequence of matrices.
> Nonsense. There is no limit in enumerating the rationals

You fucking moron! In *ANY* infinite sequential process such as the one *YOU* introduced, *because* it cannot be finished in stepwise fashion (you'll perhaps remember that there are infinitely many steps), you have to think about any limiting behaviour the process might exhibit. With your matrices, it is clear what the limit is. Your denying its existence is based, once again, on your utter ignorance of all things mathematical.

And now, since you have clearly run out of any potential for thought of any kind, please FUCK OFF.

On 4/17/2022 11:59 AM, WM wrote:
> horand....@gmail.com schrieb am Sonntag, 17. April 2022 um 16:07:40 UTC+2:
>> On Sunday, 17 April 2022 at 05:59:27 UTC-3, WM wrote:
>> [...]
>>>> 1/1, oo, oo, oo, ...
>>>> 1/2, oo, oo, oo, ...
>>>> 1/3, oo, oo, oo, ...
>>>> 2/2, oo, oo, oo, ...
>>>> ...
>>> which oo is the first one reached. Note that if you want to establish a second oo, then the first one must be realized or finished. But then all natural numbers have been exhausted.
>> *NO* oo is "reached", any more than 0 is "reached" when you step through the sequence 1/1, 1/2, 1/3, 1/4, ... Nonetheless 0 is the *LIMIT*, and
>>>> 1/1, oo, oo, oo, ...
>>>> 1/2, oo, oo, oo, ...
>>>> 1/3, oo, oo, oo, ...
>>>> 2/2, oo, oo, oo, ...
>>>> ...
>> is the limit of your sequence of matrices.
>
> Nonsense. There is no limit in enumerating the rationals but uniqueness and completeness:
>
> "Wenn zwei wohldefinierte Mannigfaltigkeiten M und N sich eindeutig und vollständig, Element für Element, einander zuordnen lassen (was, wenn es auf eine Art möglich ist, immer auch noch auf viele andere Weisen geschehen kann), so möge für das Folgende die Ausdrucksweise gestattet sein, daß diese Mannigfaltigkeiten gleiche Mächtigkeit haben, oder auch, daß sie äquivalent sind." [Cantor, p. 119]
>
> Who has confused your brain with wischi-waschi limits?
>
> Regards, WM

translation:

"If two well-defined manifolds M and N can be clearly and completely assigned to each other, element by element (which, if it is possible in one way,
can always be done in many other ways), then for the following the expression may be permitted that these manifolds have the same power, or that they
are equivalent." [Cantor, p. 119]

*which has NOTHING to do with your Intentional Fakery butcher switcharoo matrix spew*

you cant even read Cantor right.

On Sunday, April 17, 2022 at 2:05:57 PM UTC-3, WM wrote:
> All natural numbers which are not dark, can be named.

Piffle. Repeating this piece of nonsense does not make it true, "can be named" is another one of your many many ways of saying "will written down". But induction works for every element of N_p. So no element of N_p is dark, however not every element of N_p "will be written down".

--
William Hughes

horand....@gmail.com schrieb am Sonntag, 17. April 2022 um 20:05:40 UTC+2:

> > > > > 1/1, oo, oo, oo, ...
> > > > > 1/2, oo, oo, oo, ...
> > > > > 1/3, oo, oo, oo, ...
> > > > > 2/2, oo, oo, oo, ...
> > > > > ...
> > > is the limit of your sequence of matrices.
> > Nonsense. There is no limit in enumerating the rationals
> In *ANY* infinite sequential process such as the one *YOU* introduced, *because* it cannot be finished in stepwise fashion (you'll perhaps remember that there are infinitely many steps), you have to think about any limiting behaviour the process might exhibit.

No, the point is that it goes on and on with no obstacle: "und es erfährt daher der aus unsrer Regel resultierende Zuordnungsprozeß keinen Stillstand." [Cantor, p. 239]

Just this happens here: Never more fractions than before are enumerated.

Regards, WM

William schrieb am Sonntag, 17. April 2022 um 20:28:12 UTC+2:
> But induction works for every element of N_p.

It shows: Every element of N_p belongs to a finite set and has infinitely many sucessors.

Regards, WM

On 4/18/2022 10:32 AM, WM wrote:
> horand....@gmail.com schrieb am Sonntag, 17. April 2022 um 20:05:40 UTC+2:
>
>>>>>> 1/1, oo, oo, oo, ...
>>>>>> 1/2, oo, oo, oo, ...
>>>>>> 1/3, oo, oo, oo, ...
>>>>>> 2/2, oo, oo, oo, ...
>>>>>> ...
>>>> is the limit of your sequence of matrices.
>>> Nonsense. There is no limit in enumerating the rationals
>> In *ANY* infinite sequential process such as the one *YOU* introduced, *because* it cannot be finished in stepwise fashion (you'll perhaps remember that there are infinitely many steps), you have to think about any limiting behaviour the process might exhibit.
>
> No, the point is that it goes on and on with no obstacle: "und es erfährt daher der aus unsrer Regel resultierende Zuordnungsprozeß keinen Stillstand." [Cantor, p. 239]

we all ready know that...

