On 4/3/2022 1:41 PM, WM wrote:
> William schrieb am Samstag, 2. April 2022 um 22:11:59 UTC+2:
>> On Saturday, April 2, 2022 at 4:08:30 PM UTC-3, WM wrote:
>>
>>> Every union of FISONs has a last element.
>> Nope. The union of all FISONs is an infinite set. There is no such thing as a "Potentially infinite set".
>
> All that can be unioned from the sequence of FISONs has already been unioned in the sequence of FISONs. But nothing there is infinite. Therefore a final union cannot result in an infinite set.
>
> Regards, WM

there is no last FISON.

The union of all FISONs is an infinite set.

Each natural number is a finite element, the union of all natural numbers is an infinite set.

Are we clear yet ?

sergio schrieb:

> On 4/3/2022 1:41 PM, WM wrote:
>> William schrieb am Samstag, 2. April 2022 um 22:11:59 UTC+2:
>>> On Saturday, April 2, 2022 at 4:08:30 PM UTC-3, WM wrote:
>>>
>>>> Every union of FISONs has a last element.
>>> Nope. The union of all FISONs is an infinite set. There is no such thing as a "Potentially infinite set".
>>
>> All that can be unioned from the sequence of FISONs has already been unioned in the sequence of FISONs. But nothing there is infinite. Therefore a final union cannot result in an infinite set.
>>
>> Regards, WM
>
>
> there is no last FISON.
>
> The union of all FISONs is an infinite set.
>
>
>
> Each natural number is a finite element, the union of all natural numbers is an infinite set.
>
>
> Are we clear yet ?

We've heard that here at least a dozen times but WM does not accept infinity.
Because nature is finite it is at least a disgrace to teach infinity.

On Sunday, April 3, 2022 at 6:49:09 PM UTC-3, Tom Bola wrote:

> We've heard that here at least a dozen times but WM does not accept infinity.

Indeed, and as has been made clear for many years, this in itself is in no way wrong. But WM's claim that infinite sets lead to contradictions is wrong. His arguments involving FISONs all have the same pattern. He assumes the Axiom of infinity is false (e.g. by stating that any set of FISONs has a largest element) and then goes on to show that under this assumption the Axiom of infinity is false. Don't stop the presses!

--
William Hughes

On Sunday, 3 April 2022 at 21:42:04 UTC+3, WM wrote:
> William schrieb am Samstag, 2. April 2022 um 22:11:59 UTC+2:
> > On Saturday, April 2, 2022 at 4:08:30 PM UTC-3, WM wrote:
> >
> > > Every union of FISONs has a last element.
> > Nope. The union of all FISONs is an infinite set. There is no such thing as a "Potentially infinite set".
> All that can be unioned from the sequence of FISONs has already been unioned in the sequence of FISONs. But nothing there is infinite. Therefore a final union cannot result in an infinite set.

What I must point out here for the sake of posterity:

Misguided thought is not genetic, rather it is is nurtured by society. Every human has the potential to master mathematics, but there are those who cannot cover their knowledge gaps with faith. Typically the latter kind are more intelligent and since they do not see any reason in mainstream mythmatics, they lose interest and pursue different paths. This is a shame and ultimately a loss to the human race because
no doubt these individuals could have done great things.

The garbage concept of infinity is a virus far worse than any physical virus. It infects the brain and prevents it from functioning correctly. In most cases, it is deadly and has no cure, not even monoclonal antibodies can help! :-)

The statement "The union of all FISONs is an infinite set." is a belief that is easily disproved with very simple logic:

https://www.academia.edu/45442654/There_is_no_such_thing_as_an_infinite_set

The above 2 page article is a snippet of Ancient Greek thought whose clarity remains unmatched in all the history of humanity.

Set theory (especially the ZFC crap!) is full of contradictions and full of patches (rules added to prevent erroneous conclusions from collapsing entirely). In the racist deep South of the United States, this phenomenon is called "nigger-rigging". Modern mathematics is replete with this sort of garbage and no shortage of idiots who are more than willing to fight to the death to save their idol.

