On 11/16/2022 8:35 AM, Ross A. Finlayson wrote:
> On Wednesday, November 16, 2022 at 5:48:51 AM UTC-8, Sergi o wrote:
>> On 11/15/2022 11:34 PM, Chris M. Thomasson wrote:
>>> On 11/15/2022 3:33 PM, Fritz Feldhase wrote:
>>>> On Tuesday, November 15, 2022 at 3:40:36 PM UTC+1, Sergi o wrote:
>>>>
>>>>> you use the word "define" or "definable" however you mean "finite" which is wrong.
>>>>
>>>> Indeed! Whenever he talks about "definable XXX" he means _finitely many_ XXX.
>>>>
>>>> And his darkies are "all the others" (which "makes" a set infinite).
>>>
>>> Humm... Does he really seem to believe that something does not exist if he cannot see and/or think about it? Btw, does he mean "not existing" wrt
>>> calling something dark? If so:
>>>
>>> { 0, 1, 2, 3 }
>>>
>>> Means WM thinks that 4 is somehow dark and not attainable?
>>>
>>> I must be missing something here. Humm...
>> you are not missing some
>> thing, but WM is.
>>>
>>>
>>>> What a psychotic asshole full of shit.
>>>
>>> He has to be a really hard core worshiper at the Church of UltraFinitism...
>> and an AntiAlgebraist
>
> You mean "re: roots"?
>

that too

On Wednesday, November 16, 2022 at 6:55:53 AM UTC-8, Sergi o wrote:
> On 11/16/2022 8:41 AM, Ross A. Finlayson wrote:
> > On Wednesday, November 16, 2022 at 5:45:14 AM UTC-8, Sergi o wrote:
> >> On 11/15/2022 10:56 PM, Ross A. Finlayson wrote:
> >>> On Tuesday, November 15, 2022 at 8:47:25 PM UTC-8, Ross A. Finlayson wrote:
> >>>> On Tuesday, November 15, 2022 at 7:18:11 PM UTC-8, Gus Gassmann wrote:
> >>>>> On Tuesday, 15 November 2022 at 19:27:49 UTC-4, Fritz Feldhase wrote:
> >>>>>> On Tuesday, November 15, 2022 at 3:23:38 PM UTC+1, Sergi o wrote:
> >>>>>>
> >>>>>>> so you are saying it is possible to completly verify using "step by step" on an infinite sequence ?
> >>>>>> Of course!
> >>>>>>
> >>>>>> Everybody knows that Chuck Norris can do it!
> >>>>> He does it twice, even. (Probably just to be sure, though...)
> >>>> Quit feeding the troll, you should have something better to do, like learning mathematics.
> >>>>
> >>>> Not just re-capping bull-shit with boring useless repeated bull and further bull.
> >>>>
> >>>> If you're going to be bull-headed, don't be bull-shitted.
> >>>>
> >>>> And quit pissing on that bum.
> >>>
> >>>
> >>>
> >>> For example there's the equivalency function, why don't you try to attack or defend it.
> >> => there is no equivalency function.
> >>
> >> there is an equivalence function or equivalent function, now which do you mean ?
> >>>
> >>> How about this, you take turns, assembling and disassembling it, making and breaking it,
> >>> take turns on either side of the argument until you run out.
> >>>
> >>> Or, you know, learn something or teach something.
> >>>
> >>> It's got a very _strong_ defense.
> >>>
> >>>
> >>> I challenge you to draw a line and attack any way you see fit, the equivalency function.
> >>>
> replaced your snipage,
> > For example there's the equivalency function, why don't you try to attack or defend it.
>
> => there is no equivalency function.
>
> there is an equivalence function or equivalent function, now which do you mean ?
> no answer ?
> >>>
> >
> > It's like the first lesson in pre-calc:
> >
> > "You know the function that is drawing a line the points?
> do you mean 'through' the points ?
> > It doesn't exist for this course, we'll be developing one
> > after limits in the field instead."
> that is nonsense.
> >
> > So, that instruction went right to your head, one hopes,
> > but this is part of a broader course, for more mature students.
> > If you need some help, I wrote 10,000 posts about it.
> why ?
> >
> > Really could learn something, ....
> pre-calc ?
> >
> > Up to there it's underdefined, of course.
> is your day job that boring ?

"Post-Calc".

Hey remember when we were talking about "line integral".