>
> Just this happens here: Never more fractions than before are enumerated.

No, all fractions are enumerated. If you have a doubt about a fractin, just use the formula, AND it is online too.

If you dont think so, it is because you stopped at k, stopped in the middle, just read the quotes from Cantor you posted.

>
> Regards, WM

On Monday, 18 April 2022 at 12:33:01 UTC-3, WM wrote:
> horand....@gmail.com schrieb am Sonntag, 17. April 2022 um 20:05:40 UTC+2:
>
> > > > > > 1/1, oo, oo, oo, ...
> > > > > > 1/2, oo, oo, oo, ...
> > > > > > 1/3, oo, oo, oo, ...
> > > > > > 2/2, oo, oo, oo, ...
> > > > > > ...
> > > > is the limit of your sequence of matrices.
> > > Nonsense. There is no limit in enumerating the rationals
> > In *ANY* infinite sequential process such as the one *YOU* introduced, *because* it cannot be finished in stepwise fashion (you'll perhaps remember that there are infinitely many steps), you have to think about any limiting behaviour the process might exhibit.
> No, the point is that it goes on and on with no obstacle: "und es erfährt daher der aus unsrer Regel resultierende Zuordnungsprozeß keinen Stillstand." [Cantor, p. 239]

That is exactly my point, too, whether your brain functions are sufficient still to grasp that or not. The stepwise process does not end. However, the stepwise process defined by the sequence 1/1, 1/2, 1/3, 1/4, ... does not end, either. And yet it does have a *LIMIT*. To *EVERY* stepwise infinite process one must study the limiting behavior. That you are TOO STUPID to grasp any of this marks *YOU* as the idiot. And now, kindly *FUCK OFF*.

On Monday, April 18, 2022 at 12:35:14 PM UTC-3, WM wrote:
> William schrieb am Sonntag, 17. April 2022 um 20:28:12 UTC+2:
> > But induction works for every element of N_p.
> It shows: Every element of N_p belongs to a finite set and has infinitely many sucessors.

So what? Each of the infinitely many successors is an element of N_p and, as induction works for every element of N_p, we know that all infinitely many successors are not "dark".

--
William Hughes

torsdag 14 april 2022 kl. 13:30:41 UTC+2 skrev WM:
> William schrieb am Mittwoch, 13. April 2022 um 23:41:11 UTC+2:
> > On Wednesday, April 13, 2022 at 5:22:05 PM UTC-3, WM wrote:
> > > William schrieb am Mittwoch, 13. April 2022 um 21:07:30 UTC+2:
> >
> > >You can only notice the absence of natnumbers in the intersection
> > And thus, be definition of the intersection, the intersection in empty.
> But that is contrary to mathematics.

Nope, it is according to mathematics. What it is is against is your CRANKERY.

> > >
> > > But you should be able to note that infinite inclusion-monotonic sets would not have an empty intersection.
> > Nope, this is trivially false for a set with no miminum.
> The minimum is infinite for infinite endsegments. It is larger than any finite number of natural numbers. Therefore there are infinitely many natural numbers inside.
>
> Regards, WM

torsdag 14 april 2022 kl. 14:05:20 UTC+2 skrev WM:
> horand....@gmail.com schrieb am Donnerstag, 14. April 2022 um 12:35:36 UTC+2:
> > On Wednesday, 13 April 2022 at 17:17:47 UTC-3, WM wrote:
> > > FromTheRafters schrieb am Mittwoch, 13. April 2022 um 21:02:51 UTC+2:
> > > > It happens that WM formulated :
> > > > > Both can be named inclusion-monotonic, one ascending, the other descending.
> > > > Descending from infinity?
> > > No. The FISONs are ascending by number of elements: 1, 2, 3, ...
> > > The endsegments are descending by number of elements: |ℕ|, |ℕ| - 1, |ℕ| - 2, ...
> > Crackpottery. |ℕ| - 1 = aleph_0 - 1 = aleph_0 = |ℕ|.
> Is ℕ a constant or not? If ℕ is a constant, then |ℕ| is a constant too.
> >
> > But the two statements above make it clear how your demented mind works: You think that the sequence of sizes of FISONs goes something like
> > 1, 2, 3, ..., |ℕ| - 2, |ℕ| - 1, |ℕ|.
> No, that is your mind. The sequence of FISONs goes 1, 2, 3, ... . Above, all is dark. That's why |ℕ| cannot be expressed by natural numbers, neither can |ℕ| - 1. But they are different since |ℕ| - 1 < |ℕ|.