Even a young child can tell there is no greatest number, but the prime orangutans of the Church of math academia whose father is Georg Cantor, will simply never accept this fact. The aleph_x mythology is part of the Jewish nephesh - it is almost genetic: To hope against all hope. While this is profoundly poetic, it is not part of our reality, hence the Torah.

Since I possess Jewish genes, I have from a young age a Hatikvah that has kept me going through my turbulent life and often when I am depressed beyond imagination, I sometimes close my eyes and hope, but then there is another part of my DNA which tilts my thoughts in the logical direction - realising that my hope is in fact just a mental crutch. So it is with mainstream mathematics orangutans. Their Cantorian beliefs are a crutch.

This above all: to thine own self be true!

>
> Regards, WM

måndag 4 april 2022 kl. 06:00:24 UTC+2 skrev Eram semper recta:
> On Sunday, 3 April 2022 at 21:42:04 UTC+3, WM wrote:
> > William schrieb am Samstag, 2. April 2022 um 22:11:59 UTC+2:
> > > On Saturday, April 2, 2022 at 4:08:30 PM UTC-3, WM wrote:
> > >
> > > > Every union of FISONs has a last element.
> > > Nope. The union of all FISONs is an infinite set. There is no such thing as a "Potentially infinite set".
> > All that can be unioned from the sequence of FISONs has already been unioned in the sequence of FISONs. But nothing there is infinite. Therefore a final union cannot result in an infinite set.
> What I must point out here for the sake of posterity:
>
> Misguided thought is not genetic, rather it is is nurtured by society. Every human has the potential to master mathematics, but there are those who cannot cover their knowledge gaps with faith. Typically the latter kind are more intelligent and since they do not see any reason in mainstream mythmatics, they lose interest and pursue different paths. This is a shame and ultimately a loss to the human race because
> no doubt these individuals could have done great things.
>
> The garbage concept of infinity is a virus far worse than any physical virus. It infects the brain and prevents it from functioning correctly. In most cases, it is deadly and has no cure, not even monoclonal antibodies can help! :-)
>
>
> The statement "The union of all FISONs is an infinite set." is a belief that is easily disproved with very simple logic:
>
> https://www.academia.edu/45442654/There_is_no_such_thing_as_an_infinite_set
>
> The above 2 page article is a snippet of Ancient Greek thought whose clarity remains unmatched in all the history of humanity.
>
> Set theory (especially the ZFC crap!) is full of contradictions and full of patches (rules added to prevent erroneous conclusions from collapsing entirely). In the racist deep South of the United States, this phenomenon is called "nigger-rigging". Modern mathematics is replete with this sort of garbage and no shortage of idiots who are more than willing to fight to the death to save their idol.
>
> Even a young child can tell there is no greatest number, but the prime orangutans of the Church of math academia whose father is Georg Cantor, will simply never accept this fact. The aleph_x mythology is part of the Jewish nephesh - it is almost genetic: To hope against all hope. While this is profoundly poetic, it is not part of our reality, hence the Torah.
>
> Since I possess Jewish genes, I have from a young age a Hatikvah that has kept me going through my turbulent life and often when I am depressed beyond imagination, I sometimes close my eyes and hope, but then there is another part of my DNA which tilts my thoughts in the logical direction - realising that my hope is in fact just a mental crutch. So it is with mainstream mathematics orangutans. Their Cantorian beliefs are a crutch.
>
> This above all: to thine own self be true!
>
> >
> > Regards, WM
Except we have long since surpassed the ancient greeks in mathematics. Only someone as retarded as you think they are ahead.

William schrieb:

> On Sunday, April 3, 2022 at 6:49:09 PM UTC-3, Tom Bola wrote:
>
>> We've heard that here at least a dozen times but WM does not accept infinity.
>
> Indeed, and as has been made clear for many years,
> this in itself is in no way wrong.
> But WM's claim that infinite sets lead to contradictions is wrong...

WM claims that teaching infinity to pupils in school is crime.

