Dan-O-Matiks motto for mathematics:

https://www.youtube.com/watch?v=O4irXQhgMqg
I see a red door
And I want it painted black
No colors anymore
I want them to turn black
I see the girls walk by
Dressed in their summer clothes
I have to turn my head
Until my darkness goes
I see a line of cars
And they're all painted black
With flowers and my love
Both never to come back
I've seen people turn their heads
And quickly look away
Like a newborn baby
It just happens everyday
I look inside myself
And see my heart is black
I see my red door
I must have it painted black
Maybe then, I'll fade away
And not have to face the facts
It's not easy facing up
When your whole world is black
No more will my green sea
Go turn a deeper blue
I could not foresee this thing
Happening to you
If I look hard enough
Into the setting sun
My love will laugh with me
Before the morning comes
I see a red door
And I want it painted black
No colors anymore
I want them to turn black
I see the girls walk by
Dressed in their summer clothes
I have to turn my head
Until my darkness goes
I wanna see it painted
Painted black
Black as night
Black as coal
I wanna see the sun
Blotted out from the sky
I wanna see it painted, painted, painted
Painted black, yeah

Mostowski Collapse schrieb am Montag, 15. November 2021 um 00:12:17 UTC+1:
> Are you afraid of the dark like WM? Ha Ha, for Dan-O-Matik
> mathematics and logic is the same as what for WM the
> natural numbers are. For WM the natural numbers are
>
> the identifiable natural numbers, the natural numbers he
> has seen in his lifetime, basically his hands and toes.
> Same for Dan-O-Matik, he made some Peano and other
>
> proofs with DC Proof and now he thinks he has covered
> much of mathematics.
>
> LoL
> Mostowski Collapse schrieb am Montag, 15. November 2021 um 00:08:22 UTC+1:
> > Why would you need the proof? You are awfully bad in
> > statistical induction (scientific hypothesis from data).
> >
> > You see one purple flower, and then you think all flowers
> > are purple. So your NOT PURPLE is anyway always empty.
> >
> > LMAO!
> >
> > Dan Christensen schrieb am Samstag, 30. Oktober 2021 um 23:46:23 UTC+2:
> > > I wrote the attached proof in response to a discussion at Quora. Here I show that, in set theory, there exists no set of all those things that are NOT PURPLE.

See my reply to your identical posting in sci.logic just now.
..
Dan

On Sunday, November 14, 2021 at 6:08:22 PM UTC-5, Mostowski Collapse wrote:
> Why would you need the proof? ...

Try proving proposition 2.20 (goes back to Cantor 1897):
The proposition is in Basic Set Theory, Levy.

"If <A, <> is a well ordered class and B is subclass of A, then
<B, <> is isomorphic to <A,<> or to a section of <A, <>."
https://www.amazon.de/dp/0486420795

Thats a quite interesting proposition, you can of couse also
make examples from N. Like for example the even Even numbers
are a subset of N, and <N,<> and <Even,<> are indeeded isomorphic.

Cantor was not interested in the balant infinite of N. He was
interested in the transfinite. So proving existence of N is not
very interesting, since it is not a transfinite extercise,

transfinite is every thing above N.

Dan Christensen schrieb am Montag, 15. November 2021 um 02:28:05 UTC+1:
> See my reply to your identical posting in sci.logic just now.
> .
> Dan
>
> On Sunday, November 14, 2021 at 6:08:22 PM UTC-5, Mostowski Collapse wrote:
> > Why would you need the proof? ...

I demanded a proof in ZFC, for some definition def of
omega, that we can show existence:

- EXIST(omega):Def(omega)

And not only:

- ALL(omega):[Def(omega) => Peano(omega)]

What I never asked was whether we can also show uniqueness:

- ALL(omega1):ALL(omega2):[Def(omega1) & Def(omega2) => omega1 = omega2]

It seems the axiom of foundation becomes now necessary!
And Halmos might really have botched it.

