On Monday, April 4, 2022 at 3:14:48 PM UTC-3, WM wrote:
> 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.

Simply false. Let P be a Peano set. The identity function from P to P shows that P has a cardinality. The cardinality of P is greater than n for any natrual number n. ℵo is the smallest cardinality that is greater than n for any natural number n. Thus the cardinality of P is greater than or equal to ℵo. The fact that the cardinality of P is less than or equal to ℵo is left as an exercise to the reader.

> But for FISONs this is obvious. You said that all FISONs required in finite sets would be enough for an infinite set.

Indeed. There is no single finite set of FISONs from which you can form all finite sets of FISONs So "all FISONs required in finite sets" is not a finite set of FISONs. You can form all finite sets of FISONsfrom "all FISONs" . Thus "all FISONs" is infinite.

--
William Hughes

On Monday, April 4, 2022 at 3:09:36 PM UTC-3, WM wrote:

> 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.

Simply false.

--
William Hughes

William schrieb am Montag, 4. April 2022 um 20:59:39 UTC+2:
> On Monday, April 4, 2022 at 3:14:48 PM UTC-3, WM wrote:
> > William schrieb am Montag, 4. April 2022 um 18:31:35 UTC+2:

> > No Peano set has cardinality ℵo.
> Simply false. Let P be a Peano set. The identity function from P to P

does not exist.

> > But for FISONs this is obvious. You said that all FISONs required in finite sets would be enough for an infinite set.
> Indeed.

That is nonsense. No reason to continue.

> There is no single finite set of FISONs from which you can form all finite sets of FISONs.

But there are all finite sets. And all are not infinite. So "all FISONs required in finite sets" is not a finite set of FISONs.

It is not an ℵo-set either. But further arguments are useless as long as you insist on "there are ℵo o's in the set, but there are only a finite number of o's in any *element* of the set". Here you violate simplest logic. There is no use to continue.

Regards, WM

William schrieb am Montag, 4. April 2022 um 20:59:56 UTC+2:
> On Monday, April 4, 2022 at 3:09:36 PM UTC-3, WM wrote:
>
> > 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.
> Simply false.

Obvious. But no further arguments are required as long as you insist on "there are ℵo o's in the set, but there are only a finite number of o's in any *element* of the set". Here you violate simplest logic. There is no use to continue.

Regards, WM

On Monday, April 4, 2022 at 4:18:35 PM UTC-3, WM wrote:
> William schrieb am Montag, 4. April 2022 um 20:59:39 UTC+2:
> > On Monday, April 4, 2022 at 3:14:48 PM UTC-3, WM wrote:
> > > William schrieb am Montag, 4. April 2022 um 18:31:35 UTC+2:
>
> > > No Peano set has cardinality ℵo.
> > Simply false. Let P be a Peano set. The identity function from P to P
> does not exist.

Piffle. The identity function is simply PxP

--
William Hughes

On 4/4/2022 3:24 PM, William wrote:
> On Monday, April 4, 2022 at 4:18:35 PM UTC-3,
> WM wrote:
>> William schrieb
>> am Montag, 4. April 2022 um 20:59:39 UTC+2:
>>> On Monday, April 4, 2022 at 3:14:48 PM UTC-3,
>>> WM wrote:

>>>> No Peano set has cardinality ℵo.
>>>
>>> Simply false. Let P be a Peano set.
>>> The identity function from P to P
>>
>> does not exist.
>
> Piffle. The identity function is simply PxP

I'm sure you meant to write something like
{ ⟨x,y⟩ ∈ P⨯P | x = y }

On Monday, April 4, 2022 at 4:18:35 PM UTC-3, WM wrote:
> William schrieb am Montag, 4. April 2022 um 20:59:39 UTC+2:
> > On Monday, April 4, 2022 at 3:14:48 PM UTC-3, WM wrote:
> > > William schrieb am Montag, 4. April 2022 um 18:31:35 UTC+2:
>
> > > No Peano set has cardinality ℵo.
> > Simply false. Let P be a Peano set. The identity function from P to P
> does not exist.