WM wants to "discuss" all this shit and you are the idiots he needs.

söndag 3 april 2022 kl. 20:42:04 UTC+2 skrev WM:
> William schrieb am Samstag, 2. April 2022 um 22:11:59 UTC+2:
> > On Saturday, April 2, 2022 at 4:08:30 PM UTC-3, WM wrote:
> >
> > > Every union of FISONs has a last element.
> > Nope. The union of all FISONs is an infinite set. There is no such thing as a "Potentially infinite set".
> All that can be unioned from the sequence of FISONs has already been unioned in the sequence of FISONs. But nothing there is infinite. Therefore a final union cannot result in an infinite set.
>
> Regards, WM

You assume only finite number of FISONs here, which is a false assumption

On Saturday, April 2, 2022 at 9:08:30 PM UTC+2, WM wrote:
>
> Every union of FISONs has a last element. This fact is forced by construction.

No, you psychotic asshole full of shit, the union of ALL FISONs does not have a last element. this fact is forced by the AoI (and the definition of union).

zelos...@gmail.com schrieb am Montag, 4. April 2022 um 09:48:17 UTC+2:
> söndag 3 april 2022 kl. 20:42:04 UTC+2 skrev WM:
> > William schrieb am Samstag, 2. April 2022 um 22:11:59 UTC+2:
> > > On Saturday, April 2, 2022 at 4:08:30 PM UTC-3, WM wrote:
> > >
> > > > Every union of FISONs has a last element.
> > > Nope. The union of all FISONs is an infinite set. There is no such thing as a "Potentially infinite set".
> > All that can be unioned from the sequence of FISONs has already been unioned in the sequence of FISONs. But nothing there is infinite. Therefore a final union cannot result in an infinite set.

> You assume only finite number of FISONs here, which is a false assumption

No, less than ℵo FISONs is dictated by mathematics. FISONs are finite sets, no matter how many of them are concerned. Since in FISONs the numbers cannot change places 1, 2, 3, 4, 5 expresses the same as ooooo. Any finite set of n FISONs has at least one FISON with n symbols. This holds for all finite n. If there should be more (ℵo) than any finite number of FISONs then there must be a FISON with more (ℵo) than any finite number of symbols.

Regards, WM

Fritz Feldhase schrieb am Montag, 4. April 2022 um 12:25:22 UTC+2:
> On Saturday, April 2, 2022 at 9:08:30 PM UTC+2, WM wrote:
> >
> > Every union of FISONs has a last element. This fact is forced by construction.
> the union of ALL FISONs does not have a last element.

FISONs are finite sets, no matter how many of them are concerned. Since in FISONs the numbers cannot change places 1, 2, 3, 4, 5 expresses the same as ooooo. Any finite set of n FISONs has at least one FISON with n symbols. This holds for all finite n. If there should be more (ℵo) than any finite number of FISONs then there must be a FISON with more (ℵo) than any finite number of symbols.

This fact is forced by mathematics.

> this fact is forced by the AoI (and the definition of union).

Obviously AOI is nonsense. At least it does not concern FISONs.

Regards, WM

William schrieb am Montag, 4. April 2022 um 05:47:59 UTC+2:
> On Sunday, April 3, 2022 at 6:49:09 PM UTC-3, Tom Bola wrote:
>
> > We've heard that here at least a dozen times but WM does not accept infinity.
> Indeed, and as has been made clear for many years, this in itself is in no way wrong. But WM's claim that infinite sets lead to contradictions is wrong. His arguments involving FISONs all have the same pattern. He assumes the Axiom of infinity is false

No, I prove it. FISONs are finite sets, no matter how many of them are concerned. Since in FISONs the numbers cannot change places 1, 2, 3, 4, 5 expresses the same as ooooo. Any finite set of n FISONs has at least one FISON with n symbols. This holds for all finite n. If there should be more (ℵo) than any finite number of FISONs then there must be a FISON with more (ℵo) than any finite number of symbols.

This fact is enforced by mathematics. The AOI is invalid, at least for FISONs.

Regards, WM

William schrieb am Sonntag, 3. April 2022 um 21:24:15 UTC+2:
> On Sunday, April 3, 2022 at 3:42:04 PM UTC-3, WM wrote:
> > All that can be unioned from the sequence of FISONs has already been unioned in the sequence of FISONs.
> Nope, False.

