On 12/5/2023 9:53 AM, WM wrote:
> On 05.12.2023 15:44, FromTheRafters wrote:
>> WM pretended :
>>> Fritz Feldhase schrieb am Montag, 4. Dezember 2023 um 17:56:48 UTC+1:
>>>
>>>  > On the other hand, starting with the matrix A(0)
>>>  >
>>>  > > 1 0 0...
>>>  > > 2 0 0...
>>>  > > 3 0 0...
>>>  > > ...
>>>  > >
>>>  > it is impossible [to "reach" the matrix B] by exchanging [the numbers
>>> 1, 2, 3, ... with 0's successively]
>>>
>>> So it is. But since every step k is defined by Cantor's formula
>>> k = (m + n - 1)(m + n - 2)/2 + m, the sequence 1/1, 1/2, 2/1, 1/3, 2/2,
>>> 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, 2/4, 3/3, 4/2, 5/1, 1/6, 2/5, 3/4, 4/3,
>>> 5/2, 6/1, ... is completely reproduced by the exchanges. There is no
>>> step missing. Therefore your alleged distinction between both ways does
>>> not exist and is not justified. Both lead to the same result. But my
>>> procedure shows that not all fractions are indexed.
>>
>> Therefore your procedure *FAILS* to show the bijection.
>
> My procedure shows that Cantor's alleged bijection is none.

Keep dreaming and polluting the minds of your students... Well done,
asshole? Humm.... ;^o

>
>> This is not the same as showing that there is no bijection, especially
>> when there is.
>
> But it is the same as showing that Cantor's alleged bijection is none.
> Because I copy Cantor's procedure precisely. The only difference is that
> I take the indices from the first column. If this destroys the effect,
> then there is no bijection n <--> 1/n.
>
> Regards, WM
>

On 12/5/2023 10:26 AM, WM wrote:
> Fritz Feldhase schrieb am Dienstag, 5. Dezember 2023 um 15:06:50 UTC+1:
> > On Tuesday, December 5, 2023 at 10:42:52 AM UTC+1, WM wrote:
> > > Fritz Feldhase schrieb am Montag, 4. Dezember 2023 um 17:56:48 UTC+1:
> > > >
> > > > On the other hand, starting with the matrix A(0)
> > > >
> > > > 1 0 0...
> > > > 2 0 0...
> > > > 3 0 0...
> > > > ...
> > > >
> > > > it is impossible to "reach" the matrix B [in a finite number of
> steps] by exchanging the numbers 1, 2, 3, ... with 0's successively.
> > > >
> > > [By my] procedure [never] all fractions are indexed.
> >
> > Right.
>
> The only difference to Cantor's procedure is that I use the first column
> as the source of indices.
> >
> > I contrast to that, the matrix B = (b_n,m) defined by b_n,m = (m + n
> - 1)(m + n - 2)/2 + m for all n,m e IN represents a complete enumeration
> of the fractions.
>
> If that would be right, then there is no bijection between unit
> fractions and natnumbers.

Yes there is! Keep in mind that Cantor pairing deals with pairs. So, we
can use these pairs to say... Okay, any pair (a, b) is a fraction (a
over b) as long as b is non-zero? Fair enough?

On Friday, December 1, 2023 at 7:38:49 PM UTC-8, Ross Finlayson wrote:
> On Tuesday, November 28, 2023 at 12:02:00 AM UTC-8, Ross Finlayson wrote:
> > On Tuesday, November 21, 2023 at 12:23:54 AM UTC-8, Ross Finlayson wrote:
> > > 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, ....
> >
> > Hello. Well, I started reading Gadamer and his hermeneutics on Plato. From Smith the translator's
> > introduction, it seems that getting into Gadamer's Being and Truth bit has it's sort of a Tarski truth,
> > so it sort of seems for a reading through a lens where Gadamer's elusive truth is let out under
> > Kant's sublime, so that there's still makings for a theory with a real truth, while at the same time
> > acknowledging human limits, about the mutual provability and lack thereof or the undecideability,
> > that there really is a true truth then of course that there must be, or there isn't. Then though
> > Gadamer as Heidegger's student, he lived later in the 20'th century so he makes some readings
> > and so on from his desk, while though he seems rather stern, that it's possible to be quite
> > serious and rather, sincere, about hermeneutics of truth, and philosophy and its canon,
> > while not necessarily having that the entire gravity of it is without its sublime brilliance
> > for what it is.
> >
> > Then, I'll be reading it for what he denies himself, then figure it's as of a usual approach
> > of an object/subject distinction, just to have it so that for the extra-ordinary logic and
> > the usual reading of a Plato's "One" besides a usual multitudinous "Two", that they're
> > to be read as both, each other, for the dialog and dialectic, what results a dialectic as
> > reflective, and not just another lengthening shadow, in the cave.
> Leafing through a volume on philosophy and physics, the fellow starts "well it seems
> when you adopt a study of philosophy, it's a choice of either Plato or Aristotle".
>
> Then, Gadamer spends quite a while on Plato then more or less says there's only
> the lens of Aristotle or observing Plato, carrying on that Plato can't really be beheld
> and this sort of thing, that the aletheia or disconcealment is just an understanding
> of what's revealed that the limits of comprehension can't but attain to Plato.
>
> So, Gadamer carries on quite a while that Aristotle is somehow more didactic,
> that Plato doesn't have artifacts, that Aristotle wrote a regular bit, that Aristotle
> is his anti-Plato or inverse Plato or bizarro Plato, that Aristotle is in the usual
> course of a semantical development and a maturation what would be the usual
> grant of subjectivity, that Aristotle is more for a reasoned "unknowable" than
> Plato's sort of "divine truth", that Aristotle is simpler for a thinking being to arrive
> at its sound limits, that Aristotle is at some point in philosophical maturation,
> the viewpoint of reasonable skeptic and the sort of idol that usual students at
> a usual stage of philosophical maturity can emulate, for Aristotleanism or
> Aristoteleanism if you will.
>
> Then, though, as he concludes and summarizes, it's because Aristotle is a Platonist,
> or, as it ends, "amicus Plato", and a footnote.
>
>
> Then these days it's like "well, Wittgenstein is our anti-Plato, also he's a very
> strong Platonist".
>
> So, platonism and that there are absolute truths objective our objective our subjective,
> makes for that at some point in philosophical maturity it's arrived at, Platonism,
> then here for a modern sort of acknowledgment of "limits, limits", a,
> "strong mathematical platonism".
>
> Then that the objects of the mathematical, logical universe have to be all the
> mathematical, logical things, in a universe of mathematical objects and for a theory
> of it, is a pretty strong grounds for foundations that makes a usual abstraction and
> axiomatics just a brief resting point in a philosophical maturation toward a
> fully holistic sort of theory for an absolute abstraction of axiomatics.
>
> "Theoria", as he puts it, Gadamer, then "amicus Plato".
>
>
> An entire universe, ....

