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DC Proof is the biggest teaching mistake
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Profilbild von Mostowski Collapse
Mostowski Collapse
22.11.2021, 11:38:04
That an empty universe of discourse is allowed has recently become a hiding space for being lazy.
Profilbild von Dan Christensen
Dan Christensen
22.11.2021, 14:15:04
On Monday, November 22, 2021 at 5:38:04 AM UTC-5, Mostowski Collapse wrote: > That an empty
Profilbild von Mostowski Collapse
Mostowski Collapse
22.11.2021, 17:33:54
Shouldn't be provable in a logic with a possibly empty domain of discourse. Because any statement
Profilbild von Dan Christensen
Dan Christensen
22.11.2021, 21:16:13
On Monday, November 22, 2021 at 11:33:54 AM UTC-5, Mostowski Collapse wrote: > Dan Christensen
Profilbild von Kip Foh
Kip Foh
23.11.2021, 01:36:40
Dan Christensen wrote: >> So how should it be possible to prove some EXIST(a):A(a) sentence
Profilbild von Mostowski Collapse
Mostowski Collapse
23.11.2021, 01:45:07
Why would you even be interested in proving this? > 2) EXIST(f):[Dedekind(f) => EXIST(w):Peano(
Profilbild von Dan Christensen
Dan Christensen
23.11.2021, 03:17:05
On Monday, November 22, 2021 at 7:45:07 PM UTC-5, Mostowski Collapse wrote: > Why would you even
Profilbild von Mostowski Collapse
Mostowski Collapse
23.11.2021, 08:39:59
Mathematics proves things like, using some foundational axioms. Thats standard routine: 3) EXIST(f):
Profilbild von Mostowski Collapse
Mostowski Collapse
23.11.2021, 08:50:16
For example when constructing the reals, its standard to then prove: 1) EXIST(x):[xe R & x^2 = 2]
Profilbild von Mostowski Collapse
Mostowski Collapse
23.11.2021, 09:01:08
When constructing the reals bottom up, you will likely need countable infinite sequences, and to show
Profilbild von Mostowski Collapse
Mostowski Collapse
23.11.2021, 09:10:24
If you don't have sqrt(2) as a real number object, you might have it as a class. But you refuse
Die Nachricht wurde gelöscht
Profilbild von Dan Christensen
Dan Christensen
23.11.2021, 18:30:57
> Dan Christensen schrieb am Dienstag, 23. November 2021 um 03:17:05 UTC+1: > > On Monday,
Profilbild von Mostowski Collapse
Mostowski Collapse
23.11.2021, 19:39:56
Nope you cannot introduce this as an axiom. It would consume the name f. Thats the whole point of
Profilbild von Mostowski Collapse
Mostowski Collapse
23.11.2021, 19:46:05
And this here is not FOL, when you use this here as an axiom: EXIST(x):EXIST(f):[Set(x) & ALL(a):
Profilbild von Mostowski Collapse
Mostowski Collapse
23.11.2021, 19:52:34
FOL = First Order Logic A function symbols is a second order logic object.. If U is the universe of
Profilbild von Mostowski Collapse
Mostowski Collapse
23.11.2021, 20:00:23
And this is buggy nonsense, it refers to x, but when you have an axiom EXIST(x):... how can you refer
Profilbild von Dan Christensen
Dan Christensen
23.11.2021, 21:18:06
On Tuesday, November 23, 2021 at 1:39:56 PM UTC-5, Mostowski Collapse wrote: > > The first line
Profilbild von Mostowski Collapse
Mostowski Collapse
23.11.2021, 22:54:45
Why do you talk nonsense all day? Its only equivalent when you have the axiom of regularity, or
Profilbild von Dan Christensen
Dan Christensen
24.11.2021, 01:27:13
On Tuesday, November 23, 2021 at 4:54:45 PM UTC-5, Mostowski Collapse wrote: > Dan Christensen
Profilbild von Mostowski Collapse
Mostowski Collapse
24.11.2021, 01:35:31
You continue talking nonsense as usual. Dan Christensen schrieb am Mittwoch, 24. November 2021 um 01:
Profilbild von Fritz Feldhase
Fritz Feldhase
24.11.2021, 05:49:56
On Tuesday, November 23, 2021 at 6:30:57 PM UTC+1, Dan Christensen wrote: > Again, I proved: &
Profilbild von Dan Christensen
Dan Christensen
24.11.2021, 05:58:08
On Tuesday, November 23, 2021 at 11:49:56 PM UTC-5, Fritz Feldhase wrote: > On Tuesday, November
Profilbild von Mostowski Collapse
Mostowski Collapse
24.11.2021, 15:16:53
Dan-O-Matik was talking nonsense: > And while Dedekind infinite sets are often mentioned in math
Profilbild von Mostowski Collapse
Mostowski Collapse
24.11.2021, 15:19:38
Additionally assuming f : x -> y for some x,y is not required to prove it in FOL+ZF. It would be
Profilbild von Mostowski Collapse
Mostowski Collapse
24.11.2021, 15:36:03
I am not suggesting Borel determinancy as an exercise: “Skolem needed a snack, so he ate enough for
Profilbild von Mostowski Collapse
Mostowski Collapse
05.12.2021, 16:59:15
Can we buy these double chimpazee copper bracelets already on Amazon? Here is your fallacy explained.
