bassam karzeddin schrieb am Donnerstag, 14. September 2023 um 03:22:24 UTC+2:
> our Pi in mind for the so-called 🔵 circle doesn’t exist nor it is a number FOR MORE THAN SURE

Pi is not a number that can be fixed by digits. But for every rational number we can find out the trichotomy properties. That is possible because there is no bound to the number of digits which can be used to approximate pi.

Regards, WM

On 9/15/2023 9:07 AM, WM wrote:
> bassam karzeddin schrieb am Donnerstag,
> 14. September 2023 um 03:22:24 UTC+2:

>> our Pi in mind for the so-called 🔵 circle
>> doesn’t exist nor it is a number
>> FOR MORE THAN SURE
>
> Pi is not a number that can be fixed by digits.

The smallest set which contains
each π.digit which can be counted to
is sufficient to determine
no more than one point for pi = π

Also,
in order for "continuous" functions to
behave continuously,
for example, to _not_ jump over values
while being continuous at each argument,
the π.digits must determine
no less than one point for pi = π

Therefore,
the 1x1 1.ended π.digit sequence 3.1415926535...
fixes no more and no less than
one point for π = 4⋅arctan(1)

> But for every rational number
> we can find out the trichotomy properties.
> That is possible because
> there is no bound to the number of digits
> which can be used to approximate pi.

On Wednesday, September 13, 2023 at 6:18:44 PM UTC+3, WM wrote:
> bassam karzeddin schrieb am Mittwoch, 13. September 2023 um 03:16:42 UTC+2:
>
> > Between two given distinct "constructible " numbers, no matter however close to each other YOU may think, or no matter however far from each others You may think, then Between them there are infinitely many more & only "constructible "numbers between them, where no other types of real numbers ever exist between them
> >
> > .Where if you think otherwise, then simply prove your insight 😉!
> That is impossible. Numbers that are not constructible do only exist because Cantor's actual infinity is assumed. Without that only potential infinity exists and you are right.
>
> Regards, WM

But world school students have grown up nowadays to realize finally that natural numbers are infact an endless chain of successive integers with no existing largest natural number, I.e, they aren't bounded by any silly human mind fictions like the so-called infinity ♾️, beside that infinity in mathematics isn't a number nor anything else FOR SURE

BKK

On Friday, September 15, 2023 at 4:07:12 PM UTC+3, WM wrote:
> bassam karzeddin schrieb am Donnerstag, 14. September 2023 um 03:22:24 UTC+2:
> > our Pi in mind for the so-called 🔵 circle doesn’t exist nor it is a number FOR MORE THAN SURE
> Pi is not a number that can be fixed by digits. But for every rational number we can find out the trichotomy properties. That is possible because there is no bound to the number of digits which can be used to approximate pi..
>
> Regards, WM

For any obtained approximations of the believed existing number like Pi among humans, there is a corresponding regular polygon, where the ratio of the perimeter distance to the longest distance between its vertices is the same approximations of that belived number as Pi, FOR SURE

Hence, Pi is purely a property of regular existing polygons, which is never any constant number but a variable constructible number that can be comparable with rational numbers

In short, Circle 🔵 is a non-existing mathematical object nor Pi is any existing real number (as per common human perception)

And people must not be shocked by the non-existence of the circle, since simply the regular heptagon never exists!

Even though, any skilled carpenter can make it to a degree of accuracy that pleases ALL humans on earth 🌎 & sky as well

BKK

On 9/15/2023 12:38 PM, bassam karzeddin wrote:
> On Wednesday, September 13, 2023 at 6:18:44 PM UTC+3, WM wrote:
>> bassam karzeddin schrieb am Mittwoch, 13. September 2023 um 03:16:42 UTC+2:
>>
>>> Between two given distinct "constructible " numbers, no matter however close to each other YOU may think, or no matter however far from each others You may think, then Between them there are infinitely many more & only "constructible "numbers between them, where no other types of real numbers ever exist between them
>>>
>>> .Where if you think otherwise, then simply prove your insight 😉!
>> That is impossible. Numbers that are not constructible do only exist because Cantor's actual infinity is assumed. Without that only potential infinity exists and you are right.
>>
>> Regards, WM
>
> But world school students have grown up nowadays to realize finally that natural numbers are infact an endless chain of successive integers with no existing largest natural number,

> I.e, they aren't bounded by any silly human mind fictions like the so-called infinity ♾️,
^^^^^^^^^^^^

Since when does infinity hold anybody back? An endless infinity is not a
boundary.