Gadamer describes Xenocrates having for Plato that the "moving numbers"
of Xenocrates make that Plato says that a number-sense is "the gods' gift" to
man, and the Promethean fire, and that such observance of passage is the
notice of the, "Soul", itself.

I.e., man having an object-sense after a number-sense after a word-sense,
is sort of what makes for language and mathematics and reason,
right in the middle of the noumena and phenomena, and connected to both.

These days after the Christian ethos then it's also associated with
communion, if though that modern logical positivists sort of left
it there missing in their rush to ban the belfry. I.e. a "stronger logical
positivist" is retrieving and returning word-sense, number-sense,
and object-sense, as having objects for discourse that are "real"
enough for mathematical infinity. (Which otherwise gets pushed
back out, ...).

So, it's also as for hope, sort of like what's "Pandora's box", after
all the apeiron and also fallacy of the box escape, a bit of hope's left.

So, for some modern critics, a usual image is Russell, Cantor, and
logical positivism, playing "stop hitting yourself".

On Tuesday, December 5, 2023 at 7:10:19 PM UTC-8, Ross Finlayson wrote:
> On Friday, December 1, 2023 at 7:38:49 PM UTC-8, Ross Finlayson wrote:
> > On Tuesday, November 28, 2023 at 12:02:00 AM UTC-8, Ross Finlayson wrote:
> > > On Tuesday, November 21, 2023 at 12:23:54 AM UTC-8, Ross Finlayson wrote:
> > > > 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, ....
> > >
> > > Hello. Well, I started reading Gadamer and his hermeneutics on Plato. From Smith the translator's
> > > introduction, it seems that getting into Gadamer's Being and Truth bit has it's sort of a Tarski truth,
> > > so it sort of seems for a reading through a lens where Gadamer's elusive truth is let out under
> > > Kant's sublime, so that there's still makings for a theory with a real truth, while at the same time
> > > acknowledging human limits, about the mutual provability and lack thereof or the undecideability,
> > > that there really is a true truth then of course that there must be, or there isn't. Then though
> > > Gadamer as Heidegger's student, he lived later in the 20'th century so he makes some readings
> > > and so on from his desk, while though he seems rather stern, that it's possible to be quite
> > > serious and rather, sincere, about hermeneutics of truth, and philosophy and its canon,
> > > while not necessarily having that the entire gravity of it is without its sublime brilliance
> > > for what it is.
> > >
> > > Then, I'll be reading it for what he denies himself, then figure it's as of a usual approach
> > > of an object/subject distinction, just to have it so that for the extra-ordinary logic and
> > > the usual reading of a Plato's "One" besides a usual multitudinous "Two", that they're
> > > to be read as both, each other, for the dialog and dialectic, what results a dialectic as
> > > reflective, and not just another lengthening shadow, in the cave.
> > Leafing through a volume on philosophy and physics, the fellow starts "well it seems
> > when you adopt a study of philosophy, it's a choice of either Plato or Aristotle".
> >
> > Then, Gadamer spends quite a while on Plato then more or less says there's only
> > the lens of Aristotle or observing Plato, carrying on that Plato can't really be beheld
> > and this sort of thing, that the aletheia or disconcealment is just an understanding
> > of what's revealed that the limits of comprehension can't but attain to Plato.
> >
> > So, Gadamer carries on quite a while that Aristotle is somehow more didactic,
> > that Plato doesn't have artifacts, that Aristotle wrote a regular bit, that Aristotle
> > is his anti-Plato or inverse Plato or bizarro Plato, that Aristotle is in the usual
> > course of a semantical development and a maturation what would be the usual
> > grant of subjectivity, that Aristotle is more for a reasoned "unknowable" than
> > Plato's sort of "divine truth", that Aristotle is simpler for a thinking being to arrive
> > at its sound limits, that Aristotle is at some point in philosophical maturation,
> > the viewpoint of reasonable skeptic and the sort of idol that usual students at
> > a usual stage of philosophical maturity can emulate, for Aristotleanism or
> > Aristoteleanism if you will.
> >
> > Then, though, as he concludes and summarizes, it's because Aristotle is a Platonist,
> > or, as it ends, "amicus Plato", and a footnote.
> >
> >
> > Then these days it's like "well, Wittgenstein is our anti-Plato, also he's a very
> > strong Platonist".
> >
> > So, platonism and that there are absolute truths objective our objective our subjective,
> > makes for that at some point in philosophical maturity it's arrived at, Platonism,
> > then here for a modern sort of acknowledgment of "limits, limits", a,
> > "strong mathematical platonism".
> >
> > Then that the objects of the mathematical, logical universe have to be all the
> > mathematical, logical things, in a universe of mathematical objects and for a theory
> > of it, is a pretty strong grounds for foundations that makes a usual abstraction and
> > axiomatics just a brief resting point in a philosophical maturation toward a
> > fully holistic sort of theory for an absolute abstraction of axiomatics..
> >
> > "Theoria", as he puts it, Gadamer, then "amicus Plato".
> >
> >
> > An entire universe, ....
>
>
>
> Gadamer describes Xenocrates having for Plato that the "moving numbers"
> of Xenocrates make that Plato says that a number-sense is "the gods' gift" to
> man, and the Promethean fire, and that such observance of passage is the
> notice of the, "Soul", itself.
>
> I.e., man having an object-sense after a number-sense after a word-sense,
> is sort of what makes for language and mathematics and reason,
> right in the middle of the noumena and phenomena, and connected to both.
>
> These days after the Christian ethos then it's also associated with
> communion, if though that modern logical positivists sort of left
> it there missing in their rush to ban the belfry. I.e. a "stronger logical
> positivist" is retrieving and returning word-sense, number-sense,
> and object-sense, as having objects for discourse that are "real"
> enough for mathematical infinity. (Which otherwise gets pushed
> back out, ...).
>
> So, it's also as for hope, sort of like what's "Pandora's box", after
> all the apeiron and also fallacy of the box escape, a bit of hope's left.
>
>
> So, for some modern critics, a usual image is Russell, Cantor, and
> logical positivism, playing "stop hitting yourself".

