WM laid this down on his screen :
> Eram semper recta schrieb am Freitag, 1. April 2022 um 15:29:17 UTC+2:
>> On Friday, 1 April 2022 at 13:36:19 UTC+3, WM wrote:
>>> Eram semper recta schrieb am Freitag, 1. April 2022 um 07:10:06 UTC+2:
>>>
>>>> Your arguments about Cantor are 100% sound. It is relieving to know that
>>>> mathematicians can understand this. The number is NOT the formula.
>>> Correct. But both can have the same notation. Like Millers and millers.
>> Not in this case. Any formula you give for pi never gives the number pi,
>> only a recognised constant.
>
> We had agreed long ago that it is a matter of taste whether irrationals are
> called numbers. At least I had agreed.

That figures.

William schrieb:

> On Friday, April 1, 2022 at 3:07:27 PM UTC-3, WM wrote:
>> William schrieb am Freitag, 1. April 2022 um 19:46:29 UTC+2:
>>> On Friday, April 1, 2022 at 10:51:12 AM UTC-3, WM wrote:
>>>
>>> > (There is no infinite set but only a potentially infinite collection of FISONs.)
>>> Piffle
>> (1) The union of FISONs cannot contain more than the sequence of FISONs.
>> (2) The sequence does not contain more than is already unioned in at least one term of the sequence.
>
> Piffle. There is no reason to think that the union of all elements of the sequence are contained in one element of the sequence.
> Indeed a the union of a sequence of FISONs is contained in one element of the sequence, iff the sequence has a last element.

WM does not _accept_ infinity (because "there are just 10^80 particles in
the universe") and also says it is "a criminal act to teach children infinity
or Cantor". WM is not only a true idiot, simply dull, but also a low-lifer.

William schrieb:

> On Friday, April 1, 2022 at 3:42:27 PM UTC-3, WM wrote:
> > existing FISON:
>
> More nonsense. The collection of FISONs is a set. The set of FISONs does not change. The set of FISONs does not contain a largest FISON. The union of the set of FISONs is not contained in a single FISON.

WM also does not "support" any infinity, e.g. so that Dedekind-infinite
sets have a proper subset equinumerous to itself. WM refutes to learn and
accept todays math for about 30 years in the German math newsgroup.

William schrieb am Freitag, 1. April 2022 um 20:50:40 UTC+2:
> On Friday, April 1, 2022 at 3:42:27 PM UTC-3, WM wrote:
> > existing FISON:
>
> More nonsense. The collection of FISONs is a set.

Obviously a false claim. More nonsense is the correct announcement.

> The set of FISONs does not change.

Obviously a false claim. Potentially infinite collections do change.

> The set of FISONs does not contain a largest FISON.

Every FISON contains a largest element. Every set of FISONs contains a largest FISON containing all elements of all its predecessors.

> The union of the set of FISONs is not contained in a single FISON.

Obviously a false claim. If two or more natnumbers are in some FISONs, then they are in one of them. Therefore the sequence does not contain more than is already unioned in at least one term of the sequence. This is the basic property of FISONs. It holds for all existing FISONs. If there is no last FISON, then it does not hold for this FISON, but for all others.

Regards, WM

On 4/1/2022 3:21 PM, WM wrote:
> William schrieb am Freitag, 1. April 2022 um 20:50:40 UTC+2:
>> On Friday, April 1, 2022 at 3:42:27 PM UTC-3, WM wrote:
>>> existing FISON:
>>
>> More nonsense. The collection of FISONs is a set.
>
> Obviously a false claim. More nonsense is the correct announcement.

Wrong. The collection of FISONs is a set.

>
>> The set of FISONs does not change.
>
> Obviously a false claim. Potentially infinite collections do change.

Wrong. Sets do not change, sets are not variables. If you make a change to a set, it is now a different set.
math 101.

>
>> The set of FISONs does not contain a largest FISON.
>
> Every FISON contains a largest element. Every set of FISONs contains a largest FISON containing all elements of all its predecessors.

Wrong. there is no largest FISON.

>
>> The union of the set of FISONs is not contained in a single FISON.
>
> Obviously a false claim.

Wrong again! Why dont you rethink that ?

> If two or more natnumbers are in some FISONs, then they are in one of them.

state that using MATH.