Profilbild von Mostowski Collapse
Mostowski Collapse
05.12.2021, 17:07:44
Even a blind mole can show both claims: > /* provable */ > F is hyperbola => ALL(x):[x≠0 Profilbild von Dan Christensen
Dan Christensen
05.12.2021, 17:17:24
On Sunday, December 5, 2021 at 10:59:15 AM UTC-5, Mostowski Collapse wrote: > Can we buy these
Profilbild von Mostowski Collapse
Mostowski Collapse
05.12.2021, 17:21:52
Corr.: Need to fix my blind mole proof, serial shouldn't be there. Don't know how much is
Profilbild von Mostowski Collapse
Mostowski Collapse
05.12.2021, 17:43:21
Ok here is a corrected proof, now saying for the reciprocal hyperbola, that the reciprocal hyperbola
Profilbild von FredJeffries
FredJeffries
05.12.2021, 17:54:12
On Sunday, December 5, 2021 at 8:17:24 AM UTC-8, Dan Christensen wrote: > On Sunday, December 5,
Profilbild von Dan Christensen
Dan Christensen
05.12.2021, 18:51:40
On Sunday, December 5, 2021 at 11:54:12 AM UTC-5, FredJeffries wrote: > On Sunday, December 5,
Profilbild von Dan Christensen
Dan Christensen
05.12.2021, 19:18:18
On Sunday, December 5, 2021 at 11:43:21 AM UTC-5, Mostowski Collapse wrote: > Ok here is a
Profilbild von Mostowski Collapse
Mostowski Collapse
05.12.2021, 19:50:19
Why would somebody try to prove that? When its not provable? It is easy to show that it has a counter
Profilbild von Mostowski Collapse
Mostowski Collapse
05.12.2021, 19:53:52
On the other hand one can prove: F is the reciprocal hyperbola => ~F(0,1) Here is the rather
Profilbild von Mostowski Collapse
Mostowski Collapse
05.12.2021, 20:13:43
Maybe you cannot cope with the mental disonnance between you double chimpanzee nonsense and standard
Profilbild von Dan Christensen
Dan Christensen
05.12.2021, 22:10:40
On Sunday, December 5, 2021 at 1:50:19 PM UTC-5, Mostowski Collapse wrote: > Dan Christensen
Profilbild von Mostowski Collapse
Mostowski Collapse
05.12.2021, 22:39:03
I am already telling you for the 1000-th times: hyperbola: f(0)≠1 provable double chimpanzee: f(0)≠1
Profilbild von Dan Christensen
Dan Christensen
05.12.2021, 22:56:40
On Sunday, December 5, 2021 at 4:39:03 PM UTC-5, Mostowski Collapse wrote: > Dan Christensen
Profilbild von Mostowski Collapse
Mostowski Collapse
05.12.2021, 23:05:54
Not in the hyperbola, in the f(0)≠1 provable Dan Christensen schrieb am Sonntag, 5. Dezember 2021 um
Profilbild von Mostowski Collapse
Mostowski Collapse
05.12.2021, 23:07:39
Or more precisly, when: ALL(a):ALL(b):(F(a,b) <=> a*b=1) Then ~F(0,1). F(x)=y is the reciprocal
Profilbild von FredJeffries
FredJeffries
06.12.2021, 17:46:22
On Sunday, December 5, 2021 at 9:51:40 AM UTC-8, Dan Christensen wrote: > On Sunday, December 5,
Profilbild von Mostowski Collapse
Mostowski Collapse
10.12.2021, 19:36:08
Now this is like fukushima. I guess Dan-O-Matiks brain is now melting. We finally found it: ∀x(Px →
Profilbild von Mostowski Collapse
Mostowski Collapse
10.12.2021, 19:40:54
Actually learning 3 languages would be helpful: - FOL function symbol - class-like functions - set-
Profilbild von Mostowski Collapse
Mostowski Collapse
10.12.2021, 19:46:51