Piffle. {(p,p) | p in P} is the identity function from P to P.

--
William Hughes

On 4/4/2022 2:18 PM, WM wrote:
> William schrieb am Montag, 4. April 2022 um 20:59:56 UTC+2:
>> On Monday, April 4, 2022 at 3:09:36 PM UTC-3, WM wrote:
>>
>>> 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.
>> Simply false.
>
> Obvious. But no further arguments are required as long as you insist on "there are ℵo o's in the set, but there are only a finite number of o's in any *element* of the set". Here you violate simplest logic. There is no use to continue.
>
> Regards, WM

no use to continue with a lying troll

On Monday, April 4, 2022 at 4:18:35 PM UTC-3, WM wrote:
> But there are all finite sets. And all are not infinite.

A horse has an even number of legs A horse has fore legs and two hind legs for a total of six legs. This is an odd number of legs for a horse. The only number that is both even and odd is infinity. So a horse has an infinite number of legs.

--
William Hughes

On Monday, April 4, 2022 at 4:35:17 PM UTC-3, Jim Burns wrote:
> On 4/4/2022 3:24 PM, William wrote:
> > On Monday, April 4, 2022 at 4:18:35 PM UTC-3,
> > WM wrote:
> >> William schrieb
> >> am Montag, 4. April 2022 um 20:59:39 UTC+2:
> >>> On Monday, April 4, 2022 at 3:14:48 PM UTC-3,
> >>> WM wrote:
>
> >>>> No Peano set has cardinality ℵo.
> >>>
> >>> Simply false. Let P be a Peano set.
> >>> The identity function from P to P
> >>
> >> does not exist.
> >
> > Piffle. The identity function is simply PxP
>
> I'm sure you meant to write something like
> { ⟨x,y⟩ ∈ P⨯P | x = y }

Yeah, I noticed my error and deleted the post. Unfortunately, after you had replied..

--
William Hughes

William was thinking very hard :
> On Monday, April 4, 2022 at 4:35:17 PM UTC-3, Jim Burns wrote:
>> On 4/4/2022 3:24 PM, William wrote:
>>> On Monday, April 4, 2022 at 4:18:35 PM UTC-3,
>>> WM wrote:
>>>> William schrieb
>>>> am Montag, 4. April 2022 um 20:59:39 UTC+2:
>>>>> On Monday, April 4, 2022 at 3:14:48 PM UTC-3,
>>>>> WM wrote:
>>
>>>>>> No Peano set has cardinality ℵo.
>>>>>
>>>>> Simply false. Let P be a Peano set.
>>>>> The identity function from P to P
>>>>
>>>> does not exist.
>>>
>>> Piffle. The identity function is simply PxP
>>
>> I'm sure you meant to write something like
>> { ⟨x,y⟩ ∈ P⨯P | x = y }
>
> Yeah, I noticed my error and deleted the post. Unfortunately, after you had
> replied..

Posts don't get deleted. Most NNTP servers don't honor cancels.

On Monday, 4 April 2022 at 14:54:46 UTC-3, 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.

Neither do you, obviously.

I'd be more than happy to *CONGRATULATE* you if could actually get a cogent argument together. But seeing the same boneheaded mistake over and over again I go to the simplest common denominator: "Another one of those".

On Monday, 4 April 2022 at 16:18:46 UTC-3, WM wrote:
[...]
> Obvious. But no further arguments are required as long as you insist on "there are ℵo o's in the set, but there are only a finite number of o's in any *element* of the set". Here you violate simplest logic. There is no use to continue.

then *DON'T*, for fuck sake.