What has not been unioned already?
{1} U {1, 2} = {1, 2}
{1} U {1, 2} U {1, 2, 3} = {1, 2, 3}
{1} U {1, 2} U {1, 2, 3} U {1, 2, 3, 4} = {1, 2, 3, 4,}
{1} U {1, 2} U {1, 2, 3} U {1, 2, 3, 4} U {1, 2, 3, 4, 5} = {1, 2, 3, 4, 5}
....

> True is: The union of any finite set of FISONs has already been unioned in the sequence of FISONs.

The unoon of any existing set has already been unioned. Why should an existing FISON not have been unioned?
>
> Since there are an infinite number of FISONs,

true for potential false for actual infinity (ℵ₀ larger than every finite n).

"All that can be unioned" is an infinite set.

It is not a set but only a collection. Any finite set of n FISONs has at least one FISON with n symbols. This holds for all finite n. If there should be more (ℵo) than any finite number of FISONs then there must be a FISON with more (ℵo) than any finite number of symbols. Contradiciton, but required by matheology: The existence of an infinite finite set of natural numbers.

Regards, WM

On Monday, 4 April 2022 at 07:48:38 UTC-3, WM wrote:
> [...] less than ℵo FISONs is dictated by mathematics. FISONs are finite sets, no matter how many of them are concerned. Since in FISONs the numbers cannot change places 1, 2, 3, 4, 5 expresses the same as ooooo. Any finite set of n FISONs has at least one FISON with n symbols. This holds for all finite n. If there should be more (ℵo) than any finite number of FISONs then there must be a FISON with more (ℵo) than any finite number of symbols.

Oh, bullshit. *BULLSHIT* and quantifier dyslexia, moron.

On Monday, 4 April 2022 at 07:53:11 UTC-3, WM wrote:
[...]
Saying your shit twice doesn't make it stink any less, so I emptied your cesspool. You're welcome.

On 4/4/2022 5:53 AM, WM wrote:
> William schrieb am Montag, 4. April 2022 um 05:47:59 UTC+2:
>> On Sunday, April 3, 2022 at 6:49:09 PM UTC-3, Tom Bola wrote:
>>
>>> We've heard that here at least a dozen times but WM does not accept infinity.
>> Indeed, and as has been made clear for many years, this in itself is in no way wrong. But WM's claim that infinite sets lead to contradictions is wrong. His arguments involving FISONs all have the same pattern. He assumes the Axiom of infinity is false
>
> No, I prove it. FISONs are finite sets, no matter how many of them are concerned. Since in FISONs the numbers cannot change places 1, 2, 3, 4, 5 expresses the same as ooooo.

what?

> Any finite set of n FISONs has at least one FISON with n symbols.

you are using n as a VARIABLE !

> This holds for all finite n.

no, it holes for all n. why do you say it does not hold for n+1 ?

> If there should be more (ℵo) than any finite number of FISONs then there must be a FISON with more (ℵo) than any finite number of symbols.

see you stopped at k again.

>
> This fact

it is not fact, it is Spoof.

> Regards, WM

On 4/4/2022 5:48 AM, WM wrote:
> zelos...@gmail.com schrieb am Montag, 4. April 2022 um 09:48:17 UTC+2:
>> söndag 3 april 2022 kl. 20:42:04 UTC+2 skrev WM:
>>> William schrieb am Samstag, 2. April 2022 um 22:11:59 UTC+2:
>>>> On Saturday, April 2, 2022 at 4:08:30 PM UTC-3, WM wrote:
>>>>
>>>>> Every union of FISONs has a last element.
>>>> Nope. The union of all FISONs is an infinite set. There is no such thing as a "Potentially infinite set".
>>> All that can be unioned from the sequence of FISONs has already been unioned in the sequence of FISONs. But nothing there is infinite. Therefore a final union cannot result in an infinite set.
>
>> You assume only finite number of FISONs here, which is a false assumption
>
> No, less than ℵo FISONs is dictated by mathematics.

Wrong. there are an infinite number of FISONs.

