William schrieb am Freitag, 2. Juli 2021 um 20:27:51 UTC+2:
> On Friday, July 2, 2021 at 1:52:16 PM UTC-4, WM wrote:
> > William schrieb am Freitag, 2. Juli 2021 um 18:08:44 UTC+2:
> > > On Friday, July 2, 2021 at 11:51:51 AM UTC-4, WM wrote:
> >
> > > > > You have said that "dark natural numbers" (whatever they are, they are certainly not natural numbers) are not the largest element of a FISON..
> > > > No, they cannot be counted to.
> > > So no element of |N_F is "dark" despite |N_F having no last element. Recall that a stepwise process cannot deal with subsets of |N_F that have no last element.
> > It [ a stepwise process] cannot deal with almost all elements of the set because it can deal only with defined numbers (you know that's a finite set)
>
> Indeed, so rather than a stepwise process that cannot deal with a set with no last element. use an appropriate method to get the result of applying the operator to the sequence. Recall that the set |N_F does not have a last element and does not contain a "dark" element.

Here is an appropriate method for the cursor moving from 1 to 0. It passes all unit fractions. It never passes two or more simultaneously. Therefore it must pass a last one. This would yield a contradiction if being countable to.

Regards, WM

On Friday, July 2, 2021 at 3:41:43 PM UTC-4, WM wrote:
> William schrieb am Freitag, 2. Juli 2021 um 20:20:29 UTC+2:
> > On Friday, July 2, 2021 at 1:48:23 PM UTC-4, WM wrote:
> > > William schrieb am Freitag, 2. Juli 2021 um 18:14:15 UTC+2:
> > > > On Friday, July 2, 2021 at 12:04:08 PM UTC-4, WM wrote:
> > >
> > > > > > > > > Up to every visible number counting
> > > > > > > > does not produce the outcome of applying the operator to the series.
> > > > > > > That's a very strong piece of evidence in favour
> > > > > > of not trying to use a stepwise process on something that is not a stepwise process.
> > > > > Up to every visible number counting is a stepwise process.
> > > > Indeed, You cannot use counting to obtain the result of applying the operator to the sequence.
> > > Agreed!
> > So stop trying.
> I apply it only for natnumbers which have FISONs. What should hinder me?
> > To obtain the result of applying the operator to the sequence, use an appropriate method not a stepwise method.
> I do.
Nope, you keep using a stepwise method.

--
William Hughes

On Friday, July 2, 2021 at 3:44:45 PM UTC-4, WM wrote:
> William schrieb am Freitag, 2. Juli 2021 um 20:27:51 UTC+2:
> > On Friday, July 2, 2021 at 1:52:16 PM UTC-4, WM wrote:
> > > William schrieb am Freitag, 2. Juli 2021 um 18:08:44 UTC+2:
> > > > On Friday, July 2, 2021 at 11:51:51 AM UTC-4, WM wrote:
> > >
> > > > > > You have said that "dark natural numbers" (whatever they are, they are certainly not natural numbers) are not the largest element of a FISON.
> > > > > No, they cannot be counted to.
> > > > So no element of |N_F is "dark" despite |N_F having no last element.. Recall that a stepwise process cannot deal with subsets of |N_F that have no last element.
> > > It [ a stepwise process] cannot deal with almost all elements of the set because it can deal only with defined numbers (you know that's a finite set)
> >
> > Indeed, so rather than a stepwise process that cannot deal with a set with no last element. use an appropriate method to get the result of applying the operator to the sequence. Recall that the set |N_F does not have a last element and does not contain a "dark" element.
> Here is an appropriate method for the cursor

Operator, sequence, result. No Achilles, No cursor, No stepwise process.

--
William Hughes

William schrieb am Freitag, 2. Juli 2021 um 21:47:28 UTC+2:
> On Friday, July 2, 2021 at 3:41:43 PM UTC-4, WM wrote:

> > > To obtain the result of applying the operator to the sequence, use an appropriate method not a stepwise method.
> > I do.
> Nope, you keep using a stepwise method.
>
The stepwise method is appropriate for all natnumbers which have FISONs. Further it is appropriate to show that not all natnumbers have FISONs.

Regards, WM

William schrieb am Freitag, 2. Juli 2021 um 21:50:24 UTC+2:
> On Friday, July 2, 2021 at 3:44:45 PM UTC-4, WM wrote:

> > Here is an appropriate method for the cursor
> Operator, sequence, result. No Achilles, No cursor, No stepwise process.

What application remains then for set theory except masturbation of set theorists?

Regards, WM

On Friday, July 2, 2021 at 5:19:54 PM UTC-4, WM wrote:
> William schrieb am Freitag, 2. Juli 2021 um 21:47:28 UTC+2:
> > On Friday, July 2, 2021 at 3:41:43 PM UTC-4, WM wrote:
>
> > > > To obtain the result of applying the operator to the sequence, use an appropriate method not a stepwise method.
> > > I do.
> > Nope, you keep using a stepwise method.
> >
> The stepwise method

cannot answer the question, what is the result of applying the operator to the series.