But there is cure, Dan-O-Matik could exercise and get fluent in all 3 languages by this little
Profilbild von Mostowski Collapse
Mostowski Collapse
12.12.2021, 10:47:50
Unfortunately Dan-O-Matik is only genuinely stupid: Two things are infinite: the universe and human
Profilbild von Mostowski Collapse
Mostowski Collapse
12.12.2021, 10:49:15
For example JavaScript implements undefined ⊥: Legts get back to the 10 booleans array problem. Just
Profilbild von Mostowski Collapse
Mostowski Collapse
12.12.2021, 10:53:21
Corr.: The WELL DEFINED issue arises when for example A={0} and B={0}, we then want from def(h) <Profilbild von Mostowski Collapse
Mostowski Collapse
13.12.2021, 22:26:00
How would one formulate in DC Proof, which is supposed to be the tool for mathematics textbooks, the
Profilbild von Mostowski Collapse
Mostowski Collapse
13.12.2021, 23:12:35
But Fefi was sloppy, when defining his Impredicative Theory of Operations and Classes (IOC), at least
Profilbild von Dan Christensen
Dan Christensen
14.12.2021, 03:54:02
On Monday, December 13, 2021 at 4:26:00 PM UTC-5, Mostowski Collapse wrote: > How would one
Profilbild von Mostowski Collapse
Mostowski Collapse
14.12.2021, 08:50:01
Thats not the correct approach in logic. Since Peano, we find something else: "Function
Profilbild von Mostowski Collapse
Mostowski Collapse
14.12.2021, 08:54:49
So only ALL(a):[aex => f(x) eb] , the Donnie Darko approach, like dark numbers in WM, is just WM
Profilbild von Mostowski Collapse
Mostowski Collapse
14.12.2021, 10:02:05
The only new development in logic might be these partial function logics, where we dont need f'x
Profilbild von Mostowski Collapse
Mostowski Collapse
14.12.2021, 10:07:07
Then there is a whole field where the underlying logic is changed, and where the underlying logic is
Profilbild von Dan Christensen
Dan Christensen
14.12.2021, 18:08:36
See my reply just now to your identical posting at sci.math Dan On Tuesday, December 14, 2021 at 2:50
Profilbild von Mostowski Collapse
Mostowski Collapse
14.12.2021, 19:34:41
Thats exactly why EXISTUNIQUE doesn't work. I 100'% agree with Terence Tao. When you use a
Profilbild von Mostowski Collapse
Mostowski Collapse
14.12.2021, 19:43:49
With the metamath approach you can prove EXISTUNIQUE when the undefined marker is not in the codomain
Profilbild von Mostowski Collapse
Mostowski Collapse
14.12.2021, 19:48:28
So maybe what Fefi (Solom Feferman) explains is the more cleaner approach. You don't have to
Profilbild von Mostowski Collapse
Mostowski Collapse
14.12.2021, 20:49:27
The deeper problem is not Terrence Tao versus Dan-O-Matik versus metamath. In all 3 approaches this
Profilbild von Mostowski Collapse
Mostowski Collapse
14.12.2021, 20:55:33
It prevents EXISTUNIQUE because you can find (f1,c1) and (f2, c2), where f1≠f2 and: ALL(b):[b in c1 Profilbild von Dan Christensen
Dan Christensen
14.12.2021, 22:43:06
Set my reply just now to your identical posting as sci.math. Dan On Tuesday, December 14, 2021 at 2:
Profilbild von Mostowski Collapse
Mostowski Collapse
14.12.2021, 22:48:49
You used this EXISTUNIQUE(f,a): EXISTUNIQUE(f,a):A(f) <=> EXIST(h):A(h) & ALL(f):ALL(g):[A(