There's a great book called "Cable Structures".

It has lots of empirical formulas.

Or: formulae.

On 11/15/2022 4:34 PM, WM wrote:
> Jim Burns schrieb am Dienstag,
> 15. November 2022 um 20:09:17 UTC+1:

>> Whether a number is attainable
>> does not change.
>
> That is obviously wrong.

| "Obvious" is the most dangerous word
| in mathematics.
| -- Eric Temple Bell

----
What does it mean to say
| Whether a number is attainable
| CAN change.
[1]

In its broadest sense, it says
| For some n
| there is a possible world 𝑤ₙ in which
| n is an attainable number
| and
| there is a possible world 𝑤₋ₙ in which
| n is NOT an attainable number

Different possible worlds 𝑤ₙ 𝑤₋ₙ
Different in time, different in space,
different in Marvel superhero population.
What the difference might be is entirely general.

| Assume that attainable n can change.
| In possible world 𝑤₋ₙ
| no FISON exists which n ends.
| But in possible world 𝑤ₙ
| FISON 𝐹ₙ exists which n ends.
| | In 𝑤ₙ in FISON 𝐹ₙ
| some elements can change
| (in some other possible world,
| they aren't attainable numbers)
| and some elements cannot change
| (in no possible world...)
| | A split 𝐵 𝐹ₙ\𝐵 exists in which
| in which each element which can change
| or is a follower of an element which
| can change is in 𝐹ₙ\𝐵
| | Each element of 𝐵 cannot change.
| | 𝐹ₙ is a FISON. 𝐵 𝐹ₙ\𝐵 is a split.
| Some j₁ is first in 𝐹ₙ\𝐵
| j₁ only follows elements in 𝐵
| -- elements in 𝐵 which cannot change.
| By definition of 𝐹ₙ\𝐵
| j₁ can change.
| | 𝐹ₙ is a FISON. 𝐵 𝐹ₙ\𝐵 is a split.
| Some i₁ is last in 𝐵
| i₁ cannot change.
| | 𝐹ₙ is a FISON. 𝐵 𝐹ₙ\𝐵 is a split.
| j₁ = i₁⁺⁺
| | However,
| "attainable" implies
| if i₁ is attainable and j₁ = i₁⁺⁺
| then j₁ is attainable.
| | In all possible worlds, i₁ is attainable.
| In all possible worlds, j₁ = i₁++
| [2]
| In all possible worlds, j₁ is attainable.
| j₁ cannot change.
| Contradiction.

Therefore,
attainable n cannot change.

Whether a number is attainable
does not change.

----
[1]
A number is _attainable_ iff
an ordered set exists
such that
for each split of that set,
a successor-step across that split exists,
and that set begins at 0
and that set ends at that number.

----
[2]
In all possible worlds, j₁ = i₁++

j₁ = i₁++ in possible world 𝑤ₙ
amd
whether or not j is the successor i⁺⁺ of i
does not change.

(1)
One approach to supporting this claim is to
simply recognize that _that's what we mean_
by "successor". Things for which it's not true
aren't successors.

(2)
Another approach is to give a specific definition
of i++ (there are many which would serve) and
show, from that definition, that j = i⁺⁺ doesn't
change.

(2.1)
The far and away most familiar definition
would define the natural-number successor '⁺⁺'
using a carry operator '⥆' on the digits of
a decimal numeral.
99⁺⁺ = 99⥆ = 9⥆0 = ⥆00 = 100

0 ⟼ 1 ⟼ 2 ⟼ ... ⟼ 8 ⟼ 9 ⟼ ⥆0

(2.2)
To mathematicians, the von Neumann definition
runs a close second in familiarity.
i⁺⁺ ≝ i ∪ {i}

(2.3)
Ordered pairs and non-pair 0 are also sufficient
for our purposes.
i⁺⁺ ≝ ⟨i,0⟩

None of these, 2.1, 2.2, 2.3, change.
99⁺⁺ = 100 in every possible world.

