On Wednesday, November 8, 2023 at 12:36:05 AM UTC+1, Fritz Feldhase wrote:
> On Wednesday, November 8, 2023 at 12:30:35 AM UTC+1, Chris M. Thomasson wrote:
> >
> > I was trying to build up to a case of an n-ary tree with 2-ary as an example: [...]
> >
> N/p. Seems that you have a typical programmer's view concerning mathematics. :-P

Btw. I'd recommend the folling book to you - you might like it very much:

Graham, Knuth, Patashnik: Concrete Mathematics: A Foundation for Computer Science

"Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems." The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories. Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study."

The bright guy you are, you might take advantage of it.

On Tuesday, November 7, 2023 at 3:44:07 PM UTC-8, Fritz Feldhase wrote:
> On Wednesday, November 8, 2023 at 12:36:05 AM UTC+1, Fritz Feldhase wrote:
> > On Wednesday, November 8, 2023 at 12:30:35 AM UTC+1, Chris M. Thomasson wrote:
> > >
> > > I was trying to build up to a case of an n-ary tree with 2-ary as an example: [...]
> > >
> > N/p. Seems that you have a typical programmer's view concerning mathematics. :-P
> Btw. I'd recommend the folling book to you - you might like it very much:
>
> Graham, Knuth, Patashnik: Concrete Mathematics: A Foundation for Computer Science
>
> "Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems." The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories. Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study."
>
> The bright guy you are, you might take advantage of it.

It was dead at its beginning. What is a set with nothing in it?
What can math make out of it?

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?

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.

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 :-)

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?"

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.

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.
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„.

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.

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.
"

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

wtorek, 7 listopada 2023 o 13:21:22 UTC+1 Ben Bacarisse napisał(a):
> Adam Polak <mt69...@gmail.com> writes:
>
> > Honestly, I have very little time for issues other than those related
> > to the substantive content,
> I doubt that. I expect you have lots of spare time. And don't fuss
> about not answering my question. I'm sure you post here for the same
> reasons everyone else who has "refuted Cantor" posts here.
> > Do you want to help? to be the manager of such a publication?
> Gosh, why would I do that? As soon as you clarify your refutation,
> someone else will publish it to get the credit. And if it's one of the
> other cranks, they will say you copied the points they made decades ago
> if you try to claim credit!
>
> More likely, you won't address the points put to you (you haven't so
> far) but you will have fun chatting about it. Enjoy.
>
> --
> Ben.

Ben, Thank you for this answer.
Coincidentally, it well illustrates the problem with Set Theory aspiring to be a correct description of REALITY in terms of the relationship between infinite sets and their elements.
In fact, it is just an unsubstantiated and erroneous DREAM on the subject.
Exactly like your dream/imagination of what it's like i "real" with my free time, etc.

Regards, Adam

On Wednesday, November 8, 2023 at 1:11:37 PM UTC+1, Adam Polak wrote:

> the problem with Set Theory aspiring to be a correct description of REALITY in terms of <bla>

<Holy shit!>

The aim of set theory certainly isn't "to be a correct description of REALITY" whatsoever, knucklehead.

On Wednesday, November 8, 2023 at 1:03:25 PM UTC+1, Adam Polak wrote:

> Set theory, in its various formulations, avoids presenting a single coherent definition of the concept of a SET.

Indeed! So what?

> [allowing] for [an empty] set makes it extremely difficult, if not impossible, to maintain the illusion that set theory explains the phenomenon of creating "something out of nothing'.

Huh?! Who told you that "set theory [tries to] explain[.] the phenomenon of creating 'something out of nothing'"?!

That's just nonsense.

Hint: It doesn't.

> by axiom[s], set theory [allows for] a[n] empty set containing no elements

Indeed! So what?

There's no written or unwritten law that forbids that.

> 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,

The latter is the "appropriate interpretation". Hint: A set just containing one element is not identical with this element: {a} =/= a. Moreover, the former would certainly not allow for an empty set (I'd say). Please do not mix up mereology with set theory.

> there can be no talk of any creatio ex nihilo in any case.

Again, no one is claiming that (except you, it seems).

(Sure, some physicist may have come up with such a phrase. I already told you to forget about physicists in the present context.)