Profilbild von Mostowski Collapse
Mostowski Collapse
18.12.2021, 14:20:21
I dont think DC proof correctly associates functions and function graphs. You can also try Terence
Profilbild von Mostowski Collapse
Mostowski Collapse
18.12.2021, 14:27:35
Or asked differently how many decrement functions are there in Peano arithmetic? Can you prove:
Profilbild von Mostowski Collapse
Mostowski Collapse
24.12.2021, 10:27:34
What is easier to use, DC proof or ZFC? DC proof claims that certain things are given: > ALL(a):[a
Profilbild von Mostowski Collapse
Mostowski Collapse
24.12.2021, 10:41:12
With ZFC I only need to do the following: 1) let g = { (y, x) | (x, y) in f}, show it is a set 2)
Profilbild von Dan Christensen
Dan Christensen
24.12.2021, 17:24:47
See my reply just now to your identical postings at sci.math Dan On Friday, December 24, 2021 at 4:27
Profilbild von Mostowski Collapse
Mostowski Collapse
24.12.2021, 23:52:42
You are changing topic. I dont mind if you need Set(_) as well in DC poop. The question is rather can
Profilbild von Mostowski Collapse
Mostowski Collapse
26.12.2021, 11:06:23
So you cannot show existence of g? Hiding behind some absurd claims the encoding of functions as set
Profilbild von Mostowski Collapse
Mostowski Collapse
26.12.2021, 18:11:58
Can you prove your ExistenceOfInverse without using bizzar sets, like this here: Define: f' (as
Profilbild von Dan Christensen
Dan Christensen
27.12.2021, 04:07:11
On Sunday, December 26, 2021 at 5:06:23 AM UTC-5, Mostowski Collapse wrote: > So you cannot show
Profilbild von Mostowski Collapse
Mostowski Collapse
01.01.2022, 13:00:49
Ha Ha, Dan-O-Matik is quite desperate, he now denies valid proofs in mathematics: Dan Christensen
Profilbild von Mostowski Collapse
Mostowski Collapse
02.01.2022, 20:19:53
Can this be proved in DC Proof? ALL(x):P(x)=>ALL(y):[P(y) & P(f(y))] Here is a LK calculus
Profilbild von Dan Christensen
Dan Christensen
03.01.2022, 04:01:38
See my reply to your identical posting at sci.math. Dan On Sunday, January 2, 2022 at 2:19:53 PM UTC-
Profilbild von Mostowski Collapse
Mostowski Collapse
03.01.2022, 13:27:59
Dan-O-Matik fights the evils of darkness: > In mathematics, it can't just be lurking unseen in
Profilbild von Mostowski Collapse
Mostowski Collapse
03.01.2022, 13:48:10
From ALL(a):[a in u => a in u & f(a) in u] it also follows: ALL(a):[a in u => f(a) in u]
Profilbild von Mostowski Collapse
Mostowski Collapse
03.01.2022, 14:11:17
I dont know how to fix your DC Puff and do what you want to do. Some free logics dont touch (Refl):
Profilbild von Dan Christensen
Dan Christensen
03.01.2022, 15:03:53
See my reply just now to your identical posting at sci.math. Dan On Monday, January 3, 2022 at 7:27:
Profilbild von Mostowski Collapse
Mostowski Collapse
03.01.2022, 17:25:20
You are changing topic, are you hunted by some shadows, Dr. Frankenstein? This here shouldn't be
Profilbild von Mostowski Collapse
Mostowski Collapse
03.01.2022, 23:55:46
So DC Proof has something like Emperor penguins from antarctica as functions, with the exotic USpec.