> beside that infinity in mathematics isn't a number nor anything else FOR SURE
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

On 9/15/2023 1:12 PM, Chris M. Thomasson wrote:
> On 9/15/2023 12:38 PM, bassam karzeddin wrote:
>> On Wednesday, September 13, 2023 at 6:18:44 PM UTC+3, WM wrote:
>>> bassam karzeddin schrieb am Mittwoch, 13. September 2023 um 03:16:42
>>> UTC+2:
>>>
>>>> Between two given distinct "constructible " numbers, no matter
>>>> however close to each other YOU may think, or no matter however far
>>>> from each others You may think, then Between them there are
>>>> infinitely many more & only "constructible "numbers between them,
>>>> where no other types of real numbers ever exist between them
>>>>
>>>> .Where if you think otherwise, then simply prove your insight 😉!
>>> That is impossible. Numbers that are not constructible do only exist
>>> because Cantor's actual infinity is assumed. Without that only
>>> potential infinity exists and you are right.
>>>
>>> Regards, WM
>>
>> But world school students have grown up nowadays to realize finally
>> that natural numbers are infact an endless chain of successive
>> integers with no existing largest natural number,
>
>> I.e, they aren't bounded by any silly human mind fictions like the
>> so-called infinity ♾️,
> ^^^^^^^^^^^^
>
> Since when does infinity hold anybody back? An endless infinity is not a
> boundary.

infinity as in 1, 2, 3, 4, 5, ... Has no boundary

>
>
>> beside that infinity in mathematics isn't a number nor anything else
>> FOR SURE
> ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>
>
>

Jim Burns schrieb am Freitag, 15. September 2023 um 18:41:37 UTC+2:
> On 9/15/2023 9:07 AM, WM wrote:
> > bassam karzeddin schrieb am Donnerstag,
> > 14. September 2023 um 03:22:24 UTC+2:
>
> >> our Pi in mind for the so-called 🔵 circle
> >> doesn’t exist nor it is a number
> >> FOR MORE THAN SURE
> >
> > Pi is not a number that can be fixed by digits.
> The smallest set which contains
> each π.digit which can be counted to
> is sufficient to determine
> no more than one point for pi = π

No. Pi is a limit, a matter of analysis. "Should we briefly characterize the new view of the infinite introduced by Cantor, we could certainly say: In analysis we have to deal only with the infinitely small and the infinitely large as a limit-notion, as something becoming, emerging, produced, i.e., as we put it, with the potential infinite. But this is not the proper infinite. That we have for instance when we consider the entirety of the numbers 1, 2, 3, 4, ... itself as a completed unit, or the points of a line as an entirety of things which is completely available. That sort of infinity is named actual infinite." [D. Hilbert: "Über das Unendliche", Mathematische Annalen 95 (1925) p. 167]

> the 1x1 1.ended π.digit sequence 3.1415926535...

If you maintain your nonsensical opinions, then try to fix pi by its digits..

Regards, WM

On 9/15/2023 1:19 PM, WM wrote:
> Jim Burns schrieb am Freitag, 15. September 2023 um 18:41:37 UTC+2:
>> On 9/15/2023 9:07 AM, WM wrote:
>>> bassam karzeddin schrieb am Donnerstag,
>>> 14. September 2023 um 03:22:24 UTC+2:
>>
>>>> our Pi in mind for the so-called 🔵 circle
>>>> doesn’t exist nor it is a number
>>>> FOR MORE THAN SURE
>>>
>>> Pi is not a number that can be fixed by digits.
>> The smallest set which contains
>> each π.digit which can be counted to
>> is sufficient to determine
>> no more than one point for pi = π
>
> No. Pi is a limit, a matter of analysis. "Should we briefly characterize the new view of the infinite introduced by Cantor, we could certainly say: In analysis we have to deal only with the infinitely small and the infinitely large as a limit-notion, as something becoming, emerging, produced, i.e., as we put it, with the potential infinite. But this is not the proper infinite. That we have for instance when we consider the entirety of the numbers 1, 2, 3, 4, ... itself as a completed unit, or the points of a line as an entirety of things which is completely available. That sort of infinity is named actual infinite." [D. Hilbert: "Über das Unendliche", Mathematische Annalen 95 (1925) p. 167]
>
>> the 1x1 1.ended π.digit sequence 3.1415926535...
>
> If you maintain your nonsensical opinions, then try to fix pi by its digits.
>
> Regards, WM

i[0] = 1
i[n] = i[n - 1] + 1

Its never completed, it has no limit to get closer and closer to.