On 4/4/2022 2:59 PM, FromTheRafters wrote:
> William was thinking very hard :
>> On Monday, April 4, 2022 at 4:35:17 PM UTC-3, Jim Burns wrote:
>>> On 4/4/2022 3:24 PM, William wrote:
>>>> On Monday, April 4, 2022 at 4:18:35 PM UTC-3,
>>>> WM wrote:
>>>>> William schrieb am Montag, 4. April 2022 um 20:59:39 UTC+2:
>>>>>> On Monday, April 4, 2022 at 3:14:48 PM UTC-3, WM wrote:
>>>
>>>>>>> No Peano set has cardinality ℵo.
>>>>>>
>>>>>> Simply false. Let P be a Peano set. The identity function from P to P
>>>>>
>>>>> does not exist.
>>>>
>>>> Piffle. The identity function is simply PxP
>>>
>>> I'm sure you meant to write something like { ⟨x,y⟩ ∈ P⨯P | x = y }
>>
>> Yeah, I noticed my error and deleted the post.  Unfortunately, after you had replied..
>
> Posts don't get deleted. Most NNTP servers don't honor cancels.

posts get shared between many the many servers which host newsgroups,
a few servers will honer cancel, but you have to act quick (3, 10 min) before it get propagated on out to the rest

there are not many people wading around in the newsgroups anymore, sci.math and sci.physics have high traffic numbers compared to most newsgroups, so
they act as kook collectors as most other newsgroups are doa.

How long are newsgroup posts kept ? some a year, some several years,
WM's posts are kept potentially ℵo year(s) on a hard drive buried at the dump

On Monday, April 4, 2022 at 8:14:48 PM UTC+2, WM wrote:

> No Peano set has cardinality ℵo.

Wrong, you fucking asshole full of shit: IN is a "Peano set" and has cardinality ℵo by definition.

Hint: "ℵo (aleph-nought, also aleph-zero or aleph-null) is the cardinality of the set of all natural numbers." (Wikipedia)

On Monday, April 4, 2022 at 8:09:36 PM UTC+2, WM wrote:
> William schrieb am Montag, 4. April 2022 um 18:25:58 UTC+2:
> >
> > Such a set need not have an element with cardinality ℵo, i.e. there are ℵo [elements] in the set, but the are only a finite number of [elements] in any *element* of the set.
> >
> That is <bla>

Another example: the set S = {{0}, {1}, {2}, ...}. US = {0, 1, 2, ...} = IN.

Since for all n e IN: {n} c {0, 1, 2, ..., n} its clear that IN = U {{0}, {1}, {2}, ...} c U {{0}, {0, 1}, {0, 1, 2 2}, ...}.

sergio used his keyboard to write :
> On 4/4/2022 2:59 PM, FromTheRafters wrote:
>> William was thinking very hard :
>>> On Monday, April 4, 2022 at 4:35:17 PM UTC-3, Jim Burns wrote:
>>>> On 4/4/2022 3:24 PM, William wrote:
>>>>> On Monday, April 4, 2022 at 4:18:35 PM UTC-3,
>>>>> WM wrote:
>>>>>> William schrieb am Montag, 4. April 2022 um 20:59:39 UTC+2:
>>>>>>> On Monday, April 4, 2022 at 3:14:48 PM UTC-3, WM wrote:
>>>>
>>>>>>>> No Peano set has cardinality ℵo.
>>>>>>>
>>>>>>> Simply false. Let P be a Peano set. The identity function from P to P
>>>>>>
>>>>>> does not exist.
>>>>>
>>>>> Piffle. The identity function is simply PxP
>>>>
>>>> I'm sure you meant to write something like { ⟨x,y⟩ ∈ P⨯P | x = y }
>>>
>>> Yeah, I noticed my error and deleted the post.  Unfortunately, after you
>>> had replied..
>>
>> Posts don't get deleted. Most NNTP servers don't honor cancels.
>
>
> posts get shared between many the many servers which host newsgroups,
> a few servers will honer cancel, but you have to act quick (3, 10 min)
> before it get propagated on out to the rest

I have been able to cancel on rare occasions. Like you say though, you
have to be quick. Can GG do that?

> there are not many people wading around in the newsgroups anymore, sci.math
> and sci.physics have high traffic numbers compared to most newsgroups, so
> they act as kook collectors as most other newsgroups are doa.

I thought it seemed a little kookier here as time went along.

> How long are newsgroup posts kept ? some a year, some several years,
> WM's posts are kept potentially ℵo year(s) on a hard drive buried at the
> dump

Then there's the archives, but they are *all* finite.