Profilbild von Dan Christensen
Dan Christensen
04.01.2022, 06:54:50
See my reply just now to a nearly identical posting at sci.math. Dan On Monday, January 3, 2022 at 5:
Die Nachricht wurde gelöscht
Profilbild von Mostowski Collapse
Mostowski Collapse
04.01.2022, 10:29:43
DC Proof is subject to "Fake it till you make it". You claim: Dan Christensen schrieb am
Profilbild von Mostowski Collapse
Mostowski Collapse
05.01.2022, 22:33:07
Here is a quizz, which collections are in some bijection? 1) { f | f : Q -> R }, where R the real
Profilbild von Mostowski Collapse
Mostowski Collapse
06.01.2022, 06:01:08
You find your beloved CBS theorem, together with the correct reading of function spaces, namely set
Profilbild von Mostowski Collapse
Mostowski Collapse
06.01.2022, 07:00:53
Also stop talking utter nonsense like: > Nothing there to support your claim that we can make
Profilbild von Mostowski Collapse
Mostowski Collapse
06.01.2022, 07:36:55
How flat chested is DC Proof? LoL It doesn't have a power set axiom? These two sets are provably
Profilbild von Mostowski Collapse
Mostowski Collapse
08.01.2022, 18:22:21
Warning: I am looking at the direction -->, the old topic, and not at the direction <--, the
Profilbild von Mostowski Collapse
Mostowski Collapse
08.01.2022, 18:23:22
Injectivity can now be examined, since only now by ALL(a):[g'(a)=g(a)] we have a mapping from
Profilbild von Mostowski Collapse
Mostowski Collapse
09.01.2022, 00:06:00
Actually this is a nice logic exercise, show that there is no bijection? At least in the finite case,
Profilbild von Mostowski Collapse
Mostowski Collapse
09.01.2022, 00:10:08
Check out for yourself: "Given two sets S and T, the set of all functions from T to S is denoted
Profilbild von Mostowski Collapse
Mostowski Collapse
10.01.2022, 23:08:41
Its very unclear why DC Proof even needs a Function Axiom? Litterally translating Terrence Tao, he
Profilbild von Mostowski Collapse
Mostowski Collapse
10.01.2022, 23:10:51
We can also do it Gödel style, follows also, proving seriality and functionality without the codomain
Profilbild von Dan Christensen
Dan Christensen
11.01.2022, 04:39:34
See my reply just now to your identical posting at sci.math. Dan On Monday, January 10, 2022 at 5:08:
Profilbild von Mostowski Collapse
Mostowski Collapse
12.01.2022, 23:28:55
As usual you are talking nonsense and even contradicting your own DC poop tool. Can you prove the
Profilbild von Mostowski Collapse
Mostowski Collapse
12.01.2022, 23:30:30
So stop talking nonsense about some text book paranoia. Here is the axiom your are presenting for
Profilbild von Dan Christensen
Dan Christensen
13.01.2022, 03:28:26
See my reply just now to your identical posting at sci.math On Wednesday, January 12, 2022 at 5:30:30
Profilbild von Mostowski Collapse
Mostowski Collapse
13.01.2022, 21:29:10
Fraenkel did nothing. The AOI is found in a paper by Zermelo. Its an axiom of the form: EXIST(S): ...
Profilbild von Mostowski Collapse
Mostowski Collapse
13.01.2022, 21:46:04
In FOL the schema works: (∃fDf ∧ ∀f(Df → Pc(f))) → ∃nPn is valid. https://www.umsu.de/trees/#~7fDf~1~
Profilbild von Mostowski Collapse
Mostowski Collapse
15.01.2022, 00:10:03
Of course Peano axioms have an encyclopedia entry, but its not anymore practiced. How do you now
Profilbild von Dan Christensen
Dan Christensen
15.01.2022, 05:21:05
See my reply just now to your identical posting at sci.math. Dan On Friday, January 14, 2022 at 6:10:
Profilbild von Mostowski Collapse
Mostowski Collapse
16.01.2022, 21:11:55
WHATS WRONG WITH YOU??????????????? Dan Christensen schrieb am Freitag, 14. Januar 2022 um 18:46:47
Profilbild von Dan Christensen
Dan Christensen
17.01.2022, 02:19:29
On Sunday, January 16, 2022 at 3:11:55 PM UTC-5, Mostowski Collapse wrote: > WHATS WRONG WITH YOU?