On Wednesday, November 8, 2023 at 2:09:15 PM UTC+1, Fritz Feldhase wrote:

> Again, no one is claiming that (except you, it seems).
>
> (Sure, some physicist may have come up with such a phrase. I already told you to forget about physicists in the present context.)

Hint: Mückenheim is a physicist.

So it isn't a particularly good idea to base ones views on the nonsense he wrote concerning "set theory".

On Monday, November 6, 2023 at 7:15:55 AM UTC-5, Adam Polak wrote:
> poniedziałek, 6 listopada 2023 o 12:47:47 UTC+1 Ben Bacarisse napisał(a):
> > Adam Polak <mt69...@gmail.com> writes:
> >
> > > The Set Theory [...] Cantor [...] flawed theory [...] filled with
> > > errors [...]
> >
> > > https://www.youtube.com/watch?v=s23Cz8A0BKs
> >
> > That well-known Journal, YouTube!
> >
> > So rather than publish a paper and gain the respect of mathematicians
> > round the world, you choose to post on YouTube and in this (other)
> > crank-filled corner of the Internet. If you are wrong, doing so is just
> > a wast of time, but if you right it monumentally stupid to post in the
> > only paces where the default assumption will be that you are a lunatic.
> >
> > --
> > Ben.
> Ben, I know what you mean.
> Note however, that from what you write it follows that:
> TRUTH is what is published in a "well-known scientific journal" and if the same statement is published on YouTube, it is not TRUTH but is probably stupid.
> As a result, it doesn't matter WHAT someone states,
> what matters is WHO states it, and WHERE it is stayed.
> The heart of the matter (the topic, the statement) is pushed to the margins.
> Isn't this approach completely unscientific and even unwise?
>
> Try to read and refute at least one element of what I write.
> I assure you that you won't be able to.
>
> If you refute one element, I will tell you why I am not writing to "well-known scientific journal"
>
> Regards,
> Adam

Um, I find an integrity conflict back at set and function as two fundamental concepts. When your set can be defined with a function, and your function requires a set, then a transgression has been committed. This is a compiler level error, and Cantor may have been one of the compilers, but so was Peano with his successor function.
You can certainly shrug this off as a human, and the anthropic principle will live within our systems forever. For some of us this condition is unacceptable. Simplicity was to be found another way, and computing hardware as a limited yet operable system exposes the chase, and perhaps the product and division really best pose the puzzle. In finality could it be that the product is taken, and only then? Well, says you: "I don't mind taking sums of products, nor products of sums." And yet whether the product is itself is a grandiose sum has been left adrift. Then too, the integral, and the sigma notation, so often entering the laws that we recover. Don't mathematicians regard their trade as being ultimately at the bottom of it all?

On Monday, November 6, 2023 at 4:09:22 PM UTC-5, Adam Polak wrote:
> FINITE
> A set S is finite when there exists an n ϵ N such that S has exactly n elements.
>
> INFINITE
> Consequently:
> A set S is infinite when there does not exist an n ϵ N such that S has exactly n elements.

It is really modulo behaved elements that satisfy here. All others give me the creeps.

>
> From the above, it follows that:
> Infinity is not a number, particularly not a natural number. It is not the number of elements in an infinite set, nor is it the largest or last element in an infinite set, e.g. such as the infinite set of natural numbers N.
> poniedziałek, 6 listopada 2023 o 17:37:41 UTC+1 Dan Christensen napisał(a):
> > On Monday, November 6, 2023 at 6:01:03 AM UTC-5, Adam Polak wrote:
> > [snip]
> > > 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.
> > >
> > Hilbert's Infinite Hotel should not be taken too literally. It is simply a humorous illustration that an infinite set like the set of natural numbers N = {1, 2, 3, ... } can be mapped bijectively to a proper subset of itself, namely {2, 3, 4, ... }. This property is the defining characteristic othenf ANY infinite set. In this case, the required bijection is f: N --> {2, 3, 4, ... } such that f(x)=x+1.
> >
> > For a somewhat less mind-blowing development, you might consider my alternative approach. I start by defining what we mean by a finite set. Then an infinite set is just one that is not finite.
> >
> > See my blog posting at https://dcproof.wordpress.com/2014/09/17/infinity-the-story-so-far/
> >
> > There, I present informal and formal set-theoretic developments of a non-numeric definition of a finite set. Refute it if you think you can.,
> >
> > Dan
> >
> > Download my DC Proof 2.0 freeware at http://www.dcproof.com
> > Visit my Math Blog at http://www.dcproof.wordpress.com

