måndag 6 november 2023 kl. 12:01:03 UTC+1 skrev Adam Polak:
> Dear Friends,
>
> The Set Theory, creator of which is considered to be Professor Georg Cantor, currently adhered to by the vast majority of scientists, is an undoubtedly flawed theory, based on erroneous assumptions and, as a result, filled with errors and internal contradictions.
>
> The wide "Analysis of mistakes in infinity study attempts" within set theory can be found here on YouTube:
> https://www.youtube.com/watch?v=s23Cz8A0BKs
>
> In the upcoming presentations, we will together take a colser look on numerous errors in set theory, we will identify Hilbert's Grand Hotel Paradox errors, easily solve the Continuum Hypothesis (allegedly undecidable), Russell's Paradox, the Paradox of the set of all sets, and we will confirm even more emphatically that the set theory can be seen only as erroneous and disproven.
>
> A small sample below. A comparison that decisively, in an unquestionable manner, refutes the Cantor's Diagonal Argument as evidence of the inequality of the infinite set of real numbers relative to the infinite set of natural numbers.
>
> A hotel with an infinite number of rooms.
> There is a guest in each room.
> As a result, you have two infinite sets:
>
> An infinite SET OF ROOMS containing elements with the following symbols: R1, R2, R3, ...
>
> An infinite SET OF GUEST containing elements with the following symbols: G1, G2, G3...
>
> A new guest appears: NG1
> The new guest is definitely not among the guests that are already in the hotel because he is different from them, his name is: ("NG" + its individual number ) , everyone present in the hotel is: ("G"+ individual number of each ).
>
> If you claim that you can accommodate a new guest in room 1 and move everyone currently present in the hotel to rooms n+1
> you can do exactly the same thing with a "new" real number supposedly created by diagonal method.
>
> You assign "new" real numb to 1, and you shift all the real numbers previously in the right column of the diagonal matrix down by one: the one that was assigned to 1 is now assigned to 2, the one assigned to 2 is now assigned to 3, etc.
>
> It is mutually contradictory to say that you can accommodate a new guest in Hilbert's hotel and at the same time to say that you cannot find a natural number as a pair for a "new" real number "created" by the diagonal method.
>
> The set theory is clearly contradictory in many places.
>
> Best Regards,
> Adam Polak
I don't see the contradiction.

wtorek, 21 listopada 2023 o 03:30:06 UTC+1 markus...@gmail.com napisał(a):
> måndag 6 november 2023 kl. 12:01:03 UTC+1 skrev Adam Polak:
> > Dear Friends,
> >
> > The Set Theory, creator of which is considered to be Professor Georg Cantor, currently adhered to by the vast majority of scientists, is an undoubtedly flawed theory, based on erroneous assumptions and, as a result, filled with errors and internal contradictions.
> >
> > The wide "Analysis of mistakes in infinity study attempts" within set theory can be found here on YouTube:
> > https://www.youtube.com/watch?v=s23Cz8A0BKs
> >
> > In the upcoming presentations, we will together take a colser look on numerous errors in set theory, we will identify Hilbert's Grand Hotel Paradox errors, easily solve the Continuum Hypothesis (allegedly undecidable), Russell's Paradox, the Paradox of the set of all sets, and we will confirm even more emphatically that the set theory can be seen only as erroneous and disproven.
> >
> > A small sample below. A comparison that decisively, in an unquestionable manner, refutes the Cantor's Diagonal Argument as evidence of the inequality of the infinite set of real numbers relative to the infinite set of natural numbers.
> >
> > A hotel with an infinite number of rooms.
> > There is a guest in each room.
> > As a result, you have two infinite sets:
> >
> > An infinite SET OF ROOMS containing elements with the following symbols: R1, R2, R3, ...
> >
> > An infinite SET OF GUEST containing elements with the following symbols: G1, G2, G3...
> >
> > A new guest appears: NG1
> > The new guest is definitely not among the guests that are already in the hotel because he is different from them, his name is: ("NG" + its individual number ) , everyone present in the hotel is: ("G"+ individual number of each ).
> >
> > If you claim that you can accommodate a new guest in room 1 and move everyone currently present in the hotel to rooms n+1
> > you can do exactly the same thing with a "new" real number supposedly created by diagonal method.
> >
> > You assign "new" real numb to 1, and you shift all the real numbers previously in the right column of the diagonal matrix down by one: the one that was assigned to 1 is now assigned to 2, the one assigned to 2 is now assigned to 3, etc.
> >
> > It is mutually contradictory to say that you can accommodate a new guest in Hilbert's hotel and at the same time to say that you cannot find a natural number as a pair for a "new" real number "created" by the diagonal method.
> >
> > The set theory is clearly contradictory in many places.
> >
> > Best Regards,
> > Adam Polak
> I don't see the contradiction.
Never apears the situation in which a "new real number" "created" by the diagonal method could not be added to an infinite set of real numbers which, at the same time, always remains equinumerous (one-to-one correspondence of elements ) with an infinite set of natural numbers.
Cantor's Diagonal Method is not a proof of the greater cardinality of R than N.