On 9/15/2023 1:38 PM, Chris M. Thomasson wrote:
> On 9/15/2023 1:19 PM, WM wrote:
>> Jim Burns schrieb am Freitag, 15. September 2023 um 18:41:37 UTC+2:
>>> On 9/15/2023 9:07 AM, WM wrote:
>>>> bassam karzeddin schrieb am Donnerstag,
>>>> 14. September 2023 um 03:22:24 UTC+2:
>>>
>>>>> our Pi in mind for the so-called 🔵 circle
>>>>> doesn’t exist nor it is a number
>>>>> FOR MORE THAN SURE
>>>>
>>>> Pi is not a number that can be fixed by digits.
>>> The smallest set which contains
>>> each π.digit which can be counted to
>>> is sufficient to determine
>>> no more than one point for pi = π
>>
>> No. Pi is a limit, a matter of analysis. "Should we briefly
>> characterize the new view of the infinite introduced by Cantor, we
>> could certainly say: In analysis we have to deal only with the
>> infinitely small and the infinitely large as a limit-notion, as
>> something becoming, emerging, produced, i.e., as we put it, with the
>> potential infinite. But this is not the proper infinite. That we have
>> for instance when we consider the entirety of the numbers 1, 2, 3, 4,
>> ... itself as a completed unit, or the points of a line as an entirety
>> of things which is completely available. That sort of infinity is
>> named actual infinite." [D. Hilbert: "Über das Unendliche",
>> Mathematische Annalen 95 (1925) p. 167]
>>
>>> the 1x1 1.ended π.digit sequence 3.1415926535...
>>
>> If you maintain your nonsensical opinions, then try to fix pi by its
>> digits.
>>
>> Regards, WM
>
> i[0] = 1
> i[n] = i[n - 1] + 1
>
> Its never completed, it has no limit to get closer and closer to.

Think of another type of limit where the iterates get close, and some of
them start to orbit it...

On 9/15/2023 1:39 PM, Chris M. Thomasson wrote:
> On 9/15/2023 1:38 PM, Chris M. Thomasson wrote:
>> On 9/15/2023 1:19 PM, WM wrote:
>>> Jim Burns schrieb am Freitag, 15. September 2023 um 18:41:37 UTC+2:
>>>> On 9/15/2023 9:07 AM, WM wrote:
>>>>> bassam karzeddin schrieb am Donnerstag,
>>>>> 14. September 2023 um 03:22:24 UTC+2:
>>>>
>>>>>> our Pi in mind for the so-called 🔵 circle
>>>>>> doesn’t exist nor it is a number
>>>>>> FOR MORE THAN SURE
>>>>>
>>>>> Pi is not a number that can be fixed by digits.
>>>> The smallest set which contains
>>>> each π.digit which can be counted to
>>>> is sufficient to determine
>>>> no more than one point for pi = π
>>>
>>> No. Pi is a limit, a matter of analysis. "Should we briefly
>>> characterize the new view of the infinite introduced by Cantor, we
>>> could certainly say: In analysis we have to deal only with the
>>> infinitely small and the infinitely large as a limit-notion, as
>>> something becoming, emerging, produced, i.e., as we put it, with the
>>> potential infinite. But this is not the proper infinite. That we have
>>> for instance when we consider the entirety of the numbers 1, 2, 3, 4,
>>> ... itself as a completed unit, or the points of a line as an
>>> entirety of things which is completely available. That sort of
>>> infinity is named actual infinite." [D. Hilbert: "Über das
>>> Unendliche", Mathematische Annalen 95 (1925) p. 167]
>>>
>>>> the 1x1 1.ended π.digit sequence 3.1415926535...
>>>
>>> If you maintain your nonsensical opinions, then try to fix pi by its
>>> digits.
>>>
>>> Regards, WM
>>
>> i[0] = 1
>> i[n] = i[n - 1] + 1
>>
>> Its never completed, it has no limit to get closer and closer to.
>
> Think of another type of limit where the iterates get close, and some of
> them start to orbit it...