<snip crap>

>
> Regards, WM

On 4/4/2022 5:48 AM, WM wrote:
> Fritz Feldhase schrieb am Montag, 4. April 2022 um 12:25:22 UTC+2:
>> On Saturday, April 2, 2022 at 9:08:30 PM UTC+2, WM wrote:
>>>
>>> Every union of FISONs has a last element. This fact is forced by construction.
>> the union of ALL FISONs does not have a last element.
>
<snip crap>

>
> Regards, WM
>
>

On Monday, April 4, 2022 at 7:48:53 AM UTC-3, WM wrote:

> FISONs are finite sets, no matter how many of them are concerned

So what? Each FISON is a finite set. No one is doubting this. The *set* of all FISONs (like any Peano set) has cardinality ℵo. You confuse the properties of the set with the properties of the elements of the set. If every element of a set has property P, the set may or may not have property P. In particular, if the elements of a set S are finite, S may or may not be finite.

> Any finite set of n FISONs has at least one FISON with n symbols.

So what? The set of all FISONs is not a finite set of n FISONs. Any finite set of FISONs, that is a set of FISONs with cardinality n < ℵo, must have an element with cardinality >=n. This is not true for a set of FISONs with cardinality ℵo. Such a set need not have an element with cardinality ℵo, i.e. there are ℵo o's in the set, but the are only a finite number of o's in any *element* of the set.

--
William Hughes

On 4/4/2022 11:25 AM, William wrote:
> On Monday, April 4, 2022 at 7:48:53 AM UTC-3, WM wrote:
>
>
>> FISONs are finite sets, no matter how many of them are concerned
>
> So what? Each FISON is a finite set. No one is doubting this. The *set* of all FISONs (like any Peano set) has cardinality ℵo. You confuse the properties of the set with the properties of the elements of the set. If every element of a set has property P, the set may or may not have property P. In particular, if the elements of a set S are finite, S may or may not be finite.
>
>> Any finite set of n FISONs has at least one FISON with n symbols.
>
> So what? The set of all FISONs is not a finite set of n FISONs. Any finite set of FISONs, that is a set of FISONs with cardinality n < ℵo, must have an element with cardinality >=n. This is not true for a set of FISONs with cardinality ℵo. Such a set need not have an element with cardinality ℵo, i.e. there are ℵo o's in the set, but the are only a finite number of o's in any *element* of the set.
>

WM the crank has ended up here again, his intentional confusitorium of FISON sets and elements, at least 5 times over the last year, I think he is going
for ℵo times...

On Monday, April 4, 2022 at 8:22:55 AM UTC-3, WM wrote:
> William schrieb am Sonntag, 3. April 2022 um 21:24:15 UTC+2:

> > "All that can be unioned" is an infinite set.
> It is not a set but only a collection.

Nope. It is a Peano set, and like all Peano sets has cardinality ℵo.

--
William Hughes

horand....@gmail.com schrieb am Montag, 4. April 2022 um 14:09:19 UTC+2:
> On Monday, 4 April 2022 at 07:48:38 UTC-3, WM wrote:
> > [...] less than ℵo FISONs is dictated by mathematics. FISONs are finite sets, no matter how many of them are concerned. Since in FISONs the numbers cannot change places 1, 2, 3, 4, 5 expresses the same as ooooo. Any finite set of n FISONs has at least one FISON with n symbols. This holds for all finite n. If there should be more (ℵo) than any finite number of FISONs then there must be a FISON with more (ℵo) than any finite number of symbols.
>
> Oh, bullshit. *BULLSHIT* and quantifier dyslexia, moron.

Of course I knew that you have no arguments. Thanks for the confimation.

Regards, WM

William schrieb am Montag, 4. April 2022 um 18:25:58 UTC+2:
> On Monday, April 4, 2022 at 7:48:53 AM UTC-3, WM wrote:
>
>
> > FISONs are finite sets, no matter how many of them are concerned
> So what? Each FISON is a finite set. No one is doubting this. The *set* of all FISONs (like any Peano set) has cardinality ℵo. You confuse the properties of the set with the properties of the elements of the set. If every element of a set has property P, the set may or may not have property P. In particular, if the elements of a set S are finite, S may or may not be finite.
> > Any finite set of n FISONs has at least one FISON with n symbols.
> So what? The set of all FISONs is not a finite set of n FISONs. Any finite set of FISONs, that is a set of FISONs with cardinality n < ℵo, must have an element with cardinality >=n. This is not true for a set of FISONs with cardinality ℵo.