FromTheRafters <FTR@nomail.afraid.org> writes:
> Adam Polak wrote on 11/24/2023 :
>> piątek, 24 listopada 2023 o 08:25:12 UTC+1 FromTheRafters napisał(a):
>> "
>> Set: { 1, 3, 4/4, 18 } how many elements contain ?
>>> Four symbols separated by three commas. I would say four elements.
>>> Cardinality four.
>> "
>> what happened that you didn't recognize 4/4 as 1 as "the number ONE"
>
> I didn't recognize that collection as a set, but as a multiset,
> because ZFC sets don't have duplicate elements.
>
>> and that, in accordance with Set theory, you did not answer: three elements ?
>> just think it over
>
> Yes, you are correct. I should have because the symbol 4/4 and the
> symbol 1 are the same number just like 1/2 and .5 and .4(9) are all
> the same number.

If the subject is sets, I really couldn't countainance { 1, 4/4, 1.0 }
as being anything apart from a perfectly valid 3-element set containing
a natural number, a distinct rational, and a distinct real
number. Representation matters, not value across canonicalisations
thereof.

Phil
--
We are no longer hunters and nomads. No longer awed and frightened, as we have
gained some understanding of the world in which we live. As such, we can cast
aside childish remnants from the dawn of our civilization.
-- NotSanguine on SoylentNews, after Eugen Weber in /The Western Tradition/

On Monday 6 November 2023 at 12:01:03 UTC+1, 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.

Did you mean MATHEMATICIANS? Scientists rarely use set theory.

You make loads of big claims, none of which will be correct.

>
> 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.

Less babbling more showing any substance.f

>
> 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.

Yes, you can add more real number to the list used in the diagonal method, and I will show you YET ANOTHER you missed, no matter how much you do this, I can always show you have missed a real number.

>
> 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.

No it isn't because applying the diagonal argument again, we show yet another one you missed, which is the entire point of the fucking proof!

>
> The set theory is clearly contradictory in many places.

Yet you have not shown one here. All you showed is your lack of understanding.

>
> Best Regards,
> Adam Polak

On Wednesday 8 November 2023 at 13:03:25 UTC+1, Adam Polak wrote:
> środa, 8 listopada 2023 o 12:48:09 UTC+1 FromTheRafters napisał(a):
> > Python presented the following explanation :
> > > Le 08/11/2023 à 05:29, FromTheRafters a écrit :
> > >> Fritz Feldhase wrote on 11/7/2023 :
> > >>> On Wednesday, November 8, 2023 at 2:49:56 AM UTC+1, mitchr....@gmail.com
> > >>> wrote:
> > >>>>
> > >>>> What is a set with nothing in it?
> > >>>
> > >>> An empty set?
> > >>
> > >> The empty set.
> > >
> > > We could do memes from this :-)
> > I asked the grocer for an empty box, he asked "An empty box of what?"
> these doubts are explained in my presentation (link in the first message) page 23 and around :
>
> "
> Set theory, in its various formulations, avoids presenting a single coherent definition of the concept of a SET.

Have you ever heard of a PRIMITIVE CONCEPT!? They are not defined in terms of other things!

>
> Defining this concept based on the notion of an ELEMENT of a set reveals that the so-called "empty set" does not satisfy the definition of a set and should not be considered as part of a coherent set theory.

Except by the axioms of set theory it SATISFIES the critierias of a set and thus is.

> On the other hand, defining the concept of a SET in a way that allows for the omission of having elements as a condition for the existence of a set makes it extremely difficult, if not impossible, to maintain the illusion that set theory explains the phenomenon of creating "something out of nothing„.

It doesn't create anything, they are ABSTRACT CONCEPTS YOU MORON!

>
> In practice, the concept of a SET is usually described through the concept of the elements of the set. At the same time, by force, by axiom, set theory introduces a concept of empty set containing no elements, even though it does not fulfill the description /definition of a set in terms of having elements.

ZFC does not define it in any such things and the empty set must exist by the axioms of ZFC and that is not a problem.

>
> There should be no doubt that regardless of whether a SET is understood as a collection of mushrooms or as a basket into which mushrooms have been collected, there can be no talk of any creatio ex nihilo in any case.

That is INTUITIVE understanding, not FORMAL understanding you idiot.

> "
>
> I have many tasks and limited time, so I may not visit and reply here often
> BR, Adam

Phil Carmody formulated on Wednesday :
> FromTheRafters <FTR@nomail.afraid.org> writes:
>> Adam Polak wrote on 11/24/2023 :
>>> piątek, 24 listopada 2023 o 08:25:12 UTC+1 FromTheRafters napisał(a):
>>> "
>>> Set: { 1, 3, 4/4, 18 } how many elements contain ?
>>>> Four symbols separated by three commas. I would say four elements.
>>>> Cardinality four.
>>> "
>>> what happened that you didn't recognize 4/4 as 1 as "the number ONE"
>>
>> I didn't recognize that collection as a set, but as a multiset,
>> because ZFC sets don't have duplicate elements.
>>
>>> and that, in accordance with Set theory, you did not answer: three elements
>>> ? just think it over
>>
>> Yes, you are correct. I should have because the symbol 4/4 and the
>> symbol 1 are the same number just like 1/2 and .5 and .4(9) are all
>> the same number.
>
> If the subject is sets, I really couldn't countainance { 1, 4/4, 1.0 }
> as being anything apart from a perfectly valid 3-element set containing
> a natural number, a distinct rational, and a distinct real
> number. Representation matters, not value across canonicalisations
> thereof.
>
> Phil

That was my original thought, by roster form it indicates three
elements separated by commas. If it is meant as a multiset, square
brackets would be more appropriate.