On Wednesday, November 8, 2023 at 6:55:13 AM UTC-8, Timothy Golden wrote:
> On Monday, November 6, 2023 at 4:09:22 PM UTC-5, Adam Polak wrote:
> > FINITE
> > A set S is finite when there exists an n ϵ N such that S has exactly n elements.
> >
> > INFINITE
> > Consequently:
> > A set S is infinite when there does not exist an n ϵ N such that S has exactly n elements.
> It is really modulo behaved elements that satisfy here. All others give me the creeps.
> >
> > From the above, it follows that:
> > Infinity is not a number, particularly not a natural number. It is not the number of elements in an infinite set, nor is it the largest or last element in an infinite set, e.g. such as the infinite set of natural numbers N.
> > poniedziałek, 6 listopada 2023 o 17:37:41 UTC+1 Dan Christensen napisał(a):
> > > On Monday, November 6, 2023 at 6:01:03 AM UTC-5, Adam Polak wrote:
> > > [snip]
> > > > 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.
> > > >
> > > Hilbert's Infinite Hotel should not be taken too literally. It is simply a humorous illustration that an infinite set like the set of natural numbers N = {1, 2, 3, ... } can be mapped bijectively to a proper subset of itself, namely {2, 3, 4, ... }. This property is the defining characteristic othenf ANY infinite set. In this case, the required bijection is f: N --> {2, 3, 4, ... } such that f(x)=x+1.
> > >
> > > For a somewhat less mind-blowing development, you might consider my alternative approach. I start by defining what we mean by a finite set. Then an infinite set is just one that is not finite.
> > >
> > > See my blog posting at https://dcproof.wordpress.com/2014/09/17/infinity-the-story-so-far/
> > >
> > > There, I present informal and formal set-theoretic developments of a non-numeric definition of a finite set. Refute it if you think you can.,
> > >
> > > Dan
> > >
> > > Download my DC Proof 2.0 freeware at http://www.dcproof.com
> > > Visit my Math Blog at http://www.dcproof.wordpress.com

Hmm, "SET THEORY, is dead", I like it, Adam.

It's fair of you to say "here's a theory where I've axiomatized away my model of
a trust in set theory, I must make myself another way to trust", the set theory,
then you constructively bring up what you want, while then pointing out a
crankish argument in set theory, that shows something you've hobbled yourself, from.

Powers of 2?

What you get is ordering, numbering, and counting, and when numbering invoves counting.

Set theory models these sufficiently all their "regular" way, "well-founded", for example,
the regular set theory.

You can make inconsistent models of set theory and show how they're inconsistent.
It's not considered constructivist, say, insofar as formal rigor and "can't not trust it".

So, you want to square away your Aleph numbers, cardinals, and the Omega-many ordinals.
The Aleph, is the counting infinity, while the Omega, is moreso the numbering infinity
and the ordering infinity, in ordinals.

The counting infinities the Aleph numbers, their arithmetic builds the orders of the spaces,
above each constructive, regular, ordinary, ..., theory of words like sets, here elementary
objects.

That's one reason why cardinals and ordinals are different, different infinities.

Anyways usually insofar as any mistake you write here someone will point it out to you.

Anyways what results I enjoyed this for some time, currently looking at my own slates,
I sort of organize analysis in continuum mechanics.

"Infinitely-many", ....

So, what you want to do, I think to really get an understanding of the cardinal and ordinal
numbers, and, the cardinal and ordinal infinities, is give yourself axioms for example "inverse",
but for example "counting" or whatever other results "infinity" axioms, then figuring out
where their sameness and differences, do or strongly do or don't or strongly don't, hold,
what do.

"It's a continuum mechanics, ...", just saying, Adam, that if you're looking for a theory that
really digs up set theory, I made one with both cardinals and ordinals and their infinities
what otherwise sometimes aren't "extra" enough to be real.

I've even gone so far as to stand up letting a simplest mathematical infinity, back into
the philosophy, of the theory, the one that science is missing.