Wrong. If all finite sets with cardinality n < ℵo, must have an element with cardinality >=n (and all n are exhausted by these sets), then it is impossible to build a larger set by the same FISONs.

> Such a set need not have an element with cardinality ℵo, i.e. there are ℵo o's in the set, but the are only a finite number of o's in any *element* of the set.

That is impossible because of pigeonhole principle as well as inclusion monotony. It is a blatant contradiction with the construction of FISONs. Look here:

o
oo
ooo
....

Height = Width. This is true up to every FISON. It does never change.

All finite sets of o's are exhausted by all finite sets of FISONs.

Regards, WM

William schrieb am Montag, 4. April 2022 um 18:31:35 UTC+2:
> On Monday, April 4, 2022 at 8:22:55 AM UTC-3, WM wrote:
> > William schrieb am Sonntag, 3. April 2022 um 21:24:15 UTC+2:
>
> > > "All that can be unioned" is an infinite set.
> > It is not a set but only a collection.
> Nope. It is a Peano set, and like all Peano sets has cardinality ℵo.

No Peano set has cardinality ℵo. But for FISONs this is obvious. You said that all FISONs required in finite sets would be enough for an infinite set. Are there some FISONs as doublettes?

Regards, WM

On 4/4/2022 12:54 PM, WM wrote:
> horand....@gmail.com schrieb am Montag, 4. April 2022 um 14:09:19 UTC+2:
>> On Monday, 4 April 2022 at 07:48:38 UTC-3, WM wrote:
>>> [...] less than ℵo FISONs is dictated by mathematics. FISONs are finite sets, no matter how many of them are concerned. Since in FISONs the numbers cannot change places 1, 2, 3, 4, 5 expresses the same as ooooo. Any finite set of n FISONs has at least one FISON with n symbols. This holds for all finite n. If there should be more (ℵo) than any finite number of FISONs then there must be a FISON with more (ℵo) than any finite number of symbols.
>>
>> Oh, bullshit. *BULLSHIT* and quantifier dyslexia, moron.
>
> Of course I knew that you have no arguments. Thanks for the confimation.

WM is a mind reader too! Besides WM's bad math, like "1, 2, 3, 4, 5 expresses the same as ooooo", WM says he know what people think.

>
> Regards, WM

On 4/4/2022 1:09 PM, WM wrote:
> William schrieb am Montag, 4. April 2022 um 18:25:58 UTC+2:
>> On Monday, April 4, 2022 at 7:48:53 AM UTC-3, WM wrote:
>>
>>
>>> FISONs are finite sets, no matter how many of them are concerned
>> So what? Each FISON is a finite set. No one is doubting this. The *set* of all FISONs (like any Peano set) has cardinality ℵo. You confuse the properties of the set with the properties of the elements of the set. If every element of a set has property P, the set may or may not have property P. In particular, if the elements of a set S are finite, S may or may not be finite.
>>> Any finite set of n FISONs has at least one FISON with n symbols.
>> So what? The set of all FISONs is not a finite set of n FISONs. Any finite set of FISONs, that is a set of FISONs with cardinality n < ℵo, must have an element with cardinality >=n. This is not true for a set of FISONs with cardinality ℵo.
>
> Wrong. If all finite sets with cardinality n < ℵo, must have an element with cardinality >=n (and all n are exhausted by these sets), then it is impossible to build a larger set by the same FISONs.
>
>> Such a set need not have an element with cardinality ℵo, i.e. there are ℵo o's in the set, but the are only a finite number of o's in any *element* of the set.
>
> That is impossible because of pigeonhole principle as well as inclusion monotony. It is a blatant contradiction with the construction of FISONs. Look here:
>
> o
> oo
> ooo
> ...
>
> Height = Width. This is true up to every FISON. It does never change.
>
> All finite sets of o's are exhausted by all finite sets of FISONs.
>
> Regards, WM

another reposting of WMs SOS, of failed math, exhausted by errors and inexperience, falls DOA in a dust bin on the internet.