At least this take, an Agda and HoTT paper, has it that in AFA
there might be multiple omega's, which isn't good:

See Example 1 on Page 8
Non-wellfounded sets in homotopy type theory
Håkon Robbestad Gylterud, Elisabeth Bonnevier
6 Jul 2020
https://arxiv.org/abs/2001.06696

On Sunday, November 21, 2021 at 2:45:09 AM UTC+1, Mostowski Collapse wrote:

> I demanded a proof in ZFC [...]

without using the Axiom of Foundation, I guess.

> Halmos might really have botched it.

What a silly claim.

Now I have doubts that the Agda example applies. Usually
proving uniqueness is not that much an issue, if omega
is defined, in def, as a least element.

It then usually follows that omega is unique. Since there
cannot be two different least elements. The construction
usually doesn't need axiom of regularity, definining

the least element, in the form an infinite intersection
is already possible with classes, and needs only a little
axioms of ZFC. Right? But Agda does a lot of things

different from Zermelos 1908 original idea. For example they
don't use the simple definition of an inductive set:

ind(S) <=> 0 e S /\ forall x (x e S => x u {x} e S)

They rather use already the stronger definition, that all
elements have a predecessor:

ind_comp(S) <=> 0 e S /\ forall x (x e S => x u {x} e S)
/\ forall x(x e S /\ x <> 0 => exist y(y e S /\ y u {y} = x))

Usually such things are proved later, and the Zermelo 1908
axiom of infinity doesn't require it either.

Fritz Feldhase schrieb am Sonntag, 21. November 2021 um 03:23:18 UTC+1:
> On Sunday, November 21, 2021 at 2:45:09 AM UTC+1, Mostowski Collapse wrote:
>
> > I demanded a proof in ZFC [...]
>
> without using the Axiom of Foundation, I guess.
> > Halmos might really have botched it.
> What a silly claim.

Mostowski Collapse wrote:

> I demanded a proof in ZFC, for some definition def of omega, that we can
> show existence: - EXIST(omega):Def(omega) And not only:
> - ALL(omega):[Def(omega) => Peano(omega)]

intriguing. You ladies are hard to convince. It's NOT a "vaccine", but a
*genetic_synthetic_pathogen* (makes you sick). Calling it a "vaccine"
makes you stupid, and wrong.

DR DAVID MARTIN - THIS IS NOT A VACCINE - WATCH TO SEE WHAT THEY'RE GIVING
YOU https://www.bitchute.com/video/or5kdfK3mKr8/

Proof From The WHO's Own Mouth These Injections ARE NOT DOCUMENTED AS
'Vaccines' https://www.bitchute.com/video/31OxSBo3EPLb/

Mostowski Collapse wrote:

> Now I have doubts that the Agda example applies. Usually proving
> uniqueness is not that much an issue, if omega is defined, in def, as a
> least element.

sure, Members and alumni

Notable members and alumni of Young Global Leaders include:[9]

Jacinda Ardern
Lera Auerbach
Sergei Brin
Anderson Cooper
Leonardo DiCaprio
Ólafur Elíasson
Florian Henckel von Donnersmarck
Sebastian Kurz
Ashton Kutcher
Jack Ma
Emmanuel Macron
Larry Page
Michael Schumacher
Charlize Theron
Leo Tilman
Fasi Zaka
Ivanka Trump
Mark Zuckerberg
El Krebat
Sandeep P Parekh

Luigi imitates AP brain farto and posts name lists?

How original?

LMAO!