On 4/4/2022 6:34 PM, FromTheRafters wrote:
> sergio used his keyboard to write :
>> On 4/4/2022 2:59 PM, FromTheRafters wrote:
>>> William was thinking very hard :
>>>> On Monday, April 4, 2022 at 4:35:17 PM UTC-3, Jim Burns wrote:
>>>>> On 4/4/2022 3:24 PM, William wrote:
>>>>>> On Monday, April 4, 2022 at 4:18:35 PM UTC-3,
>>>>>> WM wrote:
>>>>>>> William schrieb am Montag, 4. April 2022 um 20:59:39 UTC+2:
>>>>>>>> On Monday, April 4, 2022 at 3:14:48 PM UTC-3, WM wrote:
>>>>>
>>>>>>>>> No Peano set has cardinality ℵo.
>>>>>>>>
>>>>>>>> Simply false. Let P be a Peano set. The identity function from P to P
>>>>>>>
>>>>>>> does not exist.
>>>>>>
>>>>>> Piffle. The identity function is simply PxP
>>>>>
>>>>> I'm sure you meant to write something like { ⟨x,y⟩ ∈ P⨯P | x = y }
>>>>
>>>> Yeah, I noticed my error and deleted the post.  Unfortunately, after you had replied..
>>>
>>> Posts don't get deleted. Most NNTP servers don't honor cancels.
>>
>>
>> posts get shared between many the many servers which host newsgroups,
>>   a few servers will honer cancel, but you have to act quick (3, 10 min) before it get propagated on out to the rest
>
> I have been able to cancel on rare occasions. Like you say though, you have to be quick. Can GG do that?
>
>> there are not many people wading around in the newsgroups anymore, sci.math and sci.physics have high traffic numbers compared to most newsgroups, so
>> they act as kook collectors as most other newsgroups are doa.
>
> I thought it seemed a little kookier here as time went along.
>
>> How long are newsgroup posts kept ?  some a year, some several years,
>>     WM's posts are kept potentially ℵo year(s) on a hard drive buried at the dump
>
> Then there's the archives, but they are *all* finite.

yep, even on Hard drives the little magnetic domains(bits) degrade over time, 7 to 10 years... AND the dHard drives are very plastic construction now
days, a 1T for $75 ? not rugged, you drop it 1/4 inch while read/write and it is toast, gone, fried. forget the recovery services, slim change from them

Mag tape may be slower, as the bits are a lot bigger, but the substrate goes (sticks to the adjacent tape, you have to rewind them every 3 years or so)

Solid state drives, well cosmic rays over time, you can loose bits, but they can be corrected, but it could blow out a decoder section.
CD, archival quality is good for 10 years, then re record to a new CD, archival... (and many drives run hot, which lowers lifetime, and the imput
protection is typically crappy, how many thumb drives have you fried ?

Cheap CDs have thin coat of AL which catchup will eat through in 2 days, ...

Internet archives, bulk copied to several sites, then recopied later on, the big storage companies do that, but disgruntaled employee, fire, company
goes out of business, or is sold... and the internet archive will loose old non used data on some sites, to free up space

best to have multiple copies on different media, and re fresh every 3 to 5 years

or Paper Tape! how many miles of paper tape would windows 10 backup take ?

måndag 4 april 2022 kl. 12:48:38 UTC+2 skrev WM:
> 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.

And the union of all is N

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

Individually yes, but the union of all is not.

>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.

Just because it is true for any finite, does that not mean it is true for infinite.

>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

False

måndag 4 april 2022 kl. 13:22:55 UTC+2 skrev 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).

Those have no meaning in mathematics.

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

it is a set

>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.

False, you are assuming again what is true for finite is true for infinite, false.

>Contradiciton, but required by matheology: The existence of an infinite finite set of natural numbers.

False, there is no contradiction, only you being an idiot.

>
> Regards, WM

On Monday, 4 April 2022 at 13:48:38 UTC+3, 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

See Wolfgang? You can't discuss mathematics based on assumptions, only on cold, hard facts.