On 11/16/2022 11:03 AM, Ross A. Finlayson wrote:
> On Wednesday, November 16, 2022 at 6:55:53 AM UTC-8, Sergi o wrote:
>> On 11/16/2022 8:41 AM, Ross A. Finlayson wrote:
>>> On Wednesday, November 16, 2022 at 5:45:14 AM UTC-8, Sergi o wrote:
>>>> On 11/15/2022 10:56 PM, Ross A. Finlayson wrote:
>>>>> On Tuesday, November 15, 2022 at 8:47:25 PM UTC-8, Ross A. Finlayson wrote:
>>>>>> On Tuesday, November 15, 2022 at 7:18:11 PM UTC-8, Gus Gassmann wrote:
>>>>>>> On Tuesday, 15 November 2022 at 19:27:49 UTC-4, Fritz Feldhase wrote:
>>>>>>>> On Tuesday, November 15, 2022 at 3:23:38 PM UTC+1, Sergi o wrote:
>>>>>>>>
>>>>>>>>> so you are saying it is possible to completly verify using "step by step" on an infinite sequence ?
>>>>>>>> Of course!
>>>>>>>>
>>>>>>>> Everybody knows that Chuck Norris can do it!
>>>>>>> He does it twice, even. (Probably just to be sure, though...)
>>>>>> Quit feeding the troll, you should have something better to do, like learning mathematics.
>>>>>>
>>>>>> Not just re-capping bull-shit with boring useless repeated bull and further bull.
>>>>>>
>>>>>> If you're going to be bull-headed, don't be bull-shitted.
>>>>>>
>>>>>> And quit pissing on that bum.
>>>>>
>>>>>
>>>>>
>>>>> For example there's the equivalency function, why don't you try to attack or defend it.
>>>> => there is no equivalency function.
>>>>
>>>> there is an equivalence function or equivalent function, now which do you mean ?
>>>>>
>>>>> How about this, you take turns, assembling and disassembling it, making and breaking it,
>>>>> take turns on either side of the argument until you run out.
>>>>>
>>>>> Or, you know, learn something or teach something.
>>>>>
>>>>> It's got a very _strong_ defense.
>>>>>
>>>>>
>>>>> I challenge you to draw a line and attack any way you see fit, the equivalency function.
>>>>>
>> replaced your snipage,
>>> For example there's the equivalency function, why don't you try to attack or defend it.
>>
>> => there is no equivalency function.
>>
>> there is an equivalence function or equivalent function, now which do you mean ?
>> no answer ?
>>>>>
>>>
>>> It's like the first lesson in pre-calc:
>>>
>>> "You know the function that is drawing a line the points?
>> do you mean 'through' the points ?
>>> It doesn't exist for this course, we'll be developing one
>>> after limits in the field instead."
>> that is nonsense.
>>>
>>> So, that instruction went right to your head, one hopes,
>>> but this is part of a broader course, for more mature students.
>>> If you need some help, I wrote 10,000 posts about it.
>> why ?
>>>
>>> Really could learn something, ....
>> pre-calc ?
>>>
>>> Up to there it's underdefined, of course.
>> is your day job that boring ?
>
> "Post-Calc".
>
>
> Hey remember when we were talking about "line integral".
>
> There's a great book called "Cable Structures".
>
> It has lots of empirical formulas.
>
> Or: formulae.
>

will try to find it.

the free book site got shut down by the FBI,copyright violation probably, millions of books there too, lots of technical ones,
https://booksc.org or https://1lib.us/

