Greg Cunt schrieb am Freitag, 1. Oktober 2021 um 00:11:04 UTC+2:
> On Thursday, September 30, 2021 at 9:08:41 PM UTC+2, WM wrote:
> > Greg Cunt schrieb am Dienstag, 28. September 2021 um 18:35:00 UTC+2:
> > >
> > > Due to von Neumann (in ZFC) IN just *IS* the set of all FISONs.
> > >
> > von Neumann was wrong.
> Huh?!
>
> No, there's nothing "wrong" with von Neumann's approach.
>
> That IN just *IS* the set of all FISONs follows TRIVIALLY from the definition of IN (due to von Neumann).

∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo.
You don't like mathematical proofs like this one?

Regards, WM

Jim Burns schrieb am Donnerstag, 30. September 2021 um 23:00:01 UTC+2:
> On 9/30/2021 3:12 PM, WM wrote:

> > If ℕ is actually infinite, then
> > ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo
> > shows that FISONs are not sufficient to fill it.
> Define

Why? Would you please read and comment the above statement?

> FE to be the collection of all and only FISON-enders.
>
> Is there any FISON-ender which is not-in FE?

Potentially infinite sets are changing.
>
> Is there anything in FE which is not a FISON-ender?

Potentially infinite sets are changing.

Regards, WM

On 10/1/2021 3:08 PM, Transfinity wrote:
> Jim Burns schrieb
> am Donnerstag, 30. September 2021 um 23:00:01 UTC+2:
>> On 9/30/2021 3:12 PM, WM wrote:

>>> If ℕ is actually infinite, then
>>> ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo
>>> shows that FISONs are not sufficient to fill it.
>>
>> Define
>
> Why?

You are determined not to see my definition of N.
So I call N something else.
I define the set FE of all and only FISON-enders.

The FISONs are sufficient to fill FE.

FE is recognizable as N by anyone who isn't determined
not to see.

Therefore,
the FISONs are sufficient to fill N.

> Would you please read and comment the above statement?

I'm happy to oblige:
You're wrong.

>> FE to be the collection of all and only FISON-enders.
>>
>> Is there any FISON-ender which is not-in FE?
>
> Potentially infinite sets are changing.

Whether something is a FISON-ender does not change.

Either
there is a collection {0,...,k} which
starts at 0, ends at k, and,
for each split of {0,...,k}, a crossing-pair j,j+1 exists,
or
there isn't.

>> Is there anything in FE which is not a FISON-ender?
>
> Potentially infinite sets are changing.

Whether something is a FISON-ender does not change.

Etc.

On 10/1/2021 2:03 PM, Transfinity wrote:
> Greg Cunt schrieb am Freitag, 1. Oktober 2021 um 00:11:04 UTC+2:
>> On Thursday, September 30, 2021 at 9:08:41 PM UTC+2, WM wrote:
>>> Greg Cunt schrieb am Dienstag, 28. September 2021 um 18:35:00 UTC+2:
>>>>
>>>> Due to von Neumann (in ZFC) IN just *IS* the set of all FISONs.
>>>>
>>> von Neumann was wrong.
>> Huh?!
>>
>> No, there's nothing "wrong" with von Neumann's approach.
>>
>> That IN just *IS* the set of all FISONs follows TRIVIALLY from the definition of IN (due to von Neumann).
>
> ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo.
> You don't like mathematical proofs like this one?

you must be joking, that is not a proof, dude.

>
> Regards, WM
>

Jim Burns schrieb am Freitag, 1. Oktober 2021 um 22:43:04 UTC+2:
> On 10/1/2021 3:08 PM, Transfinity wrote:

> >>> If ℕ is actually infinite, then
> >>> ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo
> >>> shows that FISONs are not sufficient to fill it.
> >>
> > Would you please read and comment the above statement?
> I'm happy to oblige:
> You're wrong.

You dismiss logic. Therefore any further discussion is useless.

> > Potentially infinite sets are changing.
> Whether something is a FISON-ender does not change.
>
You are in error, but your state is helpless. Therefore any further discussion is useless.

Regards, WM

On 10/2/2021 1:27 PM, WM wrote:
> Jim Burns schrieb am Freitag, 1. Oktober 2021 um 22:43:04 UTC+2:
>> On 10/1/2021 3:08 PM, Transfinity wrote:
>
>>>>> If ℕ is actually infinite, then
>>>>> ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo
>>>>> shows that FISONs are not sufficient to fill it.
>>>>
>>> Would you please read and comment the above statement?
>> I'm happy to oblige:
>> You're wrong.
>
> You dismiss logic. Therefore any further discussion is useless.
>
>>> Potentially infinite sets are changing.
>> Whether something is a FISON-ender does not change.
>>
> You are in error, but your state is helpless. Therefore any further discussion is useless.
>
> Regards, WM
>

"If ℕ is actually infinite, then
∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo
shows that FISONs are not sufficient to fill it."