Fritz Feldhase schrieb am Mittwoch, 6. Dezember 2023 um 09:53:22 UTC+1:
> On Wednesday, December 6, 2023 at 9:03:53 AM UTC+1, Fritz Feldhase
wrote:

> > Hint: If you accept 1 = 4/4 = 1.0, then you have to accept card {1,
4/4, 1.0} = 1.

Only if the values are meant. But who decides that?
>
> In addition you may check this: https://en.wikipedia.org/wiki/0.999...
>
> There you will find the statement: 0.999... = 1.

It is not quite correct. Correct is 0.999... --> 1.
>
> Hence: card {0.999... , 1} = 1.

Only if the limits are meant. Five is not the same as 5 and not the same
as V, if the set of different symbols is meant.

Regards, WM

On 06.12.2023 09:53, zelos...@gmail.com wrote:

> Scientists rarely use set theory.

They rarely use the rules set up by Vatican either. Both with good reason.
>
> You make loads of big claims, none of which will be correct.

There are some claims prohibited in sciences. For instance you could
divide a square of area 1 m^2, formally, into infinitely many vertical
and horizontal stripes with descending width 1/2 m, 1/4 m, 1/8 m, ... .
Fill the first vertical stripe with matter. Then move, formally, this
matter like the X in
XOOO...
XOOO...
XOOO...
XOOO...
....
and find that in the result all stripes have been covered like
XXXX...
XXXX...
XXXX...
XXXX...
....
such that the matter has doubled. By starting with another stripe, the
result could even by multiplied.

Could any science tolerate that nonsense?

Regards, WM

On Wednesday 6 December 2023 at 17:32:32 UTC+1, WM wrote:
> On 06.12.2023 09:53, zelos...@gmail.com wrote:
>
> > Scientists rarely use set theory.
> They rarely use the rules set up by Vatican either. Both with good reason..

Invalid comparison. Set theory is a legit part of mathematics. It just isn't a useful to most of physics.

> >
> > You make loads of big claims, none of which will be correct.
> There are some claims prohibited in sciences.

We are talking mathematics, retard.

>For instance you could
> divide a square of area 1 m^2, formally, into infinitely many vertical
> and horizontal stripes with descending width 1/2 m, 1/4 m, 1/8 m, ... .
> Fill the first vertical stripe with matter. Then move, formally, this
> matter like the X in
> XOOO...
> XOOO...
> XOOO...
> XOOO...
> ...
> and find that in the result all stripes have been covered like
> XXXX...
> XXXX...
> XXXX...
> XXXX...
> ...
> such that the matter has doubled. By starting with another stripe, the
> result could even by multiplied.
>
> Could any science tolerate that nonsense?
>
> Regards, WM

You are complaining that mathematics, which has no relation to reality, gives result that if translated to reality in its wierdest parts, is wierd. That is invalid because the only thing that says is that the thing given is not useful in reality. And Banarch-Tarski is as far as we can say, in of itself, not useful to reality. Big fucking whoop. Maybe it leads to something that owrks in the end? Who knows!

zelos...@gmail.com schrieb am Mittwoch, 6. Dezember 2023 um 17:35:58 UTC+1:
> On Wednesday 6 December 2023 at 17:32:32 UTC+1, WM wrote:

> > divide a square of area 1 m^2, formally, into infinitely many vertical
> > and horizontal stripes with descending width 1/2 m, 1/4 m, 1/8 m,
.... .
> > Fill the first vertical stripe with matter. Then move, formally, this
> > matter like the X in
> > XOOO...
> > XOOO...
> > XOOO...
> > XOOO...
> > ...
> > and find that in the result all stripes have been covered like
> > XXXX...
> > XXXX...
> > XXXX...
> > XXXX...
> > ...
> > such that the matter has doubled. By starting with another stripe, the
> > result could even by multiplied.
> >
> > Could any science tolerate that nonsense?

> You are complaining that mathematics, which has no relation to reality,

Mathematics is used to predict the results of real experiments. If set
theory were correct, it would correctly predict the result of the above
procedure. It does not.

> And Banarch-Tarski is as far as we can say, in of itself, not useful
to reality.

Here we do not use Banach-Tarski but simply Cantor's indexing of all
matrix positions with the integer fractions of the first column. The
only difference is that the infinite matrix has been compressed a bit to
fit into an square meter.

Regards, WM

On Wednesday 6 December 2023 at 17:55:31 UTC+1, WM wrote:
> zelos...@gmail.com schrieb am Mittwoch, 6. Dezember 2023 um 17:35:58 UTC+1:
> > On Wednesday 6 December 2023 at 17:32:32 UTC+1, WM wrote:
>
> > > divide a square of area 1 m^2, formally, into infinitely many vertical
> > > and horizontal stripes with descending width 1/2 m, 1/4 m, 1/8 m,
> ... .
> > > Fill the first vertical stripe with matter. Then move, formally, this
> > > matter like the X in
> > > XOOO...
> > > XOOO...
> > > XOOO...
> > > XOOO...
> > > ...
> > > and find that in the result all stripes have been covered like
> > > XXXX...
> > > XXXX...
> > > XXXX...
> > > XXXX...
> > > ...
> > > such that the matter has doubled. By starting with another stripe, the
> > > result could even by multiplied.
> > >
> > > Could any science tolerate that nonsense?
> > You are complaining that mathematics, which has no relation to reality,
> Mathematics is used to predict the results of real experiments.

Because it has shown to strangely good at that despite mathematics not giving a shit. Strange isn't it, retard?

>If set
> theory were correct,

It is as correct as any axiomatic system.

>it would correctly predict the result of the above
> procedure. It does not.

Only if the real system satisfies the axioms of set theory, which it does not so of course it does NOT.