Wilm Dulin schrieb am Sonntag, 21. November 2021 um 17:54:59 UTC+1:
> Mostowski Collapse wrote:
>
> > Now I have doubts that the Agda example applies. Usually proving
> > uniqueness is not that much an issue, if omega is defined, in def, as a
> > least element.
> sure, Members and alumni
>
> Notable members and alumni of Young Global Leaders include:[9]
>
> Jacinda Ardern
> Lera Auerbach
> Sergei Brin
> Anderson Cooper
> Leonardo DiCaprio
> Ólafur Elíasson
> Florian Henckel von Donnersmarck
> Sebastian Kurz
> Ashton Kutcher
> Jack Ma
> Emmanuel Macron
> Larry Page
> Michael Schumacher
> Charlize Theron
> Leo Tilman
> Fasi Zaka
> Ivanka Trump
> Mark Zuckerberg
> El Krebat
> Sandeep P Parekh

But can you cook spaghetti assasin?

Spaghetti all'Assassina "Killa Spaghetti"
https://www.youtube.com/watch?v=3NaOZ9IzIu4&t=5s

Mostowski Collapse schrieb am Sonntag, 21. November 2021 um 18:48:28 UTC+1:
> Luigi imitates AP brain farto and posts name lists?
>
> How original?
>
> LMAO!

Mostowski Collapse wrote:

> Luigi imitates AP brain farto and posts name lists?
> How original? LMAO!

another inbreed imbecile not understanding tensors, 4D.
you don't understand shit, you stupid wannabe capitalist mazafaka.
They are killing you and your kids, you inbreed cretin. Listen at what
those men and woman hast to say. The /* capitalists_fascists */ are
doing it, they are all capitalists, not communists. You imbecile with
a mouth on your face.

KLAUS SCHWAB'S SCHOOL FOR COVID DICTATORS TRAINED TO SERVE CABAL'S ORDERS
(Pt 2) https://www.bitchute.com/video/Cgkut0hFZjGx/

>> Notable members and alumni of Young Global Leaders include:[9]
>>
>> Jacinda Ardern
>> Lera Auerbach
>> Sergei Brin
>> Anderson Cooper
>> Leonardo DiCaprio
>> Ólafur Elíasson
>> Florian Henckel von Donnersmarck
>> Sebastian Kurz
>> Ashton Kutcher
>> Jack Ma
>> Emmanuel Macron
>> Larry Page
>> Michael Schumacher
>> Charlize Theron
>> Leo Tilman
>> Fasi Zaka
>> Ivanka Trump
>> Mark Zuckerberg
>> El Krebat
>> Sandeep P Parekh

Ma que luigi!

eurotrip - creepy italian guy
https://www.youtube.com/watch?v=nioOj6FTZQ8

Mostowski Collapse wrote:
> Luigi imitates AP brain farto and posts name lists?
> How original? LMAO!

Quizz for Dan-O-Matik:

If one encodes functions as set of pairs. Call such a function f
purple. Must there not always be a pair (x, y) that isnt purple,

or even stronger we can prove:

EXIST(x) : ALL(y) : ~(x, y) in f

How bizzar, how bizzar...
https://youtu.be/C2cMG33mWVY

Mostowski Collapse wrote:

> Quizz for Dan-O-Matik:
> If one encodes functions as set of pairs. Call such a function f purple.
> Must there not always be a pair (x, y) that isnt purple,
> or even stronger we can prove: EXIST(x) : ALL(y) : ~(x, y) in f
> How bizzar, how bizzar... https://youtu.be/C2cMG33mWVY

You are stupid like a fake vaccine.

I nowhere used handwaving. These two are provable,
it says that a set like function cannot have a domain
that is all elements from the domain of discourse:

> /* Provable, Not Purple Theorem */
> EXIST(x):ALL(y):~(x,y) e h

And this here is provable. It says that a FOL function
symbol on the other hand has a domain that is
all elements from the domain of discourse:

> /* Provable */
> ALL(x):EXIST(y):g(x)=y

Do you deny these two theorems? They are provable in DC Proof.