False, in cardinal arithmetic |ℕ| - 1 = |ℕ|

> > So then, tell us: which is the first infinite FISON?
> There is none.
> > Likewise: What would a finite end segment look like? Name one!
> They are dark. That's why transfinity needs dark numbers.
>
> Regards, WM

horand....@gmail.com schrieb am Montag, 18. April 2022 um 18:24:04 UTC+2:
> On Monday, 18 April 2022 at 12:33:01 UTC-3, WM wrote:
> > horand....@gmail.com schrieb am Sonntag, 17. April 2022 um 20:05:40 UTC+2:
> >
> > > > > > > 1/1, oo, oo, oo, ...
> > > > > > > 1/2, oo, oo, oo, ...
> > > > > > > 1/3, oo, oo, oo, ...
> > > > > > > 2/2, oo, oo, oo, ...
> > > > > > > ...
> > > > > is the limit of your sequence of matrices.
> > > > Nonsense. There is no limit in enumerating the rationals
> > > In *ANY* infinite sequential process such as the one *YOU* introduced, *because* it cannot be finished in stepwise fashion (you'll perhaps remember that there are infinitely many steps), you have to think about any limiting behaviour the process might exhibit.
> > No, the point is that it goes on and on with no obstacle: "und es erfährt daher der aus unsrer Regel resultierende Zuordnungsprozeß keinen Stillstand." [Cantor, p. 239]
> That is exactly my point, too,

It is not filling the matrix places by oo.

> The stepwise process does not end. However, the stepwise process defined by the sequence 1/1, 1/2, 1/3, 1/4, ... does not end, either. And yet it does have a *LIMIT*.

which is not reached.

> To *EVERY* stepwise infinite process one must study the limiting behavior..

I did. It is this: Exchanging X and O will never change the numbers of X's and O's. That is the "limit-behaviour".

Regards, WM

William schrieb am Montag, 18. April 2022 um 18:40:41 UTC+2:
> On Monday, April 18, 2022 at 12:35:14 PM UTC-3, WM wrote:
> > William schrieb am Sonntag, 17. April 2022 um 20:28:12 UTC+2:
> > > But induction works for every element of N_p.
> > It shows: Every element of N_p belongs to a finite set and has infinitely many sucessors.
> So what? Each of the infinitely many successors is an element of N_p and, as induction works for every element of N_p, we know that all infinitely many successors are not "dark".

That is potential infinity. It is not in contradiction with the fact that every element of N_p has ℵo successors, ℵo of which are dark because they cannot be named.

Regards, WM

zelos...@gmail.com schrieb am Dienstag, 19. April 2022 um 09:38:32 UTC+2:
> torsdag 14 april 2022 kl. 13:30:41 UTC+2 skrev WM:
> > William schrieb am Mittwoch, 13. April 2022 um 23:41:11 UTC+2:
> > > On Wednesday, April 13, 2022 at 5:22:05 PM UTC-3, WM wrote:
> > > > William schrieb am Mittwoch, 13. April 2022 um 21:07:30 UTC+2:
> > >
> > > >You can only notice the absence of natnumbers in the intersection
> > > And thus, be definition of the intersection, the intersection in empty.
> > But that is contrary to mathematics.
>
> Nope, it is according to mathematics.

Non-empty endsegments have a nonempty intersection with all their precedessors. All definable endsegments are predecessors of non-empty endsegments. This fact cannot be countered by quantifier magic.

Regards, WM

zelos...@gmail.com schrieb am Dienstag, 19. April 2022 um 09:39:46 UTC+2:
> torsdag 14 april 2022 kl. 14:05:20 UTC+2 skrev WM:

> > Is ℕ a constant or not? If ℕ is a constant, then |ℕ| is a constant too.

> > The sequence of FISONs goes 1, 2, 3, ... . Above, all is dark. That's why |ℕ| cannot be expressed by natural numbers, neither can |ℕ| - 1. But they are different since |ℕ| - 1 < |ℕ|.
>
> False, in cardinal arithmetic |ℕ| - 1 = |ℕ|

That is why cardinal arithmetic is false.

Regards, WM

On Tuesday, 19 April 2022 at 12:29:56 UTC-3, WM wrote:
> horand....@gmail.com schrieb am Montag, 18. April 2022 um 18:24:04 UTC+2:
[...]
> > The stepwise process does not end. However, the stepwise process defined by the sequence 1/1, 1/2, 1/3, 1/4, ... does not end, either. And yet it does have a *LIMIT*.
> which is not reached.

Congratulations. Yes, the limit is not reached, in the same way that the limit 0 is not reached by the sequence 1/1, 1/2, 1/3, 1/4, ... . Nonetheless, it is the limit. I repeat for the umpteenth time: You have NO FUCKING CLUE about limits.