The above claim "You assume only finite number of FISONs here..." is wrong on so many levels apart from the "assumptions".

1. The expression "finite number" is both illogical and anti-mathematical nonsense. The adjective "finite" cannot appear before "number". A number is represented by a fixed (not "finite" because then this might imply something else (pretty absurd) is possible) number of symbols.

2. The above drivel is equivalent to claiming that 1/3 cannot be represented in base 10 "finitely" which is a result of the same misguided thinking. 1/3 either can or can't be represented in decimal. A very important number theorem tells us clearly that 1/3 has no representation in decimal. To say:

"You can't represent 1/3 finitely" is drivel. I just did ... look: "1 / 3"

Measuring 1/3 in a given base is possible if and only if, that base contains 3 as one of its prime factors. THIS AND NOTHING ELSE.

3. I don't ever allow ill-formed concepts in a discussion. So when someone makes foolish claims about "infinity", I cut that one off right away. There is no such thing as infinity and if you are deluded enough to think you can convince one who believes in this garbage, well then I am sorry to say you are yourself deluded.

To say that you can't represent 1/3 finitely and then in the same breath that you can represent 1/3 "infinitely" with a fixed number of symbols, that is, 0.333... is absurd in every possible sense.

The brain circuitry of such individuals is obviously faulty. You cannot fix stupid. Period.

> 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

On Tuesday, 5 April 2022 at 09:52:52 UTC+3, Eram semper recta wrote:
> On Monday, 4 April 2022 at 13:48:38 UTC+3, 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
> See Wolfgang? You can't discuss mathematics based on assumptions, only on cold, hard facts.
>
> The above claim "You assume only finite number of FISONs here..." is wrong on so many levels apart from the "assumptions".
>
> 1. The expression "finite number" is both illogical and anti-mathematical nonsense. The adjective "finite" cannot appear before "number". A number is represented by a fixed (not "finite" because then this might imply something else (pretty absurd) is possible) number of symbols.
>
> 2. The above drivel is equivalent to claiming that 1/3 cannot be represented in base 10 "finitely" which is a result of the same misguided thinking. 1/3 either can or can't be represented in decimal. A very important number theorem tells us clearly that 1/3 has no representation in decimal. To say:
>
> "You can't represent 1/3 finitely" is drivel. I just did ... look: "1 / 3"
>
> Measuring 1/3 in a given base is possible if and only if, that base contains 3 as one of its prime factors. THIS AND NOTHING ELSE.
>
> 3. I don't ever allow ill-formed concepts in a discussion. So when someone makes foolish claims about "infinity", I cut that one off right away. There is no such thing as infinity and if you are deluded enough to think you can convince one who believes in this garbage, well then I am sorry to say you are yourself deluded.
>
> To say that you can't represent 1/3 finitely and then in the same breath that you can represent 1/3 "infinitely" with a fixed number of symbols, that is, 0.333... is absurd in every possible sense.
>
> The brain circuitry of such individuals is obviously faulty. You cannot fix stupid. Period.

See, the psychology of one who makes a statement such as 1/3 = 0.333... is truly quite perplexing.

Does "..." mean that the 3s are all there?
---> The 3s can never all be there. FACT.

Does it mean that 1/3 actually has a measure in base 10?
---> No, because an important number theorem instantly dismisses this erroneous thinking.

Does it mean that the limit of the series 3/10+3/100+... is 1/3 ? And if so, how can this be applied to magnitudes that have no measure, for example pi or the square root of two?
---> The limit cannot be represented by a convergent sequence because a number by definition ***is a measure of a given magnitude***. Convergent sequences do not measure anything. A number is a name. 0.333... is the NAME of a convergent sequence.

Mainstream mathematics professors are incorrigibly stupid creatures who cannot be corrected and don't even understand the very theory they advocate:

https://www.academia.edu/45001199/Mainstream_mathematics_professors_are_incorrigibly_stupid_creatures_who_cannot_be_corrected

Is 1/3 not a well-represented number?
---> Of course it is. It doesn't have to be represented in any other way although there are innumerable other ways to represent (measure) it, for example, 0.1 (base 3), 0.2 (base 6), etc.