The above, is just one of several observations refuting the diagonal argument. Another, more important, point is that using Cantor's Diagonal Method the so-called "NEW real number" can never be really created.

poniedziałek, 20 listopada 2023 o 12:57:59 UTC+1 WM napisał(a):
> On 20.11.2023 12:20, Adam Polak wrote:
>
> > the "tail" of this symbol/object
> > has no meaning, no influence
> > has nothing in common with "the number: one thousandth"
>
> Therefore it is irrelevant whether or not the tail is written. With and
> without tail it denotes the number.
>
> Regards, WN

Yes,
cow with a cowboy on its back: 0.0010000000...
and simply a cow: 0.001
it's exactly the same, one and the same cow.

If the cowboy sitting on the cow will put on sunglasses: 0.0010010000...
would you say you created a new cow?
Regards, Adam

wtorek, 21 listopada 2023 o 06:56:02 UTC+1 Adam Polak napisał(a):
> poniedziałek, 20 listopada 2023 o 12:57:59 UTC+1 WM napisał(a):
> > On 20.11.2023 12:20, Adam Polak wrote:
> >
> > > the "tail" of this symbol/object
> > > has no meaning, no influence
> > > has nothing in common with "the number: one thousandth"
> >
> > Therefore it is irrelevant whether or not the tail is written. With and
> > without tail it denotes the number.
> >
> > Regards, WN
> Yes,
> cow with a cowboy on its back: 0.0010000000...
> and simply a cow: 0.001
> it's exactly the same, one and the same cow.
>
> If the cowboy sitting on the cow will put on sunglasses: 0.0010010000...
> would you say you created a new cow?
>
> Regards, Adam

ps:
symbols and numerical values

cow + cowboy + sunglasses = 0.0010010000...
where:
cow = 0.001
sunglasses = 0.000001
cowboy = 0

The cowboy is a zero,
how do you think, why he requires to be noted as "infinite zero": 0.0000000000...
is it his ego?

On Tuesday, November 21, 2023 at 6:42:39 AM UTC+1, Adam Polak wrote:
>
> Never apears the situation in which a "new real number" "created" by the diagonal method could not be added to an infinite set of real numbers which, at the same time, always remains equinumerous (one-to-one correspondence of elements ) with an infinite set of natural numbers.

Holy shit! You idiot do not even understand the very "proof idea" of the proof. <faceplam>

> The above, is just one of several observations refuting the diagonal argument.

"Your observation" is just some cranky shit, you silly monkey.

> Another, more important, point is that using Cantor's Diagonal Method the so-called "NEW real number" can never be really created.