*FIVE 5 Mistakes*

1. ℕ is infinite.
2. there is no If, Then relationship between the two.
3. there is no such thing as "_def" (beeps, flashes, hooves a hoofin, come on man!)
4. FISONs do not fill anything. they are fixed sets that do not change.
5. statement ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo is unrelated to "shows that FISONs are not sufficient to fill it."

fredag 1 oktober 2021 kl. 20:58:06 UTC+2 skrev WM:
> zelos...@gmail.com schrieb am Freitag, 1. Oktober 2021 um 06:59:41 UTC+2:
> > torsdag 30 september 2021 kl. 21:12:23 UTC+2 skrev WM:
>
> > >No. There is always an infinite remainder. The numbers of this remainder have no FISONs, because then they would not remain.
> >
> > ALL natural numbers are in a FISON. No exception and it is provably so.
> aleph_0 natural numbers are not in FISONs:
>
> ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo .
>
> Regards, WM

Empty assertion, every natural number can be found in a FISON

On Saturday, October 2, 2021 at 2:27:33 PM UTC-4, WM wrote:
> Jim Burns schrieb am Freitag, 1. Oktober 2021 um 22:43:04 UTC+2:
> > On 10/1/2021 3:08 PM, Transfinity wrote:
>
> > >>> If ℕ is actually infinite, then
> > >>> ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo
> > >>> shows that FISONs are not sufficient to fill it.
> > >>
> > > Would you please read and comment the above statement?
> > I'm happy to oblige:
> > You're wrong.
> You dismiss logic. Therefore any further discussion is useless.
> > > Potentially infinite sets are changing.
> > Whether something is a FISON-ender does not change.
> >
> You are in error, but your state is helpless. Therefore any further discussion is useless.
>
> Regards, WM

It is as if there is nothing left to push the boundary on other than the infinite quality of the natural number.
Therefore all concerned land here.
It is a shame that so much energy can go to such an end.
What is gained in this process?
If there is no consequence to the 'dark numbers' then what of this task?
Actual numbers are grey, such as the number of oranges on Earth at this moment.
Even the number of humans will have to be accepted as a grey value.
The number of planets in the solar system is provably even a grey number.
A carefully controlled attempt at producing a quartz ball exposed that even the number of atoms in that ball after careful polishing was wavering.
This of course goes back to the daze of Uncle Al.
May his quartz balls forever shrink in peace.
The level of control which mathematicians assume or grant themselves is above and beyond realistic.
In that this proves mathematics as fiction you all must join science fiction here.
This is alright. You are not alone. Numerous branches are practicing thus.
We are all gambling.
Grey numbers.
Epsilon/Delta unchallenged.
In time we have no assurance of any physically controlled system.
To arrive in a time analysis is effectively a call back to reality.
Address the false divide of physics, philosophy, and mathematics.
Return to the ways of old.
Academic fraud is upon you.
Wee humans ought to cover more ground while we still can.
Polysign is the way forward.
http://bandtechnology.com/PolySigned
Get n-ary, sir.

zelos...@gmail.com schrieb am Montag, 4. Oktober 2021 um 07:37:24 UTC+2:
> > aleph_0 natural numbers are not in FISONs:
> >
> > ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo .

> Empty assertion, every natural number can be found in a FISON

Every natural number that can be found in a FISON fails to complete the set ℕ of ℵo natural numbers. Numbers completing the set ℕ cannot be found. This set however can be completed because there is a bijection ℕ <--> ℕ that concerns all natural numbers. Hence more numbers must exist than can be found.

Regards, WM

torsdag 7 oktober 2021 kl. 11:07:11 UTC+2 skrev WM:
> zelos...@gmail.com schrieb am Montag, 4. Oktober 2021 um 07:37:24 UTC+2:
>
> > > aleph_0 natural numbers are not in FISONs:
> > >
> > > ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo .
> > Empty assertion, every natural number can be found in a FISON
> Every natural number that can be found in a FISON fails to complete the set ℕ of ℵo natural numbers. Numbers completing the set ℕ cannot be found. This set however can be completed because there is a bijection ℕ <--> ℕ that concerns all natural numbers. Hence more numbers must exist than can be found.
>
> Regards, WM
empty meaningless assertion again