So, when I suggest, "Powers of 2?", I suggest that you're thoroughly familiar with them,
all the powers of 2, then for the two infinities you call "w", omega, and "2^w", 2 to the omega,
which as a number, is an ordinal, but also results when writing ordinals regular-ly, is the
space "2^w", each of the infinite sequences of zeros and ones, with a beginning.

It's set theory, ....

On Wednesday, November 8, 2023 at 11:55:47 AM UTC-5, Ross Finlayson wrote:
> On Wednesday, November 8, 2023 at 6:55:13 AM UTC-8, Timothy Golden wrote:
> > On Monday, November 6, 2023 at 4:09:22 PM UTC-5, Adam Polak wrote:
> > > FINITE
> > > A set S is finite when there exists an n ϵ N such that S has exactly n elements.
> > >
> > > INFINITE
> > > Consequently:
> > > A set S is infinite when there does not exist an n ϵ N such that S has exactly n elements.
> > It is really modulo behaved elements that satisfy here. All others give me the creeps.
> > >
> > > From the above, it follows that:
> > > Infinity is not a number, particularly not a natural number. It is not the number of elements in an infinite set, nor is it the largest or last element in an infinite set, e.g. such as the infinite set of natural numbers N.
> > > poniedziałek, 6 listopada 2023 o 17:37:41 UTC+1 Dan Christensen napisał(a):
> > > > On Monday, November 6, 2023 at 6:01:03 AM UTC-5, Adam Polak wrote:
> > > > [snip]
> > > > > 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.
> > > > >
> > > > Hilbert's Infinite Hotel should not be taken too literally. It is simply a humorous illustration that an infinite set like the set of natural numbers N = {1, 2, 3, ... } can be mapped bijectively to a proper subset of itself, namely {2, 3, 4, ... }. This property is the defining characteristic othenf ANY infinite set. In this case, the required bijection is f: N --> {2, 3, 4, ... } such that f(x)=x+1.
> > > >
> > > > For a somewhat less mind-blowing development, you might consider my alternative approach. I start by defining what we mean by a finite set. Then an infinite set is just one that is not finite.
> > > >
> > > > See my blog posting at https://dcproof.wordpress.com/2014/09/17/infinity-the-story-so-far/
> > > >
> > > > There, I present informal and formal set-theoretic developments of a non-numeric definition of a finite set. Refute it if you think you can.,
> > > >
> > > > Dan
> > > >
> > > > Download my DC Proof 2.0 freeware at http://www.dcproof.com
> > > > Visit my Math Blog at http://www.dcproof.wordpress.com
> Hmm, "SET THEORY, is dead", I like it, Adam.
>
> It's fair of you to say "here's a theory where I've axiomatized away my model of
> a trust in set theory, I must make myself another way to trust", the set theory,
> then you constructively bring up what you want, while then pointing out a
> crankish argument in set theory, that shows something you've hobbled yourself, from.
>
> Powers of 2?
>
> What you get is ordering, numbering, and counting, and when numbering invoves counting.
>
> Set theory models these sufficiently all their "regular" way, "well-founded", for example,
> the regular set theory.
>
> You can make inconsistent models of set theory and show how they're inconsistent.
> It's not considered constructivist, say, insofar as formal rigor and "can't not trust it".
>
> So, you want to square away your Aleph numbers, cardinals, and the Omega-many ordinals.
> The Aleph, is the counting infinity, while the Omega, is moreso the numbering infinity
> and the ordering infinity, in ordinals.
>
> The counting infinities the Aleph numbers, their arithmetic builds the orders of the spaces,
> above each constructive, regular, ordinary, ..., theory of words like sets, here elementary
> objects.
>
> That's one reason why cardinals and ordinals are different, different infinities.
>
> Anyways usually insofar as any mistake you write here someone will point it out to you.
>
> Anyways what results I enjoyed this for some time, currently looking at my own slates,
> I sort of organize analysis in continuum mechanics.
>
> "Infinitely-many", ....
>
> So, what you want to do, I think to really get an understanding of the cardinal and ordinal
> numbers, and, the cardinal and ordinal infinities, is give yourself axioms for example "inverse",
> but for example "counting" or whatever other results "infinity" axioms, then figuring out
> where their sameness and differences, do or strongly do or don't or strongly don't, hold,
> what do.
>
> "It's a continuum mechanics, ...", just saying, Adam, that if you're looking for a theory that
> really digs up set theory, I made one with both cardinals and ordinals and their infinities
> what otherwise sometimes aren't "extra" enough to be real.
>
> I've even gone so far as to stand up letting a simplest mathematical infinity, back into
> the philosophy, of the theory, the one that science is missing.
>
> So, when I suggest, "Powers of 2?", I suggest that you're thoroughly familiar with them,
> all the powers of 2, then for the two infinities you call "w", omega, and "2^w", 2 to the omega,
> which as a number, is an ordinal, but also results when writing ordinals regular-ly, is the
> space "2^w", each of the infinite sequences of zeros and ones, with a beginning.
>
> It's set theory, ....