It suffices that it can be *defined*, you dumb ass.

wtorek, 21 listopada 2023 o 07:33:52 UTC+1 Fritz Feldhase napisał(a):
> On Tuesday, November 21, 2023 at 6:42:39 AM UTC+1, Adam Polak wrote:
> >
> > Never apears the situation in which a "new real number" "created" by the diagonal method could not be added to an infinite set of real numbers which, at the same time, always remains equinumerous (one-to-one correspondence of elements ) with an infinite set of natural numbers.
> Holy shit! You idiot do not even understand the very "proof idea" of the proof. <faceplam>
> > The above, is just one of several observations refuting the diagonal argument.
> "Your observation" is just some cranky shit, you silly monkey.
> > Another, more important, point is that using Cantor's Diagonal Method the so-called "NEW real number" can never be really created.
> It suffices that it can be *defined*, you dumb ass.

Dearest Fritz,
the substantive depth of your argumentation, as almost always, is stunning & overwhelms the reader,
but on the other hand it improves the mood.
Have a nice day too :)
Adam

On Saturday, November 18, 2023 at 10:57:56 PM UTC-8, Ross Finlayson wrote:
> On Saturday, November 18, 2023 at 8:58:27 AM UTC-8, Fritz Feldhase wrote:
> > On Saturday, November 18, 2023 at 3:29:05 AM UTC+1, Ross Finlayson wrote:
> >
> > > If you get to reading enough Heidegger it starts looking like Greek.
> > Agree. Though the later Heidegger is quite cool.
> Yeah, Heidegger's "Being and Time", about Da (here) and Dasein (being, here-being), is something, then though
> what follows is Heidegger's extended translations of the Greeks, mostly coat-tailing the Greeks some 2000 years
> later, while though Heidegger and for example Gadamer offer various and varying interpretations, in their
> uncovering or the a-Letheia, about the Logos (of course, written usually enough in Greek script).
>
> Eleatics - Pythagorans - Platonists
> Augustine-Scotus-Arabs-Spinoza
> DesCartes-Leibnitz-Kant-Hegel-Heidegger
> Popper-Priest
>
> I've been studying these because it's kind of an outline of the Western canon, philosophically.
> Of course, it's sort of a curated line out from logical foundations into principled science,
> "technical philosophy", for a usual sort of narrative of the development of a "The One True Logic"
> or for "an idealized Platonism", a strong mathematical platonism.
>
> ("DaDa" was a sort of zeitgeist of some Continental head-set,
> it sort of reminds of "Bob Dobbs and the pinks".)
>
>
> https://www.youtube.com/watch?v=BbO2q9WKUDQ&list=PLb7rLSBiE7F5_h5sSsWDQmbNGsmm97Fy5&index=37
>
> So, Heidegger is famous for "Dasein", presence and consciously, similarly to how there's
> Goethe and "beholding" vis-a-vis "knowing", and he coat-tails a lot of canon in his fully
> voluble deliberations, then, his following works are mostly great translations and
> interpretations of Parmenides and the Greeks and exploring the antonymous
> character of a-letheia, uncovering or revealing as for showing or knowing,
> and into the logos, as after Heraclitus or "the great obfuscator", what is so profound.
>
> Such manners of didactic dialectic of course reflect earlier into the tradition,
> back to the Vedics and Daoism as similarly, even more "obscure", obtuse,
> to be so profound. It's a broad dialectic for "ideal Platonism", strong mathematical
> platonism.
>
> It's all English to me, but, it's all one language, a language of words, logoi.
>
> MfG (Mit fielen Gruesse),

Pretty sure this thread is dead, ....

On 21.11.2023 06:42, Adam Polak wrote:
>
> Never apears the situation in which a "new real number" "created" by the diagonal method could not be added to an infinite set of real numbers which, at the same time, always remains equinumerous (one-to-one correspondence of elements ) with an infinite set of natural numbers.

So it is. Two honest tricksters. Each one wants to be the second.

> Cantor's Diagonal Method is not a proof of the greater cardinality of R than N.

So it is.
>
> The above, is just one of several observations refuting the diagonal argument.

For instance the Binary Tree having more nodes than paths.