--
William Hughes

On Friday, July 2, 2021 at 5:21:52 PM UTC-4, WM wrote:
> William schrieb am Freitag, 2. Juli 2021 um 21:50:24 UTC+2:
> > On Friday, July 2, 2021 at 3:44:45 PM UTC-4, WM wrote:
>
> > > Here is an appropriate method for the cursor
> > Operator, sequence, result. No Achilles, No cursor, No stepwise process.
> What application remains

Determining the result of applying the operator to the sequence. Since the sequence does not have a last element you need to use a method appropriate to a set with no last element. This rules out using a stepwise process.

--
William Hughes

On Friday, July 2, 2021 at 11:19:54 PM UTC+2, WM wrote:

> not all natnumbers have FISONs.

Does this claim have any meaning?

Hint: An e IN: Ex(x = {1, ..., n}) is a theorem in ZF(C).

It's getting wors with you, Mückenheim!

On Friday, July 2, 2021 at 11:21:52 PM UTC+2, WM wrote:

> What application remains then for set theory except masturbation of set theorists?

Oh, it forms a basis for (most of) contemporary math.

Didn't you know that?

On Friday, 2 July 2021 at 18:21:52 UTC-3, WM wrote:
> William schrieb am Freitag, 2. Juli 2021 um 21:50:24 UTC+2:
> > On Friday, July 2, 2021 at 3:44:45 PM UTC-4, WM wrote:
>
> > > Here is an appropriate method for the cursor
> > Operator, sequence, result. No Achilles, No cursor, No stepwise process.
> What application remains then for set theory except masturbation of set theorists?

There is only person that I see here continually indulging in self-gratification, and that is *YOU*

On Friday, July 2, 2021 at 8:33:19 PM UTC-4, Greg Cunt wrote:
> On Friday, July 2, 2021 at 11:19:54 PM UTC+2, WM wrote:
>
> > not all natnumbers have FISONs.
> Does this claim have any meaning?
>
> Hint: An e IN: Ex(x = {1, ..., n}) is a theorem in ZF(C).

You are forgetting the power of a WM syllogism

By definition every natural number is an element of a Peano set
x is not an element of a Peano set
x is a natural number

Amazing things WM syllogisms

--
William Hughes

William schrieb am Freitag, 2. Juli 2021 um 23:36:26 UTC+2:
> On Friday, July 2, 2021 at 5:19:54 PM UTC-4, WM wrote:
> > William schrieb am Freitag, 2. Juli 2021 um 21:47:28 UTC+2:
> > > On Friday, July 2, 2021 at 3:41:43 PM UTC-4, WM wrote:
> >
> > > > > To obtain the result of applying the operator to the sequence, use an appropriate method not a stepwise method.

An appropriate method can only be checked by the stepwise method.
> > > > I do.
> > > Nope, you keep using a stepwise method.
> > >
> > The stepwise method
> cannot answer the question, what is the result of applying the operator to the series.

The stepwise method is valid for definable natnumbers. What would hinder it? Do you agree?

Regards, WM

William schrieb am Freitag, 2. Juli 2021 um 23:41:06 UTC+2:
> On Friday, July 2, 2021 at 5:21:52 PM UTC-4, WM wrote:
> > William schrieb am Freitag, 2. Juli 2021 um 21:50:24 UTC+2:
> > > On Friday, July 2, 2021 at 3:44:45 PM UTC-4, WM wrote:
> >
> > > > Here is an appropriate method for the cursor
> > > Operator, sequence, result. No Achilles, No cursor, No stepwise process.
> > What application remains
> Determining the result of applying the operator to the sequence.

That is useless. Not even any real number can be determined by an endless sequence of digits withou constructing formula.

> Since the sequence does not have a last element you need to use a method appropriate to a set with no last element. This rules out using a stepwise process.

But they rule out also the cursor moving from 1 to 0 passing all unit fractions including that one which has no successors. This is process that can happen physically and can as well be imagined. My theory accepts this move and gives an explanation - up to every definable number in agreement with mathematics.

Regards, WM

Greg Cunt schrieb am Samstag, 3. Juli 2021 um 02:34:29 UTC+2:
> On Friday, July 2, 2021 at 11:21:52 PM UTC+2, WM wrote:
>
> > What application remains then for set theory except masturbation of set theorists?
> Oh, it forms a basis for (most of) contemporary math.
>
> Didn't you know that?

I know that it doesn't. It cannot even describe the cursor moving from 1 to 0 passing all unit fractions, even those without infinitely many successors. And it supplies an empty intersection for infinite endsegments. So it is both useless and wrong.

Regards, WM

On Saturday, July 3, 2021 at 9:54:13 AM UTC-4, WM wrote:
> William schrieb am Freitag, 2. Juli 2021 um 23:41:06 UTC+2:
> > On Friday, July 2, 2021 at 5:21:52 PM UTC-4, WM wrote:
> > > William schrieb am Freitag, 2. Juli 2021 um 21:50:24 UTC+2:
> > > > On Friday, July 2, 2021 at 3:44:45 PM UTC-4, WM wrote:
> > >
> > > > > Here is an appropriate method for the cursor
> > > > Operator, sequence, result. No Achilles, No cursor, No stepwise process.
> > > What application remains
> > Determining the result of applying the operator to the sequence.
> That is useless.

Hardly