zh.z-lib.org/

https://zh.1lib.us/

https://3lib.net/

https://z-lib.org/

https://singlelogin.org/

https://booksc.org/

https://1lib.us/

https://b-ok.org/

https://1lib.domains/

https://4lib.org/

On Wednesday, November 16, 2022 at 11:02:09 AM UTC-8, Sergi o wrote:
> On 11/16/2022 11:03 AM, Ross A. Finlayson wrote:
> > On Wednesday, November 16, 2022 at 6:55:53 AM UTC-8, Sergi o wrote:
> >> On 11/16/2022 8:41 AM, Ross A. Finlayson wrote:
> >>> On Wednesday, November 16, 2022 at 5:45:14 AM UTC-8, Sergi o wrote:
> >>>> On 11/15/2022 10:56 PM, Ross A. Finlayson wrote:
> >>>>> On Tuesday, November 15, 2022 at 8:47:25 PM UTC-8, Ross A. Finlayson wrote:
> >>>>>> On Tuesday, November 15, 2022 at 7:18:11 PM UTC-8, Gus Gassmann wrote:
> >>>>>>> On Tuesday, 15 November 2022 at 19:27:49 UTC-4, Fritz Feldhase wrote:
> >>>>>>>> On Tuesday, November 15, 2022 at 3:23:38 PM UTC+1, Sergi o wrote:
> >>>>>>>>
> >>>>>>>>> so you are saying it is possible to completly verify using "step by step" on an infinite sequence ?
> >>>>>>>> Of course!
> >>>>>>>>
> >>>>>>>> Everybody knows that Chuck Norris can do it!
> >>>>>>> He does it twice, even. (Probably just to be sure, though...)
> >>>>>> Quit feeding the troll, you should have something better to do, like learning mathematics.
> >>>>>>
> >>>>>> Not just re-capping bull-shit with boring useless repeated bull and further bull.
> >>>>>>
> >>>>>> If you're going to be bull-headed, don't be bull-shitted.
> >>>>>>
> >>>>>> And quit pissing on that bum.
> >>>>>
> >>>>>
> >>>>>
> >>>>> For example there's the equivalency function, why don't you try to attack or defend it.
> >>>> => there is no equivalency function.
> >>>>
> >>>> there is an equivalence function or equivalent function, now which do you mean ?
> >>>>>
> >>>>> How about this, you take turns, assembling and disassembling it, making and breaking it,
> >>>>> take turns on either side of the argument until you run out.
> >>>>>
> >>>>> Or, you know, learn something or teach something.
> >>>>>
> >>>>> It's got a very _strong_ defense.
> >>>>>
> >>>>>
> >>>>> I challenge you to draw a line and attack any way you see fit, the equivalency function.
> >>>>>
> >> replaced your snipage,
> >>> For example there's the equivalency function, why don't you try to attack or defend it.
> >>
> >> => there is no equivalency function.
> >>
> >> there is an equivalence function or equivalent function, now which do you mean ?
> >> no answer ?
> >>>>>
> >>>
> >>> It's like the first lesson in pre-calc:
> >>>
> >>> "You know the function that is drawing a line the points?
> >> do you mean 'through' the points ?
> >>> It doesn't exist for this course, we'll be developing one
> >>> after limits in the field instead."
> >> that is nonsense.
> >>>
> >>> So, that instruction went right to your head, one hopes,
> >>> but this is part of a broader course, for more mature students.
> >>> If you need some help, I wrote 10,000 posts about it.
> >> why ?
> >>>
> >>> Really could learn something, ....
> >> pre-calc ?
> >>>
> >>> Up to there it's underdefined, of course.
> >> is your day job that boring ?
> >
> > "Post-Calc".
> >
> >
> > Hey remember when we were talking about "line integral".
> >
> > There's a great book called "Cable Structures".
> >
> > It has lots of empirical formulas.
> >
> > Or: formulae.
> >
> will try to find it.
>
> the free book site got shut down by the FBI,copyright violation probably, millions of books there too, lots of technical ones,
> https://booksc.org or https://1lib.us/
>
> zh.z-lib.org/
>
> https://zh.1lib.us/
>
> https://3lib.net/
>
> https://z-lib.org/
>
> https://singlelogin.org/
>
> https://booksc.org/
>
> https://1lib.us/
>
> https://b-ok.org/
>
> https://1lib.domains/
>
> https://4lib.org/

It used to be open season on, "pirates".

My copy's a Dover re-print.

"Post-Calc: calculator verboten."

Jim Burns schrieb am Mittwoch, 16. November 2022 um 19:14:22 UTC+1:
> On 11/15/2022 4:34 PM, WM wrote:
> > Jim Burns schrieb am Dienstag,
> > 15. November 2022 um 20:09:17 UTC+1:
>
> >> Whether a number is attainable
> >> does not change.
> >
> > That is obviously wrong.
> | "Obvious" is the most dangerous word
> | in mathematics.

Cp. the largest attainable prime number.
For continuing go to https://groups.google.com/g/sci.math/c/LHEV4iqs5bM
For the ultimte proof go to https://groups.google.com/g/sci.logic/c/zfYogfnYMx0

Regards, WM

On 11/17/2022 5:07 AM, WM wrote:
> Jim Burns schrieb am Mittwoch
>, 16. November 2022 um 19:14:22 UTC+1:
>> On 11/15/2022 4:34 PM, WM wrote:
>>> Jim Burns schrieb am Dienstag,
>>> 15. November 2022 um 20:09:17 UTC+1:

>>>> Whether a number is attainable
>>>> does not change.
>>>
>>> That is obviously wrong.
>>
>> | "Obvious" is the most dangerous word
>> | in mathematics.
>
> Cp. the largest attainable prime number.