Regards, WM

On 21.11.2023 07:33, Fritz Feldhase wrote:
> On Tuesday, November 21, 2023 at 6:42:39 AM UTC+1, Adam Polak wrote:
>>

>> Another, more important, point is that using Cantor's Diagonal Method the so-called "NEW real number" can never be really created.
>
> It suffices that it can be *defined*

It would suffice. But a real number cannot be defined. Since the digits
are completely arbitrary, a definition would require to give all digits
such than none is missing. Impossible for an infinite sequence.

Regards, WM

WM brought next idea :
> On 21.11.2023 07:33, Fritz Feldhase wrote:
>> On Tuesday, November 21, 2023 at 6:42:39 AM UTC+1, Adam Polak wrote:
>>>
>
>>> Another, more important, point is that using Cantor's Diagonal Method the
>>> so-called "NEW real number" can never be really created.
>>
>> It suffices that it can be *defined*
>
> It would suffice. But a real number cannot be defined.

Who says?

> Since the digits are completely arbitrary,

They are not, they are deterministically produced. But even that
doesn't matter because a number is not determined by the form of
representation chosen.

> a definition would require to give all digits such than none is missing.
> Impossible for an infinite sequence.

If you don't like the representation, use another one. Maybe CFE is
better than CDE for some numbers which give you trouble.

On Tuesday, November 21, 2023 at 8:39:01 AM UTC-5, FromTheRafters wrote:
> WM brought next idea :
> > On 21.11.2023 07:33, Fritz Feldhase wrote:
> >> On Tuesday, November 21, 2023 at 6:42:39 AM UTC+1, Adam Polak wrote:
> >>>
> >
> >>> Another, more important, point is that using Cantor's Diagonal Method the
> >>> so-called "NEW real number" can never be really created.
> >>
> >> It suffices that it can be *defined*
> >
> > It would suffice. But a real number cannot be defined.
> Who says?
> > Since the digits are completely arbitrary,
> They are not, they are deterministically produced. But even that
> doesn't matter because a number is not determined by the form of
> representation chosen.
> > a definition would require to give all digits such than none is missing..
> > Impossible for an infinite sequence.
> If you don't like the representation, use another one. Maybe CFE is
> better than CDE for some numbers which give you trouble.

Set theory frames all of mathematics as far as I can tell. If not all then 'very much of' would suffice.
The entire curriculum starts in the 'progression' N->I->Q->R->C,
as if dimension somehow got born there at the end.
That is perhaps the most peculiar of the bunch. The subsetting, and then admitting that R is a subset of RxR: this puts dimension on the chopping block.
Entering the digital meadow, and I mean pertaining to the fingers of the man, in an anthropic move to remember how it all came about,
Then, after all the tricks and stunts have been pulled to land you up in C, along comes the programming language C to set things straight another way.
No: it says. You cannot simply treat a in R as if it is in C. You must convert these things formally, did you specify the phase? No. Not even the engineers bothered with it.
As if zero phase is just the way it is. Meanwhile relativity theory would have you spinning a theta dial to a random value, just like on the game shows. Oh, but that's not our R or our C, say the mathematicians. Indeed, it is not. The idea that relativity theory can ignore phase and set off only concerning itself with translational issues, working its way up to velocite and acceleration is confusing enough. Sort of like complex functions are already four dimensional and so they get ignored. Mapping a plane to a plane is not quite what you get. It's rather thicker than that, and doubly so. The idea that we might get rapidly into such far flung places from the conversation here which is to reflect upon set theroy as if it stands alone: I do hope that somebody is willing to one and one together, then put one and one and one together, and see that a few tweaks to the existing system are all that is needed. The form sx, where s is those one and one and one sorts of things, and x takes the continuous form of magnitude is a clean fit to ordinary mathematical pursuits, or at least it is very close. Committing to that which is computable rather than trickery or treachery, well, Halloween passed here uneventfully as it usually does. Of all the blunders it is the lack of polysign numbers that really has mathematicians hitting their own heads, as if they could knock the two out in order to get to the three. Yes, you've got it about right, I think. A little harder maybe.