Mostowski Collapse schrieb am Sonntag, 26. Dezember 2021 um 11:20:19 UTC+1:
> Quizz for Dan-O-Matik:
>
> If one encodes functions as set of pairs. Call such a function f
> purple. Must there not always be a pair (x, y) that isnt purple,
>
> or even stronger we can prove:
>
> EXIST(x) : ALL(y) : ~(x, y) in f
>
> How bizzar, how bizzar...
> https://youtu.be/C2cMG33mWVY

Thats also a nice exericse, show this here a proper class:

{ S | x e S }

Dan Christensen schrieb am Samstag, 30. Oktober 2021 um 23:46:23 UTC+2:
> I wrote the attached proof in response to a discussion at Quora. Here I show that, in set theory, there exists no set of all those things that are NOT PURPLE.
>
> In the language of set theory: For every set p, there does NOT exist a set p' of all those elements NOT in p.
>
> ALL(p):[Set(p) & ALL(b):[b in p <=> P(b)] => ~EXIST(p'):[Set(p') & ALL(b):[b in p' <=> ~b in p]]]
>
> Your constructive comments are welcomed.
>
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com
>
>
> THE NON-EXISTENCE OF UNIVERSAL SET COMPLEMENTS
>
> THEOREM
>
> ALL(p):[Set(p) & ALL(b):[b in p <=> P(b)]
> => ~EXIST(p'):[Set(p') & ALL(b):[b in p' <=> ~b in p]]]
>
> PROOF:
>
> Suppose we have set p such that...
>
> 1 Set(p) & ALL(b):[b in p <=> P(b)]
> Premise
>
> 2 Set(p)
> Split, 1
>
> 3 ALL(b):[b in p <=> P(b)]
> Split, 1
>
>
> Suppose to the contrary that we have set p' (the complement of p) such that...
>
> 4 Set(p') & ALL(b):[b in p' <=> ~b in p]
> Premise
>
> 5 Set(p')
> Split, 4
>
> 6 ALL(b):[b in p' <=> ~b in p]
> Split, 4
>
> Apply axiom of Pairwise Union
>
> 7 ALL(a):ALL(b):[Set(a) & Set(b) => EXIST(c):[Set(c) & ALL(d):[d in c <=> d in a | d in b]]]
> Pw Union
>
> 8 ALL(b):[Set(p) & Set(b) => EXIST(c):[Set(c) & ALL(d):[d in c <=> d in p | d in b]]]
> U Spec, 7
>
> 9 Set(p) & Set(p') => EXIST(c):[Set(c) & ALL(d):[d in c <=> d in p | d in p']]
> U Spec, 8
>
> 10 Set(p) & Set(p')
> Join, 2, 5
>
> 11 EXIST(c):[Set(c) & ALL(d):[d in c <=> d in p | d in p']]
> Detach, 9, 10
>
> 12 Set(u) & ALL(d):[d in u <=> d in p | d in p']
> E Spec, 11
>
> Define: Set u (the "universal set", the union of p and p')
>
> 13 Set(u)
> Split, 12
>
> 14 ALL(d):[d in u <=> d in p | d in p']
> Split, 12
>
>
> Suppose to the contrary that we have x such that...
>
> 15 ~x in u
> Premise
>
> 16 x in u <=> x in p | x in p'
> U Spec, 14
>
> 17 [x in u => x in p | x in p'] & [x in p | x in p' => x in u]
> Iff-And, 16
>
> 18 x in u => x in p | x in p'
> Split, 17
>
> 19 x in p | x in p' => x in u
> Split, 17
>
> 20 ~x in u => ~[x in p | x in p']
> Contra, 19
>
> 21 ~[x in p | x in p']
> Detach, 20, 15
>
> 22 ~[~x in p => x in p']
> Imply-Or, 21
>
> 23 x in p' <=> ~x in p
> U Spec, 6
>
> 24 [x in p' => ~x in p] & [~x in p => x in p']
> Iff-And, 23
>
> 25 x in p' => ~x in p
> Split, 24
>
> 26 ~x in p => x in p'
> Split, 24
>
> 27 ~[~x in p => x in p'] & [~x in p => x in p']
> Join, 22, 26
>
> By contradiction...
>
> 28 ~EXIST(a):~a in u
> Conclusion, 15
>
> 29 ~~ALL(a):~~a in u
> Quant, 28
>
> 30 ALL(a):~~a in u
> Rem DNeg, 29
>
> 31 ALL(a):a in u
> Rem DNeg, 30
>
> Apply axiom of Arbitrary Subsets
>
> 32 EXIST(r):[Set(r) & ALL(a):[a in r <=> a in u & ~a in a]]
> Subset, 13
>
> 33 Set(r) & ALL(a):[a in r <=> a in u & ~a in a]
> E Spec, 32
>
> 34 Set(r)
> Split, 33
>
> 35 ALL(a):[a in r <=> a in u & ~a in a]
> Split, 33
>
> 36 r in r <=> r in u & ~r in r
> U Spec, 35
>
> 37 [r in r => r in u & ~r in r] & [r in u & ~r in r => r in r]
> Iff-And, 36
>
> 38 r in r => r in u & ~r in r
> Split, 37
>
> 39 r in u & ~r in r => r in r
> Split, 37
>
> Suppose to the contrary...
>
> 40 r in r
> Premise
>
> 41 r in u & ~r in r
> Detach, 38, 40
>
> 42 ~r in r
> Split, 41
>
> 43 r in r & ~r in r
> Join, 40, 42
>
> By contradiction...
>
> 44 ~r in r
> Conclusion, 40
>
> 45 r in u
> U Spec, 31
>
> 46 r in u & ~r in r
> Join, 45, 44
>
> 47 r in r
> Detach, 39, 46
>
> 48 ~r in r & r in r
> Join, 44, 47
>
> By contradiction...
>
> 49 ~EXIST(p'):[Set(p') & ALL(b):[b in p' <=> ~b in p]]
> Conclusion, 4
>
> As Required:
>
> 50 ALL(p):[Set(p) & ALL(b):[b in p <=> P(b)]
> => ~EXIST(p'):[Set(p') & ALL(b):[b in p' <=> ~b in p]]]
> Conclusion, 1