There is no largest
| ordered set
| such that
| for each split of that set,
| a successor-step across that split exists,
| and 0 begins that set
| and that set ends somewhere.

Define an attainable number to be
the end of an
| ordered set
| such that
| for each split of that set,
| a successor-step across that split exists,
| and 0 begins that set
| and that set ends somewhere.

There is no largest
| attainable number.

Define
i+0 = i
i + j = k <-> i + j++ = k++

i*0 = 0
i * j = k <-> i * j++ = k + i

k = i*j -> k = i V k = j
& k /= k*k
<-> Prime(k)

There is no largest attainable prime number.

If,
in _any possible world_
something ends an
| ordered set
| such that
| for each split of that set,
| a successor-step across that split exists,
| and 0 begins that set
| and that set ends somewhere,
then,
in _every possible world_
it ends an
| ordered set
| such that
| for each split of that set,
| a successor-step across that split exists,
| and 0 begins that set
| and that set ends somewhere.

Define a _changeable_ end of an
| ordered set
| such that
| for each split of that set,
| a successor-step across that split exists,
| and 0 begins that set
| and that set ends somewhere
to end _in some possible world_ some
| ordered set
| such that
| for each split of that set,
| a successor-step across that split exists,
| and 0 begins that set
| and that set ends somewhere,
and
to NOT end _in another possible world_ ANY
| ordered set
| such that
| for each split of that set,
| a successor-step across that split exists,
| and 0 begins that set
| and that set ends somewhere.

Define a _changeable_
| attainable number
to be _in some possible world_ an
| attainable number
and
to NOT be _in another possible world_ an
| attainable number.

If,
in _any possible world_
something is an
| attainable number
then,
in _every possible world_
it is an
| attainable number.

There is no changeable
| attainable number.

>>>> Whether a number is attainable
>>>> does not change.
>>>
>>> That is obviously wrong.

There is no changeable
| attainable number.

> For continuing go to
> https://groups.google.com/g/sci.math/c/LHEV4iqs5bM
>
> For the ultimte proof go to
> https://groups.google.com/g/sci.logic/c/zfYogfnYMx0

On Thursday, November 17, 2022 at 7:47:33 AM UTC-8, Jim Burns wrote:
> On 11/17/2022 5:07 AM, WM wrote:
> > Jim Burns schrieb am Mittwoch
> >, 16. November 2022 um 19:14:22 UTC+1:
> >> On 11/15/2022 4:34 PM, WM wrote:
> >>> Jim Burns schrieb am Dienstag,
> >>> 15. November 2022 um 20:09:17 UTC+1:
>
> >>>> Whether a number is attainable
> >>>> does not change.
> >>>
> >>> That is obviously wrong.
> >>
> >> | "Obvious" is the most dangerous word
> >> | in mathematics.
> >
> > Cp. the largest attainable prime number.
> There is no largest
> | ordered set
> | such that
> | for each split of that set,
> | a successor-step across that split exists,
> | and 0 begins that set
> | and that set ends somewhere.
>
> Define an attainable number to be
> the end of an
> | ordered set
> | such that
> | for each split of that set,
> | a successor-step across that split exists,
> | and 0 begins that set
> | and that set ends somewhere.
>
> There is no largest
> | attainable number.
>
>
> Define
> i+0 = i
> i + j = k <-> i + j++ = k++
>
> i*0 = 0
> i * j = k <-> i * j++ = k + i
>
> k = i*j -> k = i V k = j
> & k /= k*k
> <-> Prime(k)
>
> There is no largest attainable prime number.
>
>
> If,
> in _any possible world_
> something ends an
> | ordered set
> | such that
> | for each split of that set,
> | a successor-step across that split exists,
> | and 0 begins that set
> | and that set ends somewhere,
> then,
> in _every possible world_
> it ends an
> | ordered set
> | such that
> | for each split of that set,
> | a successor-step across that split exists,
> | and 0 begins that set
> | and that set ends somewhere.
>
> Define a _changeable_ end of an
> | ordered set
> | such that
> | for each split of that set,
> | a successor-step across that split exists,
> | and 0 begins that set
> | and that set ends somewhere
> to end _in some possible world_ some
> | ordered set
> | such that
> | for each split of that set,
> | a successor-step across that split exists,
> | and 0 begins that set
> | and that set ends somewhere,
> and
> to NOT end _in another possible world_ ANY
> | ordered set
> | such that
> | for each split of that set,
> | a successor-step across that split exists,
> | and 0 begins that set
> | and that set ends somewhere.
>
> Define a _changeable_
> | attainable number
> to be _in some possible world_ an
> | attainable number
> and
> to NOT be _in another possible world_ an
> | attainable number.
>
> If,
> in _any possible world_
> something is an
> | attainable number
> then,
> in _every possible world_
> it is an
> | attainable number.
>
> There is no changeable
> | attainable number.
> >>>> Whether a number is attainable
> >>>> does not change.
> >>>
> >>> That is obviously wrong.
> There is no changeable
> | attainable number.
> > For continuing go to
> > https://groups.google.com/g/sci.math/c/LHEV4iqs5bM
> >
> > For the ultimte proof go to
> > https://groups.google.com/g/sci.logic/c/zfYogfnYMx0