> Therefore

< snip bla bla >
> Regards, WM

On Friday, April 1, 2022 at 5:21:11 PM UTC-3, WM wrote:
> William schrieb am Freitag, 1. April 2022 um 20:50:40 UTC+2:
> > On Friday, April 1, 2022 at 3:42:27 PM UTC-3, WM wrote:
> > > existing FISON:
> >
> > More nonsense. The collection of FISONs is a set.
> Obviously a false claim.

Nope, a simple statement of the way things are if you take the axiom of infinity.

You can if you wish, negate the axiom of infinity (so the collection of FISONs is not a set) but then you cannot use arguments based on this to show that accepting the axiom of infinity leads to contradiction.

To date you have not shown a contradiction, just results that you do not like. You will have to do better than finding results that you consider "repugnant to the nature of mathematics"

--
William Hughes

On Friday, 1 April 2022 at 15:16:35 UTC-3, WM wrote:
> [...] FISONs obey inclusion monotony. Everything contained in some FISONs is contained in one FISON by the construction of FISONs.

The union of a finite number of FISONs is a single FISON. Sure.
>
> That's why I have been using them for decades.

And using them wrongly all this time. You know FUCK ALL about mathematics.

> F(1) ⊂ F(2) ⊂ F(3) ⊂ ... There is no last FISON, but there is no infinite FISON. It is impossible that two or more elements of A are contained in FISONs but are not contained in one FISON.

"two or more" is wrong. Infinitely many (different) FISONs are not contained in a single FISON.

fredag 1 april 2022 kl. 11:34:00 UTC+2 skrev WM:
> William schrieb am Donnerstag, 31. März 2022 um 20:40:18 UTC+2:
> > On Thursday, March 31, 2022 at 2:24:11 PM UTC-3, WM wrote:
>
> > > > No single element of the sequence of all FISONs contains the union of all FISONs.
> > > Note that only single elements are in the union. What is not in the sequence cannot be in the union
> > True but does not contradict my statement.
> It contradicts the statement that the union could contain more than the sequence. The sequence however has two properties:
> (1) The sequence contains only finite FISONs and
> (2) the sequence contains all unions of FISONs which are contained in the sequence.
> > Every "single element" (every FISON) is *contained* in the union. No "single element" (No FISON) *contains* the union.
> No single element *that you can define* contains the union. The reason is the potential infinity of the sequence.
>
> But fact is that every union is contained in the sequence. Therefore the union cannot contain more than the sequence. Therefore the union cannot be actually infinite.
>
> Regards, WM

False, the union of all FISONs is N

On Friday, 1 April 2022 at 16:48:12 UTC+3, WM wrote:
> Eram semper recta schrieb am Freitag, 1. April 2022 um 15:29:17 UTC+2:
> > On Friday, 1 April 2022 at 13:36:19 UTC+3, WM wrote:
> > > Eram semper recta schrieb am Freitag, 1. April 2022 um 07:10:06 UTC+2:
> > >
> > > > Your arguments about Cantor are 100% sound.
> > > It is relieving to know that mathematicians can understand this.
> > > > The number is NOT the formula.
> > > Correct. But both can have the same notation. Like Millers and millers.
> > Not in this case. Any formula you give for pi never gives the number pi, only a recognised constant.
> We had agreed long ago that it is a matter of taste whether irrationals are called numbers.

I have never agreed.

> At least I had agreed.

Right. It is not a matter of taste that you can call irrational ratios "numbers" because by definition:

**A number is a name given to a measure that describes a magnitude or size**

If ratios without quotientness (πηλικότητα) are assumed to have a measure (meaning there is a number that describes the measure of the antecedent magnitude), then there must be a number that describes said measure.

Quotientness of a ratio means that both aliquot parts (antecedent and consequent) have a common measure (divisor).

The ratio circumference : diameter has no quotientness, therefore there is no number describing its measure.

Pi does not exist as either a magnitude or a number. It's entire concept is based on a failed measure that reveals a ***constant*** approximation.

But the topic I am discussing is not about these things. It is about your claim that a formula represents a "real number", which is obviously garbage.

Like Wildberger and Zeilberger, you fail to understand that a formula cannot represent any number in an infinite number of steps.