Did you ever consider whether the top down form could apply rather than the bottom up approach that mathematics seems to formalize?
Some will insist that this top is infinity somehow, but according to cosmology as I understand it they may be claiming a true finite albeit very large value. To what degree then we work down from this large thing which is essentially unknown to us other than to suppose it, possibly even with peculiarities built into its own actual factors, for instance, dealing symmetries and so forth, and what, so three is one of its factors? Is that it, Ross? Isn't there a one in three chance that this would occur?
And whether odd or even: you pick which by what means? Hmmm.... I think our reality is quite odd.

"This is a compiler level error, and Cantor may have been one of the compilers, but so was Peano with his successor function."

with the difference that Cantor made a mistake and Peano not (not in the definition of natural numbers at least)

"You can certainly shrug this off as a human, and the anthropic principle will live within our systems forever. For some of us this condition is unacceptable."

In a way I agree. (not only WHAT, but also who, when, why, for what purpose, etc... states labeling it as a "scientific statement")

środa, 8 listopada 2023 o 15:52:49 UTC+1 Timothy Golden napisał(a):
> On Monday, November 6, 2023 at 7:15:55 AM UTC-5, Adam Polak wrote:
> > poniedziałek, 6 listopada 2023 o 12:47:47 UTC+1 Ben Bacarisse napisał(a):
> > > Adam Polak <mt69...@gmail.com> writes:
> > >
> > > > The Set Theory [...] Cantor [...] flawed theory [...] filled with
> > > > errors [...]
> > >
> > > > https://www.youtube.com/watch?v=s23Cz8A0BKs
> > >
> > > That well-known Journal, YouTube!
> > >
> > > So rather than publish a paper and gain the respect of mathematicians
> > > round the world, you choose to post on YouTube and in this (other)
> > > crank-filled corner of the Internet. If you are wrong, doing so is just
> > > a wast of time, but if you right it monumentally stupid to post in the
> > > only paces where the default assumption will be that you are a lunatic.
> > >
> > > --
> > > Ben.
> > Ben, I know what you mean.
> > Note however, that from what you write it follows that:
> > TRUTH is what is published in a "well-known scientific journal" and if the same statement is published on YouTube, it is not TRUTH but is probably stupid.
> > As a result, it doesn't matter WHAT someone states,
> > what matters is WHO states it, and WHERE it is stayed.
> > The heart of the matter (the topic, the statement) is pushed to the margins.
> > Isn't this approach completely unscientific and even unwise?
> >
> > Try to read and refute at least one element of what I write.
> > I assure you that you won't be able to.
> >
> > If you refute one element, I will tell you why I am not writing to "well-known scientific journal"
> >
> > Regards,
> > Adam
>
> Um, I find an integrity conflict back at set and function as two fundamental concepts. When your set can be defined with a function, and your function requires a set, then a transgression has been committed. This is a compiler level error, and Cantor may have been one of the compilers, but so was Peano with his successor function.
> You can certainly shrug this off as a human, and the anthropic principle will live within our systems forever. For some of us this condition is unacceptable. Simplicity was to be found another way, and computing hardware as a limited yet operable system exposes the chase, and perhaps the product and division really best pose the puzzle. In finality could it be that the product is taken, and only then? Well, says you: "I don't mind taking sums of products, nor products of sums." And yet whether the product is itself is a grandiose sum has been left adrift. Then too, the integral, and the sigma notation, so often entering the laws that we recover. Don't mathematicians regard their trade as being ultimately at the bottom of it all?