zelos...@gmail.com schrieb am Donnerstag, 7. Oktober 2021 um 19:09:25 UTC+2:
> torsdag 7 oktober 2021 kl. 11:07:11 UTC+2 skrev WM:
> > zelos...@gmail.com schrieb am Montag, 4. Oktober 2021 um 07:37:24 UTC+2:
> >
> > > > aleph_0 natural numbers are not in FISONs:
> > > >
> > > > ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo .
> > > Empty assertion, every natural number can be found in a FISON
> > Every natural number that can be found in a FISON fails to complete the set ℕ of ℵo natural numbers. Numbers completing the set ℕ cannot be found. This set however can be completed because there is a bijection ℕ <--> ℕ that concerns all natural numbers. Hence more numbers must exist than can be found.

> empty meaningless assertion again

So appears everything that is not understood by not learned persons.

Every natural number of a FISON belongs to a set the cardinality of which is much less than ℵo. But there must be natural numbers filling a set of cardinality ℵo.

Regards, WM

fredag 8 oktober 2021 kl. 11:39:21 UTC+2 skrev WM:
> zelos...@gmail.com schrieb am Donnerstag, 7. Oktober 2021 um 19:09:25 UTC+2:
> > torsdag 7 oktober 2021 kl. 11:07:11 UTC+2 skrev WM:
> > > zelos...@gmail.com schrieb am Montag, 4. Oktober 2021 um 07:37:24 UTC+2:
> > >
> > > > > aleph_0 natural numbers are not in FISONs:
> > > > >
> > > > > ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo .
> > > > Empty assertion, every natural number can be found in a FISON
> > > Every natural number that can be found in a FISON fails to complete the set ℕ of ℵo natural numbers. Numbers completing the set ℕ cannot be found. This set however can be completed because there is a bijection ℕ <--> ℕ that concerns all natural numbers. Hence more numbers must exist than can be found.
> > empty meaningless assertion again
>
> So appears everything that is not understood by not learned persons.
>
> Every natural number of a FISON belongs to a set the cardinality of which is much less than ℵo. But there must be natural numbers filling a set of cardinality ℵo.
>
> Regards, WM

>So appears everything that is not understood by not learned persons.

No, it is empty because you assert shit without justification.

It is meaningless because most of your shit has no defined meaning in mathematics.

>Every natural number of a FISON belongs to a set the cardinality of which is much less than ℵo. But there must be natural numbers filling a set of cardinality ℵo

The natural numbers that comes after those in the FISON, there are no magical ones, it is all natural numbers and the union of all your FISONs is N

On Friday, October 8, 2021 at 5:39:21 AM UTC-4, WM wrote:
> zelos...@gmail.com schrieb am Donnerstag, 7. Oktober 2021 um 19:09:25 UTC+2:
> > torsdag 7 oktober 2021 kl. 11:07:11 UTC+2 skrev WM:
> > > zelos...@gmail.com schrieb am Montag, 4. Oktober 2021 um 07:37:24 UTC+2:
> > >
> > > > > aleph_0 natural numbers are not in FISONs:
> > > > >
> > > > > ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo .
> > > > Empty assertion, every natural number can be found in a FISON
> > > Every natural number that can be found in a FISON fails to complete the set ℕ of ℵo natural numbers. Numbers completing the set ℕ cannot be found. This set however can be completed because there is a bijection ℕ <--> ℕ that concerns all natural numbers. Hence more numbers must exist than can be found.
> > empty meaningless assertion again
>
> So appears everything that is not understood by not learned persons.
>
> Every natural number of a FISON belongs to a set the cardinality of which is much less than ℵo. But there must be natural numbers filling a set of cardinality ℵo.
>

WTF? Still spinning your wheels, eh, Mucke? After several decades of fruitless endeavor, it seems you are still no closer to demonstrating any inconsistencies in the ZFC axioms of set theory. If you can't dazzle them with brilliance, baffle them with bullshit, right, Mucke? HA, HA, HA!!!

Dan

zelos...@gmail.com schrieb am Freitag, 8. Oktober 2021 um 12:50:24 UTC+2:
> fredag 8 oktober 2021 kl. 11:39:21 UTC+2 skrev WM:

> >Every natural number of a FISON belongs to a set the cardinality of which is much less than ℵo. But there must be natural numbers filling a set of cardinality ℵo

> The natural numbers that comes after those in the FISON,

They are in FISONs too and cannot fill the gap between |N and all FISONs:
∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo.

> the union of all your FISONs is N

The union of insufficient FISONs cannot bridge the abyss of card ℵo..

Regards, WM