On 11/21/2023 3:43 AM, WM wrote:
> On 21.11.2023 06:42, Adam Polak wrote:
>>
>> Never apears the situation in which a "new real number" "created" by
>> the diagonal method could not be added to an infinite set of real
>> numbers which, at the same time, always remains equinumerous
>> (one-to-one correspondence of elements ) with an infinite set of
>> natural numbers.
>
> So it is. Two honest tricksters. Each one wants to be the second.
>
>> Cantor's Diagonal Method is not a proof of the greater cardinality of
>> R than N.
>
> So it is.
>>
>> The above, is just one of several observations refuting the diagonal
>> argument.
>
> For instance the Binary Tree having more nodes than paths.
This snapshot has 6 paths. The root node 0 has 6 children {1, 2, 3, 4,
5, 6} :
_____________________
0
/ \
/ \
1 2
/ \ / \
3 4 5 6
_____________________

On 11/21/2023 2:49 PM, Chris M. Thomasson wrote:
> On 11/21/2023 3:43 AM, WM wrote:
>> On 21.11.2023 06:42, Adam Polak wrote:
>>>
>>> Never apears the situation in which a "new real number" "created" by
>>> the diagonal method could not be added to an infinite set of real
>>> numbers which, at the same time, always remains equinumerous
>>> (one-to-one correspondence of elements ) with an infinite set of
>>> natural numbers.
>>
>> So it is. Two honest tricksters. Each one wants to be the second.
>>
>>> Cantor's Diagonal Method is not a proof of the greater cardinality of
>>> R than N.
>>
>> So it is.
>>>
>>> The above, is just one of several observations refuting the diagonal
>>> argument.
>>
>> For instance the Binary Tree having more nodes than paths.
> This snapshot has 6 paths. The root node 0 has 6 children {1, 2, 3, 4,
> 5, 6} :
> _____________________
>       0
>      / \
>     /   \
>    1     2
>   / \   / \
>  3   4 5   6
> _____________________

Or, node[0] has a family of [1, 2, 3, 4, 5, 6] in this snapshot.

On 11/6/2023 5:00 AM, Adam Polak wrote:
> Dear Friends,
>
> The Set Theory, creator of which is considered to be Professor Georg Cantor, currently adhered to by the vast majority of scientists, is an undoubtedly flawed theory, based on erroneous assumptions and, as a result, filled with errors and internal contradictions.
>

So I see you never got this memo:
https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory

*Cantor's set theory has been called naive set theory for a long time*

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 11/21/2023 6:37 PM, olcott wrote:
> On 11/6/2023 5:00 AM, Adam Polak wrote:
>> Dear Friends,
>>
>> The Set Theory, creator of which is considered to be Professor Georg
>> Cantor, currently adhered to by the vast majority of scientists, is an
>> undoubtedly flawed theory, based on erroneous assumptions and, as a
>> result, filled with errors and internal contradictions.
>>
>
> So I see you never got this memo:
> https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory
>
> *Cantor's set theory has been called naive set theory for a long time*
>

*I am surprised that no one here seemed to know this and the above*
https://en.wikipedia.org/wiki/Naive_set_theory

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On Wednesday, November 22, 2023 at 1:47:36 AM UTC+1, olcott wrote:

> *I am surprised that no one here seemed to know this and the above*
> https://en.wikipedia.org/wiki/Naive_set_theory

That's because we don't know any set theory (naive and/or axiomatic).

On 11/21/2023 7:02 PM, Fritz Feldhase wrote:
> On Wednesday, November 22, 2023 at 1:47:36 AM UTC+1, olcott wrote:
>
>> *I am surprised that no one here seemed to know this and the above*
>> https://en.wikipedia.org/wiki/Naive_set_theory
>
> That's because we don't know any set theory (naive and/or axiomatic).