Adam Polak wrote:
> [not even original nonsense]

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

Don't worry, there a lot of cranks of your kind down here, we won't
miss you.

Adam Polak expressed precisely :
> wtorek, 7 listopada 2023 o 13:21:22 UTC+1 Ben Bacarisse napisał(a):
>> Adam Polak <mt69...@gmail.com> writes:
>>
>>> Honestly, I have very little time for issues other than those related
>>> to the substantive content,
>> I doubt that. I expect you have lots of spare time. And don't fuss
>> about not answering my question. I'm sure you post here for the same
>> reasons everyone else who has "refuted Cantor" posts here.
>>> Do you want to help? to be the manager of such a publication?
>> Gosh, why would I do that? As soon as you clarify your refutation,
>> someone else will publish it to get the credit. And if it's one of the
>> other cranks, they will say you copied the points they made decades ago
>> if you try to claim credit!
>>
>> More likely, you won't address the points put to you (you haven't so
>> far) but you will have fun chatting about it. Enjoy.
>>
>> --
>> Ben.
>
> Ben, Thank you for this answer.
> Coincidentally, it well illustrates the problem with Set Theory aspiring to
> be a correct description of REALITY in terms of the relationship between
> infinite sets and their elements. In fact, it is just an unsubstantiated and
> erroneous DREAM on the subject. Exactly like your dream/imagination of what
> it's like i "real" with my free time, etc.
>
> Regards, Adam

Status confirmed.

FromTheRafters <FTR@nomail.afraid.org> writes:
> 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?"

That wound you up so much you went to the local cafe, and asked for
a strong coffee - no milk. The cafe owner replied "sorry, we're out
of milk, but I can make you one with no cream".

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 11/9/2023 4:55 PM, Phil Carmody wrote:
> FromTheRafters <FTR@nomail.afraid.org> writes:
>> 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?"

Fractalize it, Say, an empty box with smaller empty boxes in them. What
boxes are empty?

>
> That wound you up so much you went to the local cafe, and asked for
> a strong coffee - no milk. The cafe owner replied "sorry, we're out
> of milk, but I can make you one with no cream".

LOL!

On Friday, November 10, 2023 at 2:18:00 AM UTC+1, Chris M. Thomasson wrote:
> On 11/9/2023 4:55 PM, Phil Carmody wrote:
> >
> > That wound you up so much you went to the local cafe, and asked for
> > a strong coffee - no milk. The cafe owner replied "sorry, we're out
> > of milk, but I can make you one with no cream".
> >
> LOL!

No joke, in Russellian Type Theory each type has its own "empty set".

On Thursday, November 9, 2023 at 4:27:52 AM UTC+1, Python wrote:
> Adam Polak wrote:
> >
> > I have many tasks and limited time, so I may not visit and reply here often
> >
> Don't worry, there a lot of cranks of your kind down here, we won't miss you.

Ironically, the only reference this buffoon mentions is WM's cranky nonsense manuscript:

| Interesting sources and documents related to Set Theory:
| | "Transfinity - A Source Book" by Wolfgang Mückenheim
| https://www.hs-augsburg.de/~mueckenh/...

On Thursday, November 9, 2023 at 4:27:53 AM UTC+1, FromTheRafters wrote:
> Adam Polak expressed precisely :
> >
> > Ben, Thank you for this answer.
> > Coincidentally, it well illustrates the problem with Set Theory aspiring to
> > be a correct description of REALITY in terms of the relationship between
> > infinite sets and their elements. In fact, it is just an unsubstantiated and
> > erroneous DREAM on the subject. Exactly like your dream/imagination of what
> > it's like i "real" with my free time, etc.
> >
> > Regards, Adam
> >
> Status confirmed.

Yeah, a genius!

Thank you for your comment Ross. Very interesting.
e.g.:
"So, you want to square away your Aleph numbers, cardinals, and the Omega-many ordinals.
The Aleph, is the counting infinity, while the Omega, is moreso the numbering infinity and the ordering infinity, in ordinals.
The counting infinities the Aleph numbers, their arithmetic builds the orders of the spaces, above each constructive, regular, ordinary, ..., theory of words like sets, here elementary objects.
That's one reason why cardinals and ordinals are different, different infinities."
"I sort of organize analysis in continuum mechanics."