That is like bitching about that in integers we have S(-1)=0 when there is no x such that S(x)=0 in natural numbers by peano! The mathematics only predicts well if reality matches the axioms required sufficiently close.

> > And Banarch-Tarski is as far as we can say, in of itself, not useful
> to reality.
> Here we do not use Banach-Tarski but simply Cantor's indexing of all
> matrix positions with the integer fractions of the first column.

Same principle in doubling shit.

>The
> only difference is that the infinite matrix has been compressed a bit to
> fit into an square meter.
>
> Regards, WM

Again, retard, you are the one too stupid to understand that the conclusions of a mathematical dicipline only applies if the physical system satisfies the axioms of said dicipline sufficiently close. How are you this stupid?

wtorek, 5 grudnia 2023 o 14:58:01 UTC+1 Fritz Feldhase napisał(a):
> On Tuesday, December 5, 2023 at 11:09:24 AM UTC+1, Adam Polak wrote:
>
> > [What we may conclude] from the [existence of a] bijection is [...] that a[n] infinite set is "equinumerous" with another infinite set, meaning that they "contain"/should be seen as containing the same "number" of elements.
>
> Exactly [at least in the context of set theory]. (->power, cardinal numbers)
>
> Now you claim:
>
> > A bijection between [...] two infinite sets [exists] in every case
>
> Nope. This is (provably) not the case. For example, there's no bijection between IN and the power set of IN, P(IN) = {M : M c IN}. Try to define one! :-)

That is not the smallest problem.

ALL infinite sets, absolutely without exception, are described by the following model:
eα -> en(eα) -> en( en(eα)) -> en( en( en(eα))) -> … -> ∞
First element -> Successor -> Successor of the Successor -> Successor of the Successor of the Successor -> ...

As a result, the bijection between any two infinite sets is obvious and is an immanent necessity.

If this is not clear enough, understanduble for you, graphics would be needed to further translate. This forum does not support them. I hope to prepare an appropriate presentation and publish it soon.

Adam Polak brought next idea :
> wtorek, 5 grudnia 2023 o 14:58:01 UTC+1 Fritz Feldhase napisał(a):
>> On Tuesday, December 5, 2023 at 11:09:24 AM UTC+1, Adam Polak wrote:
>>
>>> [What we may conclude] from the [existence of a] bijection is [...] that
>>> a[n] infinite set is "equinumerous" with another infinite set, meaning that
>>> they "contain"/should be seen as containing the same "number" of elements.
>>
>> Exactly [at least in the context of set theory]. (->power, cardinal numbers)
>>
>> Now you claim:
>>
>>> A bijection between [...] two infinite sets [exists] in every case
>>
>> Nope. This is (provably) not the case. For example, there's no bijection
>> between IN and the power set of IN, P(IN) = {M : M c IN}. Try to define one!
>> :-)
>
> That is not the smallest problem.
>
> ALL infinite sets, absolutely without exception, are described by the
> following model: eα -> en(eα) -> en( en(eα)) -> en( en( en(eα))) -> …
> -> ∞ First element -> Successor -> Successor of the
> Successor -> Successor of the Successor of the Successor -> ...
>
> As a result, the bijection between any two infinite sets is obvious and is an
> immanent necessity.
>
> If this is not clear enough, understanduble for you, graphics would be needed
> to further translate. This forum does not support them. I hope to prepare an
> appropriate presentation and publish it soon.

What is the third real number?

środa, 6 grudnia 2023 o 17:35:58 UTC+1 zelos...@gmail.com napisał(a):
> On Wednesday 6 December 2023 at 17:32:32 UTC+1, WM wrote:
> > On 06.12.2023 09:53, zelos...@gmail.com wrote:
> >
> > > Scientists rarely use set theory.
> > They rarely use the rules set up by Vatican either. Both with good reason.
> Invalid comparison. Set theory is a legit part of mathematics. It just isn't a useful to most of physics.
> > >
> > > You make loads of big claims, none of which will be correct.
> > There are some claims prohibited in sciences.
> We are talking mathematics, retard.
> >For instance you could
> > divide a square of area 1 m^2, formally, into infinitely many vertical
> > and horizontal stripes with descending width 1/2 m, 1/4 m, 1/8 m, ... .
> > Fill the first vertical stripe with matter. Then move, formally, this
> > matter like the X in
> > XOOO...
> > XOOO...
> > XOOO...
> > XOOO...
> > ...
> > and find that in the result all stripes have been covered like
> > XXXX...
> > XXXX...
> > XXXX...
> > XXXX...
> > ...
> > such that the matter has doubled. By starting with another stripe, the
> > result could even by multiplied.
> >
> > Could any science tolerate that nonsense?
> >
> > Regards, WM
> You are complaining that mathematics, which has no relation to reality, gives result that if translated to reality in its wierdest parts, is wierd. That is invalid because the only thing that says is that the thing given is not useful in reality. And Banarch-Tarski is as far as we can say, in of itself, not useful to reality. Big fucking whoop. Maybe it leads to something that owrks in the end? Who knows!
The problem here is more that Set Theory contains assumptions (e.g. the empty set axiom) that are unacceptable from a scientific perspective.
"There is an empty set" is no different from "there is a tooth fairy" is no different from "there is a god".
As a result, Set Theory is not simply a scientific theory and cannot even be classified as science-fiction.
Set theory is pure fiction, and if someone were to insist, it could also be called a religion.