>
> Regards, WM

fredag 1 april 2022 kl. 11:53:43 UTC+2 skrev WM:
> zelos...@gmail.com schrieb am Freitag, 1. April 2022 um 06:43:53 UTC+2:
>
> > There are no "activity", no "action" in mathematics
> Generators generate. That's an activity.
>
> Regards, WM
There is no activity, things just are.

fredag 1 april 2022 kl. 12:24:40 UTC+2 skrev WM:
> zelos...@gmail.com schrieb am Freitag, 1. April 2022 um 06:45:07 UTC+2:
> > torsdag 31 mars 2022 kl. 18:26:21 UTC+2 skrev WM:
> > > Try to find a wrong step here:
> > > Every FISON is finite.
> > Correct
> > > Every FISON contains all its predecessors.
> > Correct
> > > The sequence of all FISONs contains all FISONs including all successors of all FISONs.
> > Correct
> > > The sequence of all FISONs contains the union of all FISONs.
> > False,
> Then find acounterexample, that is a FISON that is not contained in a union of FISONs contained in the sequence. Fail.

I did, N is the union of all FISONs but not in the sequence.

> > the union of all FISONs is N but the sequence does not contain N
> If |ℕ| = ℵo the union of FISONs is not ℕ. The union of all FISONs is contained in the sequence of all FISONs as a FISON. But all FISONs are finite, i.e., less than ℵo.
>
> Regards, WM

False, you assert this but cannot prove it.

I can prove that the union of all is N

On Friday, 1 April 2022 at 21:07:27 UTC+3, WM wrote:
> William schrieb am Freitag, 1. April 2022 um 19:46:29 UTC+2:
> > On Friday, April 1, 2022 at 10:51:12 AM UTC-3, WM wrote:
> >
> > > (There is no infinite set but only a potentially infinite collection of FISONs.)
> > Piffle
> (1) The union of FISONs cannot contain more than the sequence of FISONs.
> (2) The sequence does not contain more than is already unioned in at least one term of the sequence.
> (3) Every term is finite.
>
> What can't you read or understand?
>
> If you can understand, then you know: if |ℕ| = ℵo then there must be dark natural numbers.

Okay, now I see why you are calling them "dark numbers", because you are trying to educate baboons who think infinity is possible.

So, "dark number" is your way of poking fun at them?

Dark number in simple language means "number that cannot be known", which makes perfect sense in this context.

Fact of the matter is that "dark numbers" do not exist. You should try telling them these things plainly followed by 3 hail Marys.

However, you fall into a similar trap when you claim a formula defines a number. In this case there will always be "dark digits" that you can never know. Chuckle.

What I am saying is that you need to be consistent.

FISON argument is sound - always has been - it's so simple that any unpolluted brain can grasp it, but where brains infected with syphilis are concerned, all bets are off.

>
> Regards, WM

On 4/1/2022 5:53 AM, WM wrote:
> zelos...@gmail.com schrieb
> am Freitag, 1. April 2022 um 06:43:53 UTC+2:

>> There are no "activity", no "action" in mathematics
>
> Generators generate. That's an activity.

Then stepping stones must step.

William schrieb am Freitag, 1. April 2022 um 22:52:13 UTC+2:
> On Friday, April 1, 2022 at 5:21:11 PM UTC-3, WM wrote:
> > William schrieb am Freitag, 1. April 2022 um 20:50:40 UTC+2:
> > > On Friday, April 1, 2022 at 3:42:27 PM UTC-3, WM wrote:
> > > > existing FISON:
> > >
> > > More nonsense. The collection of FISONs is a set.
> > Obviously a false claim.
> Nope, a simple statement of the way things are if you take the axiom of infinity.

Here we see that this axiom leads to contradictions if applied to FISONs. If it is applied to natural numbers, then dark numbers (numbers not belonging to FISONs) must be accepted.
>
> You can if you wish, negate the axiom of infinity (so the collection of FISONs is not a set) but then you cannot use arguments based on this to show that accepting the axiom of infinity leads to contradiction.

I have shown that the axiom, if applied to FISONs, leads to a contradiction..
>
> To date you have not shown a contradiction,

That statement is a result of your blindness. I know a lot of mathematicians who agree that in the sequence of all FISONs all FISONs that can be unioned have been unioned already. There is no FISON that could increase the unions already existing in the sequence.