*Weird*
Set theory, branch of mathematics that deals with the properties of
well-defined collections of objects...
https://www.britannica.com/science/set-theory

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

środa, 22 listopada 2023 o 01:37:38 UTC+1 olcott napisał(a):
> On 11/6/2023 5:00 AM, Adam Polak wrote:
> > Dear Friends,
> >
> > The Set Theory, creator of which is considered to be Professor Georg Cantor, currently adhered to by the vast majority of scientists, is an undoubtedly flawed theory, based on erroneous assumptions and, as a result, filled with errors and internal contradictions.
> >
> So I see you never got this memo:
> https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory
>
> *Cantor's set theory has been called naive set theory for a long time*
>
> --
> Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
> hits a target no one else can see." Arthur Schopenhauer

"
> So I see you never got this memo:
> https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory
"

On the contrary.
Set theory was naive and erroneous, and it remains precisely so until TODAY..

An axiom is not an argument!
They differ in that arguments usually have justifications behind them. axioms creators, unfortunately, often don't bother to justify anything.

e.g.: axiom of EMPTY SET: "There exists an EMPTY SET"
Almost without simplification, the definition of a SET is: a collection of objects, that are en elements of the set.
So, the EMPTY SET does not fulfill the SET definition.
If the "empty set" is not a SET, what is it?
The only correct answer is : NOTHING
Thus, the semantic/logical value of the empty set axiom sounds like: "There exists a NOTHING"

Of course, one can attempt to define a SET without requiring it to have elements, for example:
SET - "extradimensional, timeless hyperspace"
Such a definition can cover any SET, including "empty set."
For a thinking person, however, there remains one problem:
this "extradimensional, timeless hyperspace" is still just another name for something commonly known as NOTHING.

Set theory takes the empty set { } (read: nothing)
and "inserts" it into another set { { } }, where the empty set (read: nothing) is an element,
and thus, a one-element set containing the empty set (read: containing NOTHING) is created.

Now, creating a two-element set is easy for Set Theory, just take:
the empty set { } (read: nothing)
and
the one-element set { { } } (read: a set containing NOTHING, which means that this so-called one-element set is logically and actually empty, just like the empty set).
The result is: { { }, { { } } } a beautiful empty set, Ooo! I apologize, a two-element set,
containing NOTHING as the first element (to avoid recognition called "empty set") and NOTHING as the second element (to avoid recognition called "set containing empty set").
Do you need bigger sets?
Set theory will easily give you, with the above method, a set with any large number of elements. Provided, of course, that each of such sets IN FACT will be just another empty set = NOTHING.

Is it really so difficult to see, to understand that Set Theory is complete absurdity? It's not even a house of cards; it's a matryoshka of soap bubbles.

Best regards,
Adam

On Wednesday, November 22, 2023 at 10:46:21 AM UTC+1, Adam Polak wrote:

> the definition of a SET is: a collection of objects, that are en elements of the set.

Fascinating!

> So, the EMPTY SET does not fulfill the SET definition.

Yeah, you're onto something! For sure!

Chris M. Thomasson expressed precisely :
> On 11/21/2023 2:49 PM, Chris M. Thomasson wrote:
>> On 11/21/2023 3:43 AM, WM wrote:
>>> On 21.11.2023 06:42, Adam Polak wrote:
>>>>
>>>> Never apears the situation in which a "new real number" "created" by the
>>>> diagonal method could not be added to an infinite set of real numbers
>>>> which, at the same time, always remains equinumerous (one-to-one
>>>> correspondence of elements ) with an infinite set of natural numbers.
>>>
>>> So it is. Two honest tricksters. Each one wants to be the second.
>>>
>>>> Cantor's Diagonal Method is not a proof of the greater cardinality of R
>>>> than N.
>>>
>>> So it is.
>>>>
>>>> The above, is just one of several observations refuting the diagonal
>>>> argument.
>>>
>>> For instance the Binary Tree having more nodes than paths.
>> This snapshot has 6 paths. The root node 0 has 6 children {1, 2, 3, 4, 5,
>> 6} :
>> _____________________
>>       0
>>      / \
>>     /   \
>>    1     2
>>   / \   / \
>>  3   4 5   6
>> _____________________
>
> Or, node[0] has a family of [1, 2, 3, 4, 5, 6] in this snapshot.