This can be considered an attractor, in a sense.

on 9/15/2023, Chris M. Thomasson supposed :
> On 9/15/2023 1:12 PM, Chris M. Thomasson wrote:
>> On 9/15/2023 12:38 PM, bassam karzeddin wrote:
>>> On Wednesday, September 13, 2023 at 6:18:44 PM UTC+3, WM wrote:
>>>> bassam karzeddin schrieb am Mittwoch, 13. September 2023 um 03:16:42
>>>> UTC+2:
>>>>
>>>>> Between two given distinct "constructible " numbers, no matter however
>>>>> close to each other YOU may think, or no matter however far from each
>>>>> others You may think, then Between them there are infinitely many more &
>>>>> only "constructible "numbers between them, where no other types of real
>>>>> numbers ever exist between them
>>>>>
>>>>> .Where if you think otherwise, then simply prove your insight ?!
>>>> That is impossible. Numbers that are not constructible do only exist
>>>> because Cantor's actual infinity is assumed. Without that only potential
>>>> infinity exists and you are right.
>>>>
>>>> Regards, WM
>>>
>>> But world school students have grown up nowadays to realize finally that
>>> natural numbers are infact an endless chain of successive integers with no
>>> existing largest natural number,
>>
>>> I.e, they aren't bounded by any silly human mind fictions like the
>>> so-called infinity ♾️,
>> ^^^^^^^^^^^^
>>
>> Since when does infinity hold anybody back? An endless infinity is not a
>> boundary.
>
> infinity as in 1, 2, 3, 4, 5, ... Has no boundary

https://www.scientificamerican.com/article/infinity-logic-law/

On 9/15/2023 2:35 PM, FromTheRafters wrote:
> on 9/15/2023, Chris M. Thomasson supposed :
>> On 9/15/2023 1:12 PM, Chris M. Thomasson wrote:
>>> On 9/15/2023 12:38 PM, bassam karzeddin wrote:
>>>> On Wednesday, September 13, 2023 at 6:18:44 PM UTC+3, WM wrote:
>>>>> bassam karzeddin schrieb am Mittwoch, 13. September 2023 um
>>>>> 03:16:42 UTC+2:
>>>>>
>>>>>> Between two given distinct "constructible " numbers, no matter
>>>>>> however close to each other YOU may think, or no matter however
>>>>>> far from each others You may think, then Between them there are
>>>>>> infinitely many more & only "constructible "numbers between them,
>>>>>> where no other types of real numbers ever exist between them
>>>>>>
>>>>>> .Where if you think otherwise, then simply prove your insight ?!
>>>>> That is impossible. Numbers that are not constructible do only
>>>>> exist because Cantor's actual infinity is assumed. Without that
>>>>> only potential infinity exists and you are right.
>>>>>
>>>>> Regards, WM
>>>>
>>>> But world school students have grown up nowadays to realize finally
>>>> that natural numbers are infact an endless chain of successive
>>>> integers with no existing largest natural number,
>>>
>>>> I.e, they aren't bounded by any silly human mind fictions like the
>>>> so-called infinity ♾️,
>>> ^^^^^^^^^^^^
>>>
>>> Since when does infinity hold anybody back? An endless infinity is
>>> not a boundary.
>>
>> infinity as in 1, 2, 3, 4, 5, ... Has no boundary
>
> https://www.scientificamerican.com/article/infinity-logic-law/

Well, 1, 2, 3, 4, 5, ... has no boundary in the sense that there is no
largest natural number? Fair enough?

On 9/15/2023 1:41 PM, Chris M. Thomasson wrote:
> On 9/15/2023 1:39 PM, Chris M. Thomasson wrote:
>> On 9/15/2023 1:38 PM, Chris M. Thomasson wrote:
>>> On 9/15/2023 1:19 PM, WM wrote:
>>>> Jim Burns schrieb am Freitag, 15. September 2023 um 18:41:37 UTC+2:
>>>>> On 9/15/2023 9:07 AM, WM wrote:
>>>>>> bassam karzeddin schrieb am Donnerstag,
>>>>>> 14. September 2023 um 03:22:24 UTC+2:
>>>>>
>>>>>>> our Pi in mind for the so-called 🔵 circle
>>>>>>> doesn’t exist nor it is a number
>>>>>>> FOR MORE THAN SURE
>>>>>>
>>>>>> Pi is not a number that can be fixed by digits.
>>>>> The smallest set which contains
>>>>> each π.digit which can be counted to
>>>>> is sufficient to determine
>>>>> no more than one point for pi = π
>>>>
>>>> No. Pi is a limit, a matter of analysis. "Should we briefly
>>>> characterize the new view of the infinite introduced by Cantor, we
>>>> could certainly say: In analysis we have to deal only with the
>>>> infinitely small and the infinitely large as a limit-notion, as
>>>> something becoming, emerging, produced, i.e., as we put it, with the
>>>> potential infinite. But this is not the proper infinite. That we
>>>> have for instance when we consider the entirety of the numbers 1, 2,
>>>> 3, 4, ... itself as a completed unit, or the points of a line as an
>>>> entirety of things which is completely available. That sort of
>>>> infinity is named actual infinite." [D. Hilbert: "Über das
>>>> Unendliche", Mathematische Annalen 95 (1925) p. 167]
>>>>
>>>>> the 1x1 1.ended π.digit sequence 3.1415926535...
>>>>
>>>> If you maintain your nonsensical opinions, then try to fix pi by its
>>>> digits.
>>>>
>>>> Regards, WM
>>>
>>> i[0] = 1
>>> i[n] = i[n - 1] + 1
>>>
>>> Its never completed, it has no limit to get closer and closer to.
>>
>> Think of another type of limit where the iterates get close, and some
>> of them start to orbit it...
>
> This can be considered an attractor, in a sense.