So complaining about set theory is not complaining about mathematics but about fiction/fantasy, which has invaded some areas of mathematics, pretending - as an element of mathematics - to be science and not fantasy.

czwartek, 7 grudnia 2023 o 10:06:29 UTC+1 Fritz Feldhase napisał(a):
> On Thursday, December 7, 2023 at 9:23:44 AM UTC+1, FromTheRafters wrote:
> > Adam Polak brought next idea :
> > > wtorek, 5 grudnia 2023 o 14:58:01 UTC+1 Fritz Feldhase napisał(a):
> > >> On Tuesday, December 5, 2023 at 11:09:24 AM UTC+1, Adam Polak wrote:
> > >>
> > >>> [What we may conclude] from the [existence of a] bijection is [...] that
> > >>> a[n] infinite set is "equinumerous" with another infinite set, meaning that
> > >>> they "contain"/should be seen as containing the same "number" of elements.
> > >>
> > >> Exactly [at least in the context of set theory]. (->power, cardinal numbers)
> > >>
> > >> Now you claim:
> > >>
> > >>> A bijection between [...] two infinite sets [exists] in every case
> > >>
> > >> Nope. This is (provably) not the case. For example, there's no bijection
> > >> between IN and the power set of IN, P(IN) = {M : M c IN}. Try to define one!
> > >> :-)
> > >
> > > That is not the smallest problem.
> > >
> > > ALL infinite sets, absolutely without exception, are described by the
> > > following model: eα -> en(eα) -> en( en(eα)) -> en( en( en(eα))) -> …
> > > -> ∞ First element -> Successor -> Successor of the
> > > Successor -> Successor of the Successor of the Successor -> ...
> > >
> > > As a result, the bijection between any two infinite sets is obvious and is an
> > > immanent necessity.
> > >
> > > If this is not clear enough, understanduble for you, graphics would be needed
> > > to further translate. This forum does not support them. I hope to prepare an
> > > appropriate presentation and publish it soon.
> > >
> > What is the third real number?
> Hint: Even Chuck Norris couldn't count _all_real numbers.

No human being can count ALL the elements of any infinite set.
Count ALL the elements of an infinite set = find the "last" element in the infinite set, an element without a successor - and such an element, by definition, does not appear in any infinite set.

Don't bother with real numbers unless you understand natural numbers.
Calling any of infinite sets countable is absurd.
Just look at the simplest case: An infinite set of natural numbers.
Based on what do you say that you are able to count its elements?
N { 1, 2, 3, 4, 5, 6, 7, ... }
is quantitativeli equivalent to 2N { 2, 4, 6, 8, 10, ...} "containing" every second element of N.
N is also quantitativeli equivalent to { 1, -1, 2, -2, 3, -3, 4, -4, ... } containing twice as many elements as N

How many elements does N have?
N or maybe 2N or maybe N/2?
You can counting but NEVER counddown ALL elements of N, exactly the same as in regard of any other infinite set.

czwartek, 7 grudnia 2023 o 11:00:19 UTC+1 Fritz Feldhase napisał(a):
> On Thursday, December 7, 2023 at 10:32:58 AM UTC+1, Adam Polak wrote:
> >
> > The problem here is more that Set Theory contains assumptions (e.g. the empty set axiom) that are unacceptable from a scientific perspective.
> Oh, really? How would you know? Are you a scientist?
>
> Hint: The assumptions of Set Theory are acceptable from a mathematical point of view (at least for most mathematicians).
>
> See: https://en.wikipedia.org/wiki/Classical_mathematics
>
> > Set Theory [...] cannot [...] be classified as science-fiction.
>
> Indeed! It's a mathematical theory!
>
> > So complaining about set theory is [...] complaining about [a certain] mathematic[l theory].
>
> Even worse, it is complaining about the basis of /classical mathematics/.
>
> See link above.
>
> It's clear that you are not a mathematican, but just a "set theory crank" (just like Mückenheim, btw.)
>
> > <nonsense deleted>

Fritz, if you had anything to do with real science you would know that

WHO states - doesn't matter at all,
as opposed to
WHAT he states.
In science, only the substantive message counts, NOT THE PERSON.
If it were otherwise,
A FAMOUS PROFESSOR who said (even by mistake, thinking about something else) : "2+2=2", would be telling the truth.
and
A PARROT repeating mindlessly:
"2+2=4" would be wrong.

czwartek, 7 grudnia 2023 o 11:09:08 UTC+1 Fritz Feldhase napisał(a):
> On Thursday, December 7, 2023 at 10:59:38 AM UTC+1, Adam Polak wrote:
> > czwartek, 7 grudnia 2023 o 10:06:29 UTC+1 Fritz Feldhase napisał(a):
> > >
> > > Hint: Even Chuck Norris couldn't count _all_ real numbers.
> > >
> > No human being can count ALL the elements of any infinite set.
> That's not true! Chuck Norris counted to infinity - twice.
>
> See: https://www.amazon.de/-/en/AA-VV-ebook/dp/B008S313HK
> > Calling any of infinite sets countable is absurd.
> No, it's not.
>
> See: https://en.wikipedia.org/wiki/Countable_set
> > Just look at the simplest case: An infinite set of natural numbers.
> Yeah, a countable set. (See link above.)
> > How many elements does N have?
> Its cardinality is aleph_0.
>
> > N or maybe 2N or maybe ...
>
> Huh?!
>
> Hint (1): card IN = card 2IN = aleph_0.
>
> Hint (2): card IR > card IN.

Analyse all above and note, that you are unable to deny any of my statements.
Your counterarguments comes down almost entirely to sending links / to repiting other peaples statements.
aren't you a parrot? think it over
There are two possibilities, either the person who taught the parrot was teaching:
truth "2+2=4"
or
untruth "2+2=2" (even in good faith and without being aware of my own mistake)

The parrot need to start thinking on its own to try to find out what is going on.

czwartek, 7 grudnia 2023 o 09:23:44 UTC+1 FromTheRafters napisał(a):
> Adam Polak brought next idea :
> > wtorek, 5 grudnia 2023 o 14:58:01 UTC+1 Fritz Feldhase napisał(a):
> >> On Tuesday, December 5, 2023 at 11:09:24 AM UTC+1, Adam Polak wrote:
> >>
> >>> [What we may conclude] from the [existence of a] bijection is [...] that
> >>> a[n] infinite set is "equinumerous" with another infinite set, meaning that
> >>> they "contain"/should be seen as containing the same "number" of elements.
> >>
> >> Exactly [at least in the context of set theory]. (->power, cardinal numbers)
> >>
> >> Now you claim:
> >>
> >>> A bijection between [...] two infinite sets [exists] in every case
> >>
> >> Nope. This is (provably) not the case. For example, there's no bijection
> >> between IN and the power set of IN, P(IN) = {M : M c IN}. Try to define one!
> >> :-)
> >
> > That is not the smallest problem.
> >
> > ALL infinite sets, absolutely without exception, are described by the
> > following model: eα -> en(eα) -> en( en(eα)) -> en( en( en(eα))) -> …
> > -> ∞ First element -> Successor -> Successor of the
> > Successor -> Successor of the Successor of the Successor -> ...
> >
> > As a result, the bijection between any two infinite sets is obvious and is an
> > immanent necessity.
> >
> > If this is not clear enough, understanduble for you, graphics would be needed
> > to further translate. This forum does not support them. I hope to prepare an
> > appropriate presentation and publish it soon.
> What is the third real number?