Aren't the paths as follows:

0 to 1
0 to 2
0 to 3
0 to 4
0 to 5
0 to 6
1 to 3
1 to 4
2 to 5
2 to 6

For a total of ten paths?

olcott explained on 11/21/2023 :
> On 11/21/2023 6:37 PM, olcott wrote:
>> On 11/6/2023 5:00 AM, Adam Polak wrote:
>>> Dear Friends,
>>>
>>> The Set Theory, creator of which is considered to be Professor Georg
>>> Cantor, currently adhered to by the vast majority of scientists, is an
>>> undoubtedly flawed theory, based on erroneous assumptions and, as a
>>> result, filled with errors and internal contradictions.
>>>
>>
>> So I see you never got this memo:
>> https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory
>>
>> *Cantor's set theory has been called naive set theory for a long time*
>>
>
> *I am surprised that no one here seemed to know this and the above*
> https://en.wikipedia.org/wiki/Naive_set_theory

You assume too much with so little evidence. Maybe we seem not to know
because we mostly tend to ignore the obvious trolls and cranks.

On Tuesday, November 21, 2023 at 7:47:36 PM UTC-5, olcott wrote:
> On 11/21/2023 6:37 PM, olcott wrote:
> > On 11/6/2023 5:00 AM, Adam Polak wrote:
> >> Dear Friends,
> >>
> >> The Set Theory, creator of which is considered to be Professor Georg
> >> Cantor, currently adhered to by the vast majority of scientists, is an
> >> undoubtedly flawed theory, based on erroneous assumptions and, as a
> >> result, filled with errors and internal contradictions.
> >>
> >
> > So I see you never got this memo:
> > https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory
> >
> > *Cantor's set theory has been called naive set theory for a long time*
> >
> *I am surprised that no one here seemed to know this and the above*
> https://en.wikipedia.org/wiki/Naive_set_theory

This one above is very nicely written.
It even bothers to discuss Cartesian order, and that is a pet study of mine..
That set theory came along so late: could it be that they simply did not have the ability to step upon the toes of the real value?
To go against such 'established mathematics' would be a knell for their work.
Yet to mildly pass by, as if compatible; did someone possibly leave a nice chunk of chocolate in the peanut butter?
Better yet, cashew butter. Ooh, if I could afford the stuff.
Getting nutty never felt so fun.
All stuck on your gums as your saliva slowly dissolves the stuff.

did anyone trouble over the operators embedded in the values?
It seems they did not. It would be like taking mathematics and throwing your hands up in the air, holding the whole ancient pile, and in a steady gentle breeze much of it drifts off as chaffe, and what remains, exactly? Did you mean to mix your elements and your operators so early and claim elemental status of the whole bunch? Did we perhaps expose a structural error in such commitments? Could we have absorbed some exceptions into our puritanical system a bit too early?

Did your language ever commit nouns to verbs, verbs to nouns, and noun verb nouns to nouns? Is our own language in this dual form compromised? Does every object have an action? Should every object have an action? Then possibly their work can be admitted, for the noun/verb disparity would be eliminated. Of course the structrural change lays waste to most of grammar. Perhaps our GI will be speaking like Indians to us?
"Tree", the native utters in his own tung, as his hands rise into the air vertically, then waving outwards, then cutting back in some, and waiving outwards again. As he get to the top; the crown of the tree, something changes in his demeanor.

As if getting divisive was going to be productive: the matter of the computation of the division operator is not trivial and dies in fact lead to the unending digits such as:
1/7 = 0.142857142857...
while in truth should we hop over to radix seven we will simply see:
1/7 = 0.1
and so the mixed radix puzzle is somewhat bearing the fruit of the seemingly magical repeating decimal. Does it go on for ever? Did Dedekind really answer that? I'll take my own short answer any day.