>
> > 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

tisdag 5 april 2022 kl. 08:52:52 UTC+2 skrev Eram semper recta:
> On Monday, 4 April 2022 at 13:48:38 UTC+3, 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
> See Wolfgang? You can't discuss mathematics based on assumptions, only on cold, hard facts.

Fact however does not mean what you want it to be.

>
> The above claim "You assume only finite number of FISONs here..." is wrong on so many levels apart from the "assumptions".

Go ahead and fail.

>
> 1. The expression "finite number" is both illogical and anti-mathematical nonsense.

That is only your opinion, of to a shitty start.

>The adjective "finite" cannot appear before "number".

Sure can, "number" is a noun, "finite" is an adjective, adjectives goes before nouns, ergo, it can :)

>A number is represented by a fixed (not "finite" because then this might imply something else (pretty absurd) is possible) number of symbols.

We represent numbers, but you are being fallacious here and using one semantic meaning, the one you prefer, over the one I clearly intended.

>
> 2. The above drivel is equivalent to claiming that 1/3 cannot be represented in base 10 "finitely" which is a result of the same misguided thinking.

Nope, that statement is perfectly accurate. You're a finitist and that is your issue.

>1/3 either can or can't be represented in decimal.

It can, just not with finite non-zero digits :)

>A very important number theorem tells us clearly that 1/3 has no representation in decimal. To say:

There is no such theorem.

>
> "You can't represent 1/3 finitely" is drivel. I just did ... look: "1 / 3"

At which the person of course means in decimal form and in amount of non-zero decimals.

>
> Measuring

No one does that in mathematics.

>1/3 in a given base is possible if and only if, that base contains 3 as one of its prime factors. THIS AND NOTHING ELSE.

Here we have your "my way or the highway", sorry but you don't decide things.

>
> 3. I don't ever allow ill-formed concepts in a discussion.

Who cares what you allow? You don't dictate mathematics.

>So when someone makes foolish claims about "infinity", I cut that one off right away.

your "cut off" amounts to crying like a baby.

>There is no such thing as infinity

Then what is the largest natural number?

Whatever it is I add 1, ergo the collection of natural numbers cannot be finite, ergo, it is infinite :)

>and if you are deluded enough to think you can convince one who believes in this garbage, well then I am sorry to say you are yourself deluded.

Yet it is trivial to show it cannot be finite, meaning it is infinite.

>
> To say that you can't represent 1/3 finitely and then in the same breath that you can represent 1/3 "infinitely" with a fixed number of symbols, that is, 0.333... is absurd in every possible sense.
>
> The brain circuitry of such individuals is obviously faulty. You cannot fix stupid. Period.
>
> > 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

William schrieb am Montag, 4. April 2022 um 21:45:48 UTC+2:
> On Monday, April 4, 2022 at 4:18:35 PM UTC-3, WM wrote:
> > But there are all finite sets. And all are not infinite.
> A horse has an even number of legs

Your nonsense cannot extinguish your silly statement: "there are ℵo o's in the set, but there are only a finite number of o's in any *element* of the set" concerning the sequence of FISONs

o
oo
ooo
oooo
ooooo
....

As long as you don't withdraw it, every arguing with mathematical or logical arguments is in vain.

Regards, WM

horand....@gmail.com schrieb am Montag, 4. April 2022 um 22:13:30 UTC+2:
> On Monday, 4 April 2022 at 14:54:46 UTC-3, 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.
> Neither do you, obviously.

Never the number of O's (= not enumerated fractions) decreases:

XOOO...
XOOO...
XOOO...
XOOO...
....

XXOO...
OOOO...
XOOO...
XOOO...
....

XXOO...
XOOO...
OOOO...
XOOO...
....

XXXO...
XOOO...
OOOO...
OOOO...
....

Never a union of all FISONs is larger than all unions of FISONs contained in the sequence of FISONs:

{1} = {1}
{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}
....

Regards, WM