You cannot find a FISON that could increase the unions already performed.

Regards, WM

horand....@gmail.com schrieb am Samstag, 2. April 2022 um 02:26:09 UTC+2:
> On Friday, 1 April 2022 at 15:16:35 UTC-3, WM wrote:

> > F(1) ⊂ F(2) ⊂ F(3) ⊂ ... There is no last FISON, but there is no infinite FISON. It is impossible that two or more elements of A are contained in FISONs but are not contained in one FISON.
> "two or more" is wrong. Infinitely many (different) FISONs are not contained in a single FISON.

Obviously you use "infinitely" with no specification in accordance with the frauds of matheology.
Potential infinity is no problem: You cannot find a FISON that could increase all unions already performed in the sequence.
Actual infinity is impossible. There are not more than any natural number of FISONs.

Regards, WM

zelos...@gmail.com schrieb am Samstag, 2. April 2022 um 09:13:41 UTC+2:
> fredag 1 april 2022 kl. 11:53:43 UTC+2 skrev WM:
> > zelos...@gmail.com schrieb am Freitag, 1. April 2022 um 06:43:53 UTC+2:
> >
> > > There are no "activity", no "action" in mathematics
> > Generators generate. That's an activity.
> >
> There is no activity, things just are.

in your brain?

Regards, WM

zelos...@gmail.com schrieb am Samstag, 2. April 2022 um 09:15:15 UTC+2:
> But all FISONs are finite, i.e., less than ℵo.

> False, you assert this but cannot prove it.

Chuckle.

Regards, WM

Eram semper recta schrieb am Samstag, 2. April 2022 um 09:24:57 UTC+2:
> On Friday, 1 April 2022 at 21:07:27 UTC+3, WM wrote:

> Okay, now I see why you are calling them "dark numbers", because you are trying to educate baboons who think infinity is possible.

If an actually infinite set is possible, then most of its elements cannot be found.
>
> Dark number in simple language means "number that cannot be known", which makes perfect sense in this context.
>
> Fact of the matter is that "dark numbers" do not exist.

If you consider the smallest positive fraction that you can consider, then there are infinitely many positive fractions smaller than this. They are either not existing or dark.

> FISON argument is sound - always has been - it's so simple that any unpolluted brain can grasp it, but where brains infected with syphilis are concerned, all bets are off.

Meanwhile several other mathematicians are of the same opinion.

(1) The union of FISONs cannot contain more than the sequence of FISONs.
(2) The sequence does not contain more than is already unioned in at least one term of the sequence.

To assume that another union will increase the FISONs already unioned is really a symptom of hypnotized brains. But this result shows that the union of all FISONs is not actually infinite. If all natnumbers with |ℕ| = ℵo exist, then there must be more than are in FISONs. I do not claim that this is the case. But the argument with the smallest fraction makes it probable because otherwise the real line would have a gap between 0 and the smallest definable fraction.

Regards, WM

On 4/2/2022 10:04 AM, WM wrote:
> horand....@gmail.com schrieb am Samstag, 2. April 2022 um 02:26:09 UTC+2:
>> On Friday, 1 April 2022 at 15:16:35 UTC-3, WM wrote:
>
>>> F(1) ⊂ F(2) ⊂ F(3) ⊂ ... There is no last FISON, but there is no infinite FISON. It is impossible that two or more elements of A are contained in FISONs but are not contained in one FISON.
>> "two or more" is wrong. Infinitely many (different) FISONs are not contained in a single FISON.

True.

>
> Obviously you use "infinitely" with no specification in accordance with the frauds of matheology.

Self-Specification is fraud, WM.

> You cannot find a FISON that could increase all unions already performed in the sequence.

Potential infinity means finite, so just use the word finite, instead of misdirecting people.

> You cannot find a FISON that could increase all unions already performed in the sequence.

you stopped at k again, just use FISON(k+1)

> Actual infinity is impossible.

wrong.

> There are not more than any natural number of FISONs.

So you agree, there are an infinity of natural numbers, so there is an infinity of FISONs.