> --
> Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
> hits a target no one else can see." Arthur Schopenhauer

On 11/22/2023 5:48 AM, FromTheRafters wrote:
> olcott explained on 11/21/2023 :
>> On 11/21/2023 6:37 PM, olcott wrote:
>>> On 11/6/2023 5:00 AM, Adam Polak wrote:
>>>> Dear Friends,
>>>>
>>>> The Set Theory, creator of which is considered to be Professor Georg
>>>> Cantor, currently adhered to by the vast majority of scientists, is
>>>> an undoubtedly flawed theory, based on erroneous assumptions and, as
>>>> a result, filled with errors and internal contradictions.
>>>>
>>>
>>> So I see you never got this memo:
>>> https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory
>>>
>>> *Cantor's set theory has been called naive set theory for a long time*
>>>
>>
>> *I am surprised that no one here seemed to know this and the above*
>> https://en.wikipedia.org/wiki/Naive_set_theory
>
> You assume too much with so little evidence. Maybe we seem not to know
> because we mostly tend to ignore the obvious trolls and cranks.

No one bothered to tell the guy that his fantastic insights about
Russell's Paradox have been known for a long time. So in other words
the people here that might know these things are also mere Trolls.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On Wednesday, November 22, 2023 at 11:57:07 AM UTC+1, Fritz Feldhase wrote:
> On Wednesday, November 22, 2023 at 10:46:21 AM UTC+1, Adam Polak wrote:
> >
> > ... the EMPTY SET ...
> >
> Yeah, you're onto something! For sure!

See: https://www.researchgate.net/publication/38327298_The_Empty_Set_The_Singleton_and_the_Ordered_Pair

On 11/22/2023 3:43 AM, FromTheRafters wrote:
> Chris M. Thomasson expressed precisely :
>> On 11/21/2023 2:49 PM, Chris M. Thomasson wrote:
>>> On 11/21/2023 3:43 AM, WM wrote:
>>>> On 21.11.2023 06:42, Adam Polak wrote:
>>>>>
>>>>> Never apears the situation in which a "new real number" "created"
>>>>> by the diagonal method could not be added to an infinite set of
>>>>> real numbers which, at the same time, always remains equinumerous
>>>>> (one-to-one correspondence of elements ) with an infinite set of
>>>>> natural numbers.
>>>>
>>>> So it is. Two honest tricksters. Each one wants to be the second.
>>>>
>>>>> Cantor's Diagonal Method is not a proof of the greater cardinality
>>>>> of R than N.
>>>>
>>>> So it is.
>>>>>
>>>>> The above, is just one of several observations refuting the
>>>>> diagonal argument.
>>>>
>>>> For instance the Binary Tree having more nodes than paths.
>>> This snapshot has 6 paths. The root node 0 has 6 children {1, 2, 3,
>>> 4, 5, 6} :
>>> _____________________
>>>        0
>>>       / \
>>>      /   \
>>>     1     2
>>>    / \   / \
>>>   3   4 5   6
>>> _____________________
>>
>> Or, node[0] has a family of [1, 2, 3, 4, 5, 6] in this snapshot.
>
> Aren't the paths as follows:
>
> 0 to 1
> 0 to 2
> 0 to 3
> 0 to 4
> 0 to 5
> 0 to 6
> 1 to 3
> 1 to 4
> 2 to 5
> 2 to 6
>
> For a total of ten paths?

I am thinking of a path going down from parent to children in this
finite snapshot of a 2-ary tree. So:

0 is root origin:

0 has two children
1 has two children
2 has two children

3, 4, 5, 6 are the end of the snapshot.

2 + 2 + 2 is six

However, there are including (root) seven nodes. The root node 0 has 6
members wrt its "offspring", or family if you will...
_____________________
0
/ \
/ \
1 2
/ \ / \
3 4 5 6
_____________________

Fair enough to think about it like this?

0 has six nodes in its family wrt to the finite snapshot of the infinite
tree.