If you want to understand what an infinite set don't bother with real numbers unless you understand natural numbers.
"What is the third real number?"
tell me what is the first and what is the second, and you will get the answer yourself

czwartek, 7 grudnia 2023 o 11:47:17 UTC+1 Fritz Feldhase napisał(a):
> On Thursday, December 7, 2023 at 11:36:50 AM UTC+1, Fritz Feldhase wrote:
> > On Thursday, December 7, 2023 at 11:26:14 AM UTC+1, Adam Polak might
> > >
> > > start thinking [...] to try to find out what is going on.
> > >
> > Good idea. Please do so!
> >
> > But learning some set theory in advance before trying to talk about set theory might be helpful.
> You might start here:
> ___________________________________________________________________________________________________
> On Tuesday, December 5, 2023 at 11:09:24 AM UTC+1, Adam Polak wrote:
>
> > > A bijection between [...] two infinite sets [exists] in every case
> > >
> > Nope. This is (provably) not the case. For example, there's no bijection between IN and the power set of IN, P(IN) = {M : M c IN}.
> Proof: Let f be a function from IN into {M : M c IN}.
>
> Now consider the set A := {n e IN : n !e f(n)}. This set clearly is an element in P(IN) (since A c IN), but it is not in the image of f _hence f is not a bijection_: For any n e IN: either n e f(n) or n !e f(n). If n e f(n), then n !e A, hence f(n) =/= A. If n !e f(n), then n e A, hence again f(n) =/= A. Hence in any case f(n) =/= A. In other words, there is no n e IN such that f(n) = A. qed

as you yourself admitted above - quoting Bertrand Russell:
"mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true."

so it's just a piece of nice intellectual play - containing logical errors

Your "proof" in no way affects the indisputable fact that every infinite set must have the following structure:
eα -> en(eα) -> en( en(eα)) -> en( en( en(eα))) -> … -> ∞
First element -> Successor -> Successor of the Successor -> Successor of the Successor of the Successor -> ...

As a result, all infinite sets should be viewed as quantitatively equal, and the elements of any two infinite sets obviously form a bijection.
NO EXCEPTIONS

(exceptions "can appear" only as a result of errors - as it is in your "proof")

Adam Polak wrote :
> czwartek, 7 grudnia 2023 o 10:06:29 UTC+1 Fritz Feldhase napisał(a):
>> On Thursday, December 7, 2023 at 9:23:44 AM UTC+1, FromTheRafters wrote:
>>> Adam Polak brought next idea :
>>>> wtorek, 5 grudnia 2023 o 14:58:01 UTC+1 Fritz Feldhase napisał(a):
>>>>> On Tuesday, December 5, 2023 at 11:09:24 AM UTC+1, Adam Polak wrote:
>>>>>
>>>>>> [What we may conclude] from the [existence of a] bijection is [...] that
>>>>>> a[n] infinite set is "equinumerous" with another infinite set, meaning
>>>>>> that they "contain"/should be seen as containing the same "number" of
>>>>>> elements.
>>>>>
>>>>> Exactly [at least in the context of set theory]. (->power, cardinal
>>>>> numbers)
>>>>>
>>>>> Now you claim:
>>>>>
>>>>>> A bijection between [...] two infinite sets [exists] in every case
>>>>>
>>>>> Nope. This is (provably) not the case. For example, there's no bijection
>>>>> between IN and the power set of IN, P(IN) = {M : M c IN}. Try to define
>>>>> one! :-)
>>>>
>>>> That is not the smallest problem.
>>>>
>>>> ALL infinite sets, absolutely without exception, are described by the
>>>> following model: eα -> en(eα) -> en( en(eα)) -> en( en( en(eα))) -> …
>>>> -> ∞ First element -> Successor -> Successor of the
>>>> Successor -> Successor of the Successor of the Successor -> ...
>>>>
>>>> As a result, the bijection between any two infinite sets is obvious and is
>>>> an immanent necessity.
>>>>
>>>> If this is not clear enough, understanduble for you, graphics would be
>>>> needed to further translate. This forum does not support them. I hope to
>>>> prepare an appropriate presentation and publish it soon.
>>>>
>>> What is the third real number?
>> Hint: Even Chuck Norris couldn't count _all_real numbers.
>
> No human being can count ALL the elements of any infinite set.
> Count ALL the elements of an infinite set = find the "last" element in the
> infinite set, an element without a successor - and such an element, by
> definition, does not appear in any infinite set.

Your wonky definition doesn't work. The empty set has no last element
and yet is finite.

> Don't bother with real numbers unless you understand natural numbers.
> Calling any of infinite sets countable is absurd.
> Just look at the simplest case: An infinite set of natural numbers.
> Based on what do you say that you are able to count its elements?
> N { 1, 2, 3, 4, 5, 6, 7, ... }
> is quantitativeli equivalent to 2N { 2, 4, 6, 8, 10, ...} "containing" every
> second element of N. N is also quantitativeli equivalent to { 1, -1, 2, -2,
> 3, -3, 4, -4, ... } containing twice as many elements as N

Cranksign!

> How many elements does N have?

Countably infinitely many.

> N or maybe 2N or maybe N/2?
> You can counting but NEVER counddown ALL elements of N, exactly the same as
> in regard of any other infinite set.

It is that counability that is addressed, not the ability to finish
counting one-by-one.