Strange attractors are an interesting case....

bassam karzeddin schrieb am Freitag, 15. September 2023 um 21:51:15 UTC+2:

> In short, Circle 🔵 is a non-existing mathematical object nor Pi is any existing real number (as per common human perception)

By definition, whether it can be realized or not, the circle is the set of points which have same distance from the midpoint.
>
> And people must not be shocked by the non-existence of the circle, since simply the regular heptagon never exists!

By definition, although it cannot be constructed, the regular heptagon exists because we know what is meant by this expression. But that is irrelevant for π since the 6*2^n-gon can be constructed for every n.

Regards, WM

On Sunday, September 17, 2023 at 3:21:49 PM UTC+3, WM wrote:
> bassam karzeddin schrieb am Freitag, 15. September 2023 um 21:51:15 UTC+2:
>
> > In short, Circle 🔵 is a non-existing mathematical object nor Pi is any existing real number (as per common human perception)
> By definition, whether it can be realized or not, the circle is the set of points which have same distance from the midpoint.
> >
> > And people must not be shocked by the non-existence of the circle, since simply the regular heptagon never exists!
> By definition, although it cannot be constructed, the regular heptagon exists because we know what is meant by this expression. But that is irrelevant for π since the 6*2^n-gon can be constructed for every n.
>
> Regards, WM

So you say & most likely believe that the regular heptagon exists only by human definition, ✅️ Right?

So, did you ever & truly examine the validity of that believed definition?

Or is that definition is a kind of decision or a kind of human agreement only with no rigorous proof?

BKk

On Sunday, September 17, 2023 at 3:21:49 PM UTC+3, WM wrote:
> bassam karzeddin schrieb am Freitag, 15. September 2023 um 21:51:15 UTC+2:
>
> > In short, Circle 🔵 is a non-existing mathematical object nor Pi is any existing real number (as per common human perception)
> By definition, whether it can be realized or not, the circle is the set of points which have same distance from the midpoint.
> >
> > And people must not be shocked by the non-existence of the circle, since simply the regular heptagon never exists!
> By definition, although it cannot be constructed, the regular heptagon exists because we know what is meant by this expression. But that is irrelevant for π since the 6*2^n-gon can be constructed for every n.
>
> Regards, WM

Didn't you also read about my old public published proof
About the non-existence of such believed angles among humans like Pi/7 with numerical irrefutable proofs about the non-righ & non-existing angle triangle like (1, cos(pi/7), sin(pi/7))

Or must I repeat my proof about it?
Bassam karzeddin

On Sunday, September 17, 2023 at 10:42:08 PM UTC+3, bassam karzeddin wrote:
> On Sunday, September 17, 2023 at 3:21:49 PM UTC+3, WM wrote:
> > bassam karzeddin schrieb am Freitag, 15. September 2023 um 21:51:15 UTC+2:
> >
> > > In short, Circle 🔵 is a non-existing mathematical object nor Pi is any existing real number (as per common human perception)
> > By definition, whether it can be realized or not, the circle is the set of points which have same distance from the midpoint.
> > >
> > > And people must not be shocked by the non-existence of the circle, since simply the regular heptagon never exists!
> > By definition, although it cannot be constructed, the regular heptagon exists because we know what is meant by this expression. But that is irrelevant for π since the 6*2^n-gon can be constructed for every n.
> >
> > Regards, WM
> Didn't you also read about my old public published proof
> About the non-existence of such believed angles among humans like Pi/7 with numerical irrefutable proofs about the non-righ & non-existing angle triangle like (1, cos(pi/7), sin(pi/7))
>
> Or must I repeat my proof about it?
> Bassam karzeddin

It is very necessary to invent tools & new IQ tests inorde to discover truly the clever mathematicians, since the vast majorities (even with their highest performance records) are truly too stupid beyond the normal human natural stupidity) & strictly in too elementary mathematics, FOR SURE

BKK