What if there's axiomatized each what you say no?

How is sufficed what results?

In the infinite, restriction of comprehension helps establish the regular,
but, there's the other regular, in the infinite.

Otherwise it's a sound post and you'd've soundly thrashed a troll,
but that's only following the lead you've nose-ringed yourself.

To, ..., where?

Could you please speak English, instead of making spelling errors,
you fucking moron? Your private language nonsense doesn't make
any sense. "extraordinary" technically means irregular or non-well-

founded, i.e. violating for example this axiom:

In mathematics, the axiom of regularity (also known as the
axiom of foundation) is an axiom of Zermelo–Fraenkel set theory
https://en.wikipedia.org/wiki/Axiom_of_regularity

The term is more correctly spelled "extraordinaire". There is a spelling
difference between "extraordinary" and "extraordinaire". The
terminology was used by:

Dmitry Mirimanoff (1861, Russia – 1945, Switzerland)
Mirimanoff in a 1917 paper introduced the concept of well-founded
set and the notion of rank of a set.[5] Mirimanoff called a set x "regular"
(French: "ordinaire") if every descending chain x ∋ x1 ∋ x2 ∋ ... is finite.
Mirimanoff however did not consider his notion of regularity (well-foundedness)
as an axiom to be observed by all sets;[3] in later papers Mirimanoff also
explored what are now called non-well-founded sets
("extraordinaire" in Mirimanoff's terminology).
https://en.wikipedia.org/wiki/Dmitry_Mirimanoff#Set_theory

Ross Finlayson schrieb am Montag, 21. August 2023 um 06:18:36 UTC+2:
> That's what you got there,
> where for others it's "extra-ordinary, first".

The problem is "extraordinary" is nowhere used in logic,
math or philosophy text books for irregular or non-well-founded
sets. Because its meaning tends towards a counter factual

touch above the normal, in that something deviating from
the normal is somehow judged as abnormal and this is not
expected to be factual, if the degree abnormal is too high,

the term is usually not used in logic, math or philosophy since
it is judgemental. You find "extraordinary" for example used here,
but even not with the meaning of irregular or non-well-founded sets:

Hitler and Abductive Logic: The Strategy of a Tyrant
"Thus Adolf Hitler's first idea arose from his rejection of
ordinary life. It prepared him for the conflict with ...
In abductive logic, the distinction is between the ordinary
and the extraordinary. The ordinary is what is normal and ..."
https://www.amazon.com/dp/0739194615

LoL

Poor Charles Sanders Peirce, would he agree with this use of "Abduction"?

Mild Shock schrieb am Donnerstag, 24. August 2023 um 12:49:39 UTC+2:
> Could you please speak English, instead of making spelling errors,
> you fucking moron? Your private language nonsense doesn't make
> any sense. "extraordinary" technically means irregular or non-well-
>
> founded, i.e. violating for example this axiom:
>
> In mathematics, the axiom of regularity (also known as the
> axiom of foundation) is an axiom of Zermelo–Fraenkel set theory
> https://en.wikipedia.org/wiki/Axiom_of_regularity
>
> The term is more correctly spelled "extraordinaire". There is a spelling
> difference between "extraordinary" and "extraordinaire". The
> terminology was used by:
>
> Dmitry Mirimanoff (1861, Russia – 1945, Switzerland)
> Mirimanoff in a 1917 paper introduced the concept of well-founded
> set and the notion of rank of a set.[5] Mirimanoff called a set x "regular"
> (French: "ordinaire") if every descending chain x ∋ x1 ∋ x2 ∋ ... is finite.
> Mirimanoff however did not consider his notion of regularity (well-foundedness)
> as an axiom to be observed by all sets;[3] in later papers Mirimanoff also
> explored what are now called non-well-founded sets
> ("extraordinaire" in Mirimanoff's terminology).
> https://en.wikipedia.org/wiki/Dmitry_Mirimanoff#Set_theory
>
> Ross Finlayson schrieb am Montag, 21. August 2023 um 06:18:36 UTC+2:
> > That's what you got there,
> > where for others it's "extra-ordinary, first".