I'll start from the end. I can assure you, Ross, and provide numerous independent, but logically related pieces of evidence that everything what quantitatively is represented by any infinite set, including: Alephs, cardinals, and Omegas, fits in, "happens" within the quantity represented by the infinite set of natural numbers.

The theory of infinite sets by Cantor, aspires to be a correct description of the reality in the realm of infinite sets, the relationships between infinite sets, and their elements. In reality, however, it is simply a FALLACIOUS description. It is a dream of grandeur dreamt by the mind, or perhaps the ego of Cantor (initially), and now by the minds/egos of the overwhelming majority of the scientific community. It is a beautiful dream in which a finite human comprehends infinity, e.g. infinity of natural numbers, and probably due to its beauty, it has been so infectious and widely spread. In the end, it is, unfortunately, only a waking dream with very little in common with reality, especially in terms of the true nature of infinity.

From the history of science, we know many sometimes very spectacular cases when "great" theories, accepted by "everyone," turned out to be greatly flawed or at least imperfect at some point. The same is about to happen soon with Cantor's Set Theory. I'm looking for a volunteer, preferably someone who is a "expert" in set theory professionally, someone who professionally deals with it, BUT! who allows for even the slightest possibility that there might be something wrong with set theory, just like with anything created by humans. (a person without this "BUT" will not wake up, he is simply fanatically attached to the illusion he is stuck in)

I will undertake to guide such a person through detox and awaken from the dream of cardinalities greater than N, to the reality, which I assure is no less, but more intriguing..

BR, Adam

środa, 8 listopada 2023 o 17:55:47 UTC+1 Ross Finlayson napisał(a):
> On Wednesday, November 8, 2023 at 6:55:13 AM UTC-8, Timothy Golden wrote:
> > On Monday, November 6, 2023 at 4:09:22 PM UTC-5, Adam Polak wrote:
> > > FINITE
> > > A set S is finite when there exists an n ϵ N such that S has exactly n elements.
> > >
> > > INFINITE
> > > Consequently:
> > > A set S is infinite when there does not exist an n ϵ N such that S has exactly n elements.
> > It is really modulo behaved elements that satisfy here. All others give me the creeps.
> > >
> > > From the above, it follows that:
> > > Infinity is not a number, particularly not a natural number. It is not the number of elements in an infinite set, nor is it the largest or last element in an infinite set, e.g. such as the infinite set of natural numbers N.
> > > poniedziałek, 6 listopada 2023 o 17:37:41 UTC+1 Dan Christensen napisał(a):
> > > > On Monday, November 6, 2023 at 6:01:03 AM UTC-5, Adam Polak wrote:
> > > > [snip]
> > > > > 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.
> > > > >
> > > > Hilbert's Infinite Hotel should not be taken too literally. It is simply a humorous illustration that an infinite set like the set of natural numbers N = {1, 2, 3, ... } can be mapped bijectively to a proper subset of itself, namely {2, 3, 4, ... }. This property is the defining characteristic othenf ANY infinite set. In this case, the required bijection is f: N --> {2, 3, 4, ... } such that f(x)=x+1.
> > > >
> > > > For a somewhat less mind-blowing development, you might consider my alternative approach. I start by defining what we mean by a finite set. Then an infinite set is just one that is not finite.
> > > >
> > > > See my blog posting at https://dcproof.wordpress.com/2014/09/17/infinity-the-story-so-far/
> > > >
> > > > There, I present informal and formal set-theoretic developments of a non-numeric definition of a finite set. Refute it if you think you can.,
> > > >
> > > > Dan
> > > >
> > > > Download my DC Proof 2.0 freeware at http://www.dcproof.com
> > > > Visit my Math Blog at http://www.dcproof.wordpress.com
> Hmm, "SET THEORY, is dead", I like it, Adam.
>
> It's fair of you to say "here's a theory where I've axiomatized away my model of
> a trust in set theory, I must make myself another way to trust", the set theory,
> then you constructively bring up what you want, while then pointing out a
> crankish argument in set theory, that shows something you've hobbled yourself, from.
>
> Powers of 2?
>
> What you get is ordering, numbering, and counting, and when numbering invoves counting.
>
> Set theory models these sufficiently all their "regular" way, "well-founded", for example,
> the regular set theory.
>
> You can make inconsistent models of set theory and show how they're inconsistent.
> It's not considered constructivist, say, insofar as formal rigor and "can't not trust it".
>
> So, you want to square away your Aleph numbers, cardinals, and the Omega-many ordinals.
> The Aleph, is the counting infinity, while the Omega, is moreso the numbering infinity
> and the ordering infinity, in ordinals.
>
> The counting infinities the Aleph numbers, their arithmetic builds the orders of the spaces,
> above each constructive, regular, ordinary, ..., theory of words like sets, here elementary
> objects.
>
> That's one reason why cardinals and ordinals are different, different infinities.
>
> Anyways usually insofar as any mistake you write here someone will point it out to you.
>
> Anyways what results I enjoyed this for some time, currently looking at my own slates,
> I sort of organize analysis in continuum mechanics.
>
> "Infinitely-many", ....
>
> So, what you want to do, I think to really get an understanding of the cardinal and ordinal
> numbers, and, the cardinal and ordinal infinities, is give yourself axioms for example "inverse",
> but for example "counting" or whatever other results "infinity" axioms, then figuring out
> where their sameness and differences, do or strongly do or don't or strongly don't, hold,
> what do.
>
> "It's a continuum mechanics, ...", just saying, Adam, that if you're looking for a theory that
> really digs up set theory, I made one with both cardinals and ordinals and their infinities
> what otherwise sometimes aren't "extra" enough to be real.
>
> I've even gone so far as to stand up letting a simplest mathematical infinity, back into
> the philosophy, of the theory, the one that science is missing.
>
> So, when I suggest, "Powers of 2?", I suggest that you're thoroughly familiar with them,
> all the powers of 2, then for the two infinities you call "w", omega, and "2^w", 2 to the omega,
> which as a number, is an ordinal, but also results when writing ordinals regular-ly, is the
> space "2^w", each of the infinite sequences of zeros and ones, with a beginning.
>
> It's set theory, ....