Profilbild von Mostowski Collapse
Mostowski Collapse
17.01.2022, 02:44:15
I nowhere said I would only use set theory of DC Proof. DC Proof refers to the full package. If I can
Profilbild von Mostowski Collapse
Mostowski Collapse
19.01.2022, 18:13:46
If you insist, that I should not use Peano with your Set Theory!! How should I do that? I would like
Profilbild von Dan Christensen
Dan Christensen
19.01.2022, 23:18:16
On Wednesday, January 19, 2022 at 12:13:46 PM UTC-5, Mostowski Collapse wrote: > If you insist,
Profilbild von Mostowski Collapse
Mostowski Collapse
20.01.2022, 19:03:05
Q: How do you use DC poop to prove Landau's: ∀x∀y(x + y = y + x) A: Not at all, it doesn't
Profilbild von Dan Christensen
Dan Christensen
21.01.2022, 15:38:05
On Thursday, January 20, 2022 at 1:03:05 PM UTC-5, Mostowski Collapse wrote: > Q: How do you use
Profilbild von Mostowski Collapse
Mostowski Collapse
21.01.2022, 17:32:39
I don't think you are doing the same. Why does it take 252 steps? I can do it in simple 60 steps.
Profilbild von Mostowski Collapse
Mostowski Collapse
21.01.2022, 17:37:24
STUDENTS BEWARE: Unnatural DC Proof, totally not modular nonsense proofs, only an alien species can
Die Nachricht wurde gelöscht
Profilbild von Mostowski Collapse
Mostowski Collapse
21.01.2022, 17:56:45
Ok, thats the correct timing I get. Will post an internet link later: % Wall 1 ms, gc 0 ms, 108000
Profilbild von Dan Christensen
Dan Christensen
21.01.2022, 18:25:16
On Friday, January 21, 2022 at 11:32:39 AM UTC-5, Mostowski Collapse wrote: > I don't think
Profilbild von Mostowski Collapse
Mostowski Collapse
21.01.2022, 18:34:40
WHATS WRONG WITH YOU???? Dan-O-Matik asked: > How do you express Peano's Axioms? Well like
Profilbild von Mostowski Collapse
Mostowski Collapse
21.01.2022, 18:38:53
Here is a transliteration of the screenshot from Landau: Theorem 4, and at the same time Definition 1
Profilbild von Mostowski Collapse
Mostowski Collapse
21.01.2022, 18:47:12
Theorem 4 would be: ∀x ∀y ∃z (x + y = z) ∀x ∀y ∀z ∀t (x + y = z & x + y = t => z = t) But this
Profilbild von Dan Christensen
Dan Christensen
21.01.2022, 18:51:53
On Friday, January 21, 2022 at 12:34:40 PM UTC-5, Mostowski Collapse wrote: > WHATS WRONG WITH YOU
Profilbild von Mostowski Collapse
Mostowski Collapse
21.01.2022, 18:58:50
Not interested in xe N, and a >200 step proof for commutativity. What you post below is not the
Profilbild von Dan Christensen
Dan Christensen
21.01.2022, 18:59:59
On Friday, January 21, 2022 at 12:38:53 PM UTC-5, Mostowski Collapse wrote: > Here is a
Profilbild von Mostowski Collapse
Mostowski Collapse
21.01.2022, 19:05:17
Its rather the other way around. You proved too much. Please read Landau carefully. He only said:
Profilbild von Dan Christensen
Dan Christensen
21.01.2022, 19:16:25
On Friday, January 21, 2022 at 12:58:50 PM UTC-5, Mostowski Collapse wrote: > Dan Christensen
Profilbild von Mostowski Collapse
Mostowski Collapse
21.01.2022, 19:17:49
If you want to interpret Landaus "assign" differently, in the sense of "by finite
Profilbild von Dan Christensen
Dan Christensen
21.01.2022, 19:29:21
On Friday, January 21, 2022 at 1:05:17 PM UTC-5, Mostowski Collapse wrote: > Dan Christensen
Profilbild von Mostowski Collapse
Mostowski Collapse
21.01.2022, 19:31:23
The problem is, math stackexchange is not the right place to learn anything mathematics or anything
Profilbild von Mostowski Collapse
Mostowski Collapse
23.01.2022, 23:19:01
So how meaningful is Dan-O-Matiks function space. We can show: ye S f : S -> {y} Dan-O-Matik style
Profilbild von Mostowski Collapse
Mostowski Collapse
28.01.2022, 18:24:15