Your nonsense posts, trying to impress your readers by
using "extraordinary" also imply that you judge your readers
as inflexible and judgemental, since you insinuate that

your readers would need a hint that there is the "extraordinary".
Whereas for anybody dealing with set theory irregular or
non-well-founded sets are nothing special. For example

well-foundedness can be also defined for other relations R(_,_)
than only the set membership _ ∈ _ relation, and when studying
certain principles, and one usually studies first the more abstract

concept of well-foundedness in connection with relations R(_,_),
so that its rather a simple cognitive process to then apply
the same idea to the set membership _ ∈ _ relation. So for

set theorists, this is not a friend that a cat would bring home.
"extraordinary" is not this case in set theory, it is usually studied
before, when studying relations R(_,_):

When your cat brings home a friend 🤣
https://www.youtube.com/watch?v=mjotaffmfz4

Ha Ha, except if the cat is named "Rossy Boy", it brings all kinds
of strange presents to the table, if its not the word "extraordinary",
his posts certainly contain some other nonsense.

Mild Shock schrieb am Donnerstag, 24. August 2023 um 13:00:44 UTC+2:
> The problem is "extraordinary" is nowhere used in logic,
> math or philosophy text books for irregular or non-well-founded
> sets. Because its meaning tends towards a counter factual
>
> touch above the normal, in that something deviating from
> the normal is somehow judged as abnormal and this is not
> expected to be factual, if the degree abnormal is too high,
>
> the term is usually not used in logic, math or philosophy since
> it is judgemental. You find "extraordinary" for example used here,
> but even not with the meaning of irregular or non-well-founded sets:
>
> Hitler and Abductive Logic: The Strategy of a Tyrant
> "Thus Adolf Hitler's first idea arose from his rejection of
> ordinary life. It prepared him for the conflict with ...
> In abductive logic, the distinction is between the ordinary
> and the extraordinary. The ordinary is what is normal and ..."
> https://www.amazon.com/dp/0739194615
>
> LoL
>
> Poor Charles Sanders Peirce, would he agree with this use of "Abduction"?
> Mild Shock schrieb am Donnerstag, 24. August 2023 um 12:49:39 UTC+2:
> > Could you please speak English, instead of making spelling errors,
> > you fucking moron? Your private language nonsense doesn't make
> > any sense. "extraordinary" technically means irregular or non-well-
> >
> > founded, i.e. violating for example this axiom:
> >
> > In mathematics, the axiom of regularity (also known as the
> > axiom of foundation) is an axiom of Zermelo–Fraenkel set theory
> > https://en.wikipedia.org/wiki/Axiom_of_regularity
> >
> > The term is more correctly spelled "extraordinaire". There is a spelling
> > difference between "extraordinary" and "extraordinaire". The
> > terminology was used by:
> >
> > Dmitry Mirimanoff (1861, Russia – 1945, Switzerland)
> > Mirimanoff in a 1917 paper introduced the concept of well-founded
> > set and the notion of rank of a set.[5] Mirimanoff called a set x "regular"
> > (French: "ordinaire") if every descending chain x ∋ x1 ∋ x2 ∋ ... is finite.
> > Mirimanoff however did not consider his notion of regularity (well-foundedness)
> > as an axiom to be observed by all sets;[3] in later papers Mirimanoff also
> > explored what are now called non-well-founded sets
> > ("extraordinaire" in Mirimanoff's terminology).
> > https://en.wikipedia.org/wiki/Dmitry_Mirimanoff#Set_theory
> >
> > Ross Finlayson schrieb am Montag, 21. August 2023 um 06:18:36 UTC+2:
> > > That's what you got there,
> > > where for others it's "extra-ordinary, first".