Adam Polak wrote on 12/7/2023 :
> czwartek, 7 grudnia 2023 o 09:23:44 UTC+1 FromTheRafters napisał(a):
>> Adam Polak brought next idea :
>>> wtorek, 5 grudnia 2023 o 14:58:01 UTC+1 Fritz Feldhase napisał(a):
>>>> On Tuesday, December 5, 2023 at 11:09:24 AM UTC+1, Adam Polak wrote:
>>>>
>>>>> [What we may conclude] from the [existence of a] bijection is [...] that
>>>>> a[n] infinite set is "equinumerous" with another infinite set, meaning
>>>>> that they "contain"/should be seen as containing the same "number" of
>>>>> elements.
>>>>
>>>> Exactly [at least in the context of set theory]. (->power, cardinal
>>>> numbers)
>>>>
>>>> Now you claim:
>>>>
>>>>> A bijection between [...] two infinite sets [exists] in every case
>>>>
>>>> Nope. This is (provably) not the case. For example, there's no bijection
>>>> between IN and the power set of IN, P(IN) = {M : M c IN}. Try to define
>>>> one! :-)
>>>
>>> That is not the smallest problem.
>>>
>>> ALL infinite sets, absolutely without exception, are described by the
>>> following model: eα -> en(eα) -> en( en(eα)) -> en( en( en(eα))) -> …
>>> -> ∞ First element -> Successor -> Successor of the
>>> Successor -> Successor of the Successor of the Successor -> ...
>>>
>>> As a result, the bijection between any two infinite sets is obvious and is
>>> an immanent necessity.
>>>
>>> If this is not clear enough, understanduble for you, graphics would be
>>> needed to further translate. This forum does not support them. I hope to
>>> prepare an appropriate presentation and publish it soon.
>> What is the third real number?
>
> If you want to understand what an infinite set don't bother with real numbers
> unless you understand natural numbers. "What is the third real number?"
> tell me what is the first and what is the second, and you will get the answer
> yourself

So, no answer then?

czwartek, 7 grudnia 2023 o 12:16:18 UTC+1 Fritz Feldhase napisał(a):
> On Thursday, December 7, 2023 at 12:12:42 PM UTC+1, Adam Polak wrote <bla>
>
> Fuck off, you silly asshole full of shit.
>
> Please see a good psychiatrist, soon!
>
> EOD

:))

czwartek, 7 grudnia 2023 o 13:32:14 UTC+1 FromTheRafters napisał(a):
> Adam Polak wrote :
> > czwartek, 7 grudnia 2023 o 10:06:29 UTC+1 Fritz Feldhase napisał(a):
> >> On Thursday, December 7, 2023 at 9:23:44 AM UTC+1, FromTheRafters wrote:
> >>> Adam Polak brought next idea :
> >>>> wtorek, 5 grudnia 2023 o 14:58:01 UTC+1 Fritz Feldhase napisał(a):
> >>>>> On Tuesday, December 5, 2023 at 11:09:24 AM UTC+1, Adam Polak wrote:
> >>>>>
> >>>>>> [What we may conclude] from the [existence of a] bijection is [...] that
> >>>>>> a[n] infinite set is "equinumerous" with another infinite set, meaning
> >>>>>> that they "contain"/should be seen as containing the same "number" of
> >>>>>> elements.
> >>>>>
> >>>>> Exactly [at least in the context of set theory]. (->power, cardinal
> >>>>> numbers)
> >>>>>
> >>>>> Now you claim:
> >>>>>
> >>>>>> A bijection between [...] two infinite sets [exists] in every case
> >>>>>
> >>>>> Nope. This is (provably) not the case. For example, there's no bijection
> >>>>> between IN and the power set of IN, P(IN) = {M : M c IN}. Try to define
> >>>>> one! :-)
> >>>>
> >>>> That is not the smallest problem.
> >>>>
> >>>> ALL infinite sets, absolutely without exception, are described by the
> >>>> following model: eα -> en(eα) -> en( en(eα)) -> en( en( en(eα))) -> …
> >>>> -> ∞ First element -> Successor -> Successor of the
> >>>> Successor -> Successor of the Successor of the Successor -> ...
> >>>>
> >>>> As a result, the bijection between any two infinite sets is obvious and is
> >>>> an immanent necessity.
> >>>>
> >>>> If this is not clear enough, understanduble for you, graphics would be
> >>>> needed to further translate. This forum does not support them. I hope to
> >>>> prepare an appropriate presentation and publish it soon.
> >>>>
> >>> What is the third real number?
> >> Hint: Even Chuck Norris couldn't count _all_real numbers.
> >
> > No human being can count ALL the elements of any infinite set.
> > Count ALL the elements of an infinite set = find the "last" element in the
> > infinite set, an element without a successor - and such an element, by
> > definition, does not appear in any infinite set.
> Your wonky definition doesn't work. The empty set has no last element
> and yet is finite.
> > Don't bother with real numbers unless you understand natural numbers.
> > Calling any of infinite sets countable is absurd.
> > Just look at the simplest case: An infinite set of natural numbers.
> > Based on what do you say that you are able to count its elements?
> > N { 1, 2, 3, 4, 5, 6, 7, ... }
> > is quantitativeli equivalent to 2N { 2, 4, 6, 8, 10, ...} "containing" every
> > second element of N. N is also quantitativeli equivalent to { 1, -1, 2, -2,
> > 3, -3, 4, -4, ... } containing twice as many elements as N
> Cranksign!
> > How many elements does N have?
> Countably infinitely many.
> > N or maybe 2N or maybe N/2?
> > You can counting but NEVER counddown ALL elements of N, exactly the same as
> > in regard of any other infinite set.
> It is that counability that is addressed, not the ability to finish
> counting one-by-one.

I'm sorry, but it is simply not possible to have a serious conversation this way.
If you believe/say: the "empty set" exists,
you cannot denie that in the same way also a tooth fairy exists, forest gnomes exists, etc.
And while I would be inclined to agree that in some sense:
"empty set", tooth fairy, forest gnomes "exist"
I cannot agree in any to call it a SCIENCE,
because it has nothing to do with rationality, the so-called physical reality, nor even the so-called reality of ideas in the scientific sense.
The "empty set" and the tooth fairy are pure fantasy, that's all.