On Thursday, November 9, 2023 at 9:10:23 PM UTC-8, Adam Polak wrote:
>
> The theory of infinite sets by Cantor, aspires to be a correct description of the reality in the realm of infinite sets, the relationships between infinite sets, and their elements. In reality, however, it is simply a FALLACIOUS description. It is a dream of grandeur dreamt by the mind, or perhaps the ego of Cantor (initially), and now by the minds/egos of the overwhelming majority of the scientific community. It is a beautiful dream in which a finite human comprehends infinity, e.g. infinity of natural numbers, and probably due to its beauty, it has been so infectious and widely spread. In the end, it is, unfortunately, only a waking dream with very little in common with reality, especially in terms of the true nature of infinity.
>

In fact, Cantor took great pains to disassociate and distinguish the infinities both of theology and metaphysics from his mere mathematical transfinite.

<quote translated>
The actual infinite was distinguished by three relations: first, as it is realized in the supreme perfection, in the completely independent, extra worldly existence, in Deo, where I call it absolute infinite or simply absolute; second to the extent that it is represented in the dependent, creatural world; third as it can be conceived in abstracto in thought as a mathematical magnitude, number or order type. In the latter two relations, where it obviously reveals itself as limited and capable for further proliferation and hence familiar to the finite, I call it Transfinitum and strongly contrast it with the absolute.
</quote>

<quote translated>
I have never assumed a “Genus Supremum” of the actual infinite. Quite on the contrary I have proved that there can be no such “Genus Supremum” of the actual infinite. What lies beyond all that is finite and transfinite is not a “Genus”; it is the unique, completely individual unity, in which everything is, which comprises everything, the ‘Absolute’, for human intelligence unfathomable, also that not subject to mathematics, unmeasurable, the “ens simplicissimum”, the “Actus purissimus”, which is by many called “God”.
</quote>

https://en.wikipedia.org/wiki/Absolute_Infinite

https://pointatinfinityblog.wordpress.com/2017/06/12/cantor-and-the-absolute-universal-structures-iv/