Here is a proof sketch. First a lemma about the members
S of the class. These sets S allow of course to form:

S \ {x} = { y | y e S & y =\= x }

That was just application of comprehension axiom.
Now assume to the contrary that this C here:

C = { S | x e S }

were a set. If C were a set, we could form this set:

C' = { S \ {x} | S e C }

If C were a set, then C' were also a set, and we could form again a set:

U = C u C'

But its easy to show U = V, where V is the universal class,
a contradiction that U is a set.

Q.E.D.

Mostowski Collapse schrieb am Sonntag, 23. Januar 2022 um 17:56:37 UTC+1:
> Thats also a nice exericse, show this here a proper class:
>
> { S | x e S }
> Dan Christensen schrieb am Samstag, 30. Oktober 2021 um 23:46:23 UTC+2:
> > I wrote the attached proof in response to a discussion at Quora. Here I show that, in set theory, there exists no set of all those things that are NOT PURPLE.

Not sure whether Brouwer would accept the result. We need
for an arbitrary set T even infinite, that, and x is also arbitrary:

x e T v ~x e T

We can then say that any set T is either in the class C or the
class C', so that we get C u C' = V.

Mostowski Collapse schrieb am Sonntag, 23. Januar 2022 um 18:02:35 UTC+1:
> Here is a proof sketch. First a lemma about the members
> S of the class. These sets S allow of course to form:
>
> S \ {x} = { y | y e S & y =\= x }
>
> That was just application of comprehension axiom.
> Now assume to the contrary that this C here:
>
> C = { S | x e S }
>
> were a set. If C were a set, we could form this set:
>
> C' = { S \ {x} | S e C }
>
> If C were a set, then C' were also a set, and we could form again a set:
>
> U = C u C'
>
> But its easy to show U = V, where V is the universal class,
> a contradiction that U is a set.
>
> Q.E.D.
> Mostowski Collapse schrieb am Sonntag, 23. Januar 2022 um 17:56:37 UTC+1:
> > Thats also a nice exericse, show this here a proper class:
> >
> > { S | x e S }
> > Dan Christensen schrieb am Samstag, 30. Oktober 2021 um 23:46:23 UTC+2:
> > > I wrote the attached proof in response to a discussion at Quora. Here I show that, in set theory, there exists no set of all those things that are NOT PURPLE.