>
> Regards, WM

On 4/2/2022 9:47 AM, WM wrote:
> William schrieb am Freitag, 1. April 2022 um 22:52:13 UTC+2:
>> On Friday, April 1, 2022 at 5:21:11 PM UTC-3, WM wrote:
>>> William schrieb am Freitag, 1. April 2022 um 20:50:40 UTC+2:
>>>> On Friday, April 1, 2022 at 3:42:27 PM UTC-3, WM wrote:
>>>>> existing FISON:
>>>>
>>>> More nonsense. The collection of FISONs is a set.
>>> Obviously a false claim.
>> Nope, a simple statement of the way things are if you take the axiom of infinity.
>
> Here we see that this axiom leads to contradictions if applied to FISONs. If it is applied to natural numbers, then dark numbers (numbers not belonging to FISONs) must be accepted.

Prove it.

>>
>> You can if you wish, negate the axiom of infinity (so the collection of FISONs is not a set) but then you cannot use arguments based on this to show that accepting the axiom of infinity leads to contradiction.
>
> I have shown that the axiom, if applied to FISONs, leads to a contradiction.

Bunk.

>>
>> To date you have not shown a contradiction,
>
> That statement is a result of your blindness. I know a lot of mathematicians who agree that in the sequence of all FISONs all FISONs that can be unioned have been unioned already. There is no FISON that could increase the unions already existing in the sequence.

just use the next FISON. There is no end FISON, or last FISON.

Your statement is false.

>
> You cannot find a FISON that could increase the unions already performed.

You stopped at k again, just use FISON(k+1)

>
> Regards, WM

Why do you go on like this ? are you imprisoned ?

On 4/2/2022 10:23 AM, WM wrote:
> Eram semper recta schrieb am Samstag, 2. April 2022 um 09:24:57 UTC+2:
>> On Friday, 1 April 2022 at 21:07:27 UTC+3, WM wrote:

<snip Troll to Troll broadcast>

On 4/2/2022 10:09 AM, WM wrote:
> zelos...@gmail.com schrieb am Samstag, 2. April 2022 um 09:15:15 UTC+2:
>> But all FISONs are finite, i.e., less than ℵo.
>
>> False, you assert this but cannot prove it.
>
> Chuckle.
>
> Regards, WM

WM chuckles when someone asks him to prove it.

On Saturday, April 2, 2022 at 11:47:39 AM UTC-3, WM wrote:
> William schrieb am Freitag, 1. April 2022 um 22:52:13 UTC+2:

> > Nope, a simple statement of the way things are if you take the axiom of infinity.
> Here we see that this axiom leads to contradictions if applied to FISONs.

Nope. You want "The union of a set of FISONs is a FISON". This is (trivially) false if the set has no largest element. (The union will not have a largest element and thus cannot be a FISON). This is not a contradiction. There union has no largest element, not because there is a FISON with no largest element, but because the set has no largest FISON.

--
William Hughes

On Saturday, 2 April 2022 at 18:09:55 UTC+3, WM wrote:
> idiot schrieb am Samstag, 2. April 2022 um 09:15:15 UTC+2:
> > But all FISONs are finite, i.e., less than ℵo.
> > False, you assert this but cannot prove it.

This poor idiot Zelos is telling you that ℵo exists without any proof whatsoever, but then ironically asks you to prove that ℵo does
not exist.

The same university (Oops-Allah) also teaches that:

"h*f(x)/h means h is a factor of f(x)." - Zelos Malum/Markus Klyver

You can't fix stupid I am sorry to inform you.

> Chuckle.
>
> Regards, WM

On Saturday, 2 April 2022 at 20:05:31 UTC+3, Eram semper recta wrote:
> On Saturday, 2 April 2022 at 18:09:55 UTC+3, WM wrote:
> > idiot schrieb am Samstag, 2. April 2022 um 09:15:15 UTC+2:
> > > But all FISONs are finite, i.e., less than ℵo.
> > > False, you assert this but cannot prove it.
> This poor idiot Zelos is telling you that ℵo exists without any proof whatsoever, but then ironically asks you to prove that ℵo does
> not exist.

The burden of proof lies with the cranks of mainstream academia.

>
> The same university (Oops-Allah) also teaches that:
>
> "h*f(x)/h means h is a factor of f(x)." - Zelos Malum/Markus Klyver
>
> You can't fix stupid I am sorry to inform you.
>
> > Chuckle.
> >
> > Regards, WM