Math has its imaginary side it admits to.
There is no i formula solution.

Mostowski Collapse wrote:

> Thats also a nice exericse, show this here a proper class:{ S | x e S }

how about this, still don't you think so:

Demonstrators in Brussels Clash with Police
https://www.brighteon.com/7ce393e9-f2d3-4635-9433-d85950d7de46

So you never took home some lessons from what your proved
about your nonsensical Set(_) predicate in DC Poop? As usual,
you are grapsing straws Dan - O - Matik. Check out Terrence

Tao when he uses sets? Ever seen him use this:

Set(myset)

Surely not. Mathematicians in math books if they use set theory,
heavily make use of power set like 𝒫(U) to define families of sets,
I am pretty sure you find that all over the place in Terrence Tao.

or every set x, there is a set 𝒫(x) consisting precisely of the subsets of x.
https://en.wikipedia.org/wiki/Axiom_of_power_set

Guess why set theory has this axiom? Its missing in DC Poop.
So basically one year ago your silly DC Poop didn't have function
spaces, and now you might discover that it has missing set spaces.

If you would declare purple as follows:

p ∈ 𝒫(U)

There is no problem in seeing that we also have:

U / p ∈ 𝒫(U)

Only drawback, "things" is now some set U.

See my reply just now to your similar posting at sci.logic

Dan

On Wednesday, May 3, 2023 at 7:28:38 PM UTC-4, Mostowski Collapse wrote:
> So you never took home some lessons from what your proved
> about your nonsensical Set(_) predicate in DC Poop? As usual,
> you are grapsing straws Dan - O - Matik. Check out Terrence
>
> Tao when he uses sets? Ever seen him use this:
>
> Set(myset)
>
[snip]

Your Set(_) is from some Naive set theory. And Russells
Paradox shows that it doesn't work the same way like
Russells Paradox showed Frege that is Naive comprehension

doesn't work as an axiom. Only your Set(_) doesn't
appear in an Axiom, but rather during modelling. So what
was the Frege fix by Zermelo:

Frege Naive Comprehension:
{ x | P(x) }
Zermelos Fix Non-Naive Comprehension:
{ x e A | P(x) }

Now there is an analogue problem with Dan-O-Matik now:

Dan-O-Matiks Naive Set Declaration:
Set(x)
What Mathematicians Use, i.e. "Types"
x e A

So I guess there is no escaping. Sooner or later
DC Poop would need to introduce Set Spaces as well,
and not only Function Spaces. The current approach by

DC Poop is surely doomed. And thats what the Russell
Paradox is all about, showing such bloopers.

Dan Christensen schrieb am Donnerstag, 4. Mai 2023 um 04:05:44 UTC+2:
> See my reply just now to your similar posting at sci.logic
>
> Dan
> On Wednesday, May 3, 2023 at 7:28:38 PM UTC-4, Mostowski Collapse wrote:
> > So you never took home some lessons from what your proved
> > about your nonsensical Set(_) predicate in DC Poop? As usual,
> > you are grapsing straws Dan - O - Matik. Check out Terrence
> >
> > Tao when he uses sets? Ever seen him use this:
> >
> > Set(myset)
> >
> [snip]

See my reply just now to your identical posting at sci.logic

Dan

On Thursday, May 4, 2023 at 2:44:46 AM UTC-4, Mostowski Collapse wrote:
> Your Set(_) is from some Naive set theory. And Russells
> Paradox shows that it doesn't work the same way like
> Russells Paradox showed Frege that is Naive comprehension
>
[snip]