Ha Ha, the domain of discourse and what quantifiers do in logic, the greatest miracle for Dan-O-Matik
Profilbild von Mostowski Collapse
Mostowski Collapse
28.01.2022, 21:25:56
The grandmother is very desperate. The little brat does not only not understand quantifiers and the
Profilbild von Mostowski Collapse
Mostowski Collapse
28.01.2022, 22:33:51
The grandmother is considering to give the grandson free for adoption. He is useless in the house,
Profilbild von Mostowski Collapse
Mostowski Collapse
29.01.2022, 00:39:58
Grandmother is a little angry with grandson. Grandson thinks he could just sprinkle some inference
Profilbild von Mostowski Collapse
Mostowski Collapse
04.02.2022, 05:06:10
If I take Dan-O-Matiks advice: > "Perhaps you didn't know, but two functions f and f'
Profilbild von Dan Christensen
Dan Christensen
04.02.2022, 17:05:29
On Thursday, February 3, 2022 at 11:06:10 PM UTC-5, Mostowski Collapse (aka Jan Burse) wrote: > If
Profilbild von Mostowski Collapse
Mostowski Collapse
04.02.2022, 18:22:41
The standard same-ness is: f ≈ g :<=> ∀x(f(x)=g(x)) You can then prove, for example in tree
Profilbild von Dan Christensen
Dan Christensen
04.02.2022, 20:05:25
On Friday, February 4, 2022 at 12:22:41 PM UTC-5, Mostowski Collapse wrote: > The standard same-
Profilbild von Mostowski Collapse
Mostowski Collapse
04.02.2022, 20:50:05
Well the domain of a function is easy: dom(f) = { x | ∃y (x,y) ef } You then have: f = g => dom(f)
Profilbild von Dan Christensen
Dan Christensen
04.02.2022, 22:33:39
On Friday, February 4, 2022 at 2:50:05 PM UTC-5, Mostowski Collapse wrote: > Don't you have
Profilbild von Mostowski Collapse
Mostowski Collapse
04.02.2022, 23:21:52
Dan-O-Matik halucinated: > for all x in X, we have f(x)=g(x) You cannot prove: f ≈ g => dom(f)
Profilbild von Mostowski Collapse
Mostowski Collapse
07.02.2022, 11:59:21
Ok, here is a high school exercise: f : R \ {0} -> R, identity function except for x=0 where
Profilbild von Dan Christensen
Dan Christensen
07.02.2022, 17:53:54
See my reply today to your identical posting at sci.math Dan On Monday, February 7, 2022 at 5:59:21
Profilbild von Mostowski Collapse
Mostowski Collapse
07.02.2022, 21:47:13
You see, your result is nonsense: ALL(a):[a in non0 => g(f(a))=1] Thats a strange identity
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Mostowski Collapse
07.02.2022, 22:27:54
This theorem is not provable in DC poop: dom(goh) = h^(-1)[dom(g)] Because DC poop refuses to define
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Dan Christensen
08.02.2022, 01:33:46
On Monday, February 7, 2022 at 3:47:13 PM UTC-5, Mostowski Collapse wrote: > You see, your result
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Mostowski Collapse
08.02.2022, 12:40:52
One more nonsense: > 32. ALL(a):[a in non01 => g(f(a))=a] Conclusion, 9 Try this here: 6. ALL(a
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Mostowski Collapse
09.02.2022, 19:50:41
WHATS WRONG WITH YOU????? Where do you see the domain of f' given for example for the problem f :
Profilbild von Mostowski Collapse
Mostowski Collapse
09.02.2022, 21:47:09
Just read Terence Tao. From f you construct a function: Step 1: g(x,h) = (f(x+h) - f(x)) / h And from
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Dan Christensen
10.02.2022, 04:23:43
See my reply earlier today to your identical posting at sci.math Dan On Wednesday, February 9, 2022
Profilbild von Mostowski Collapse
Mostowski Collapse
28.04.2022, 09:47:57 (gestern)
The Fritz definitions are here, which allow you to prove the disputed theorem that I gave. I am 100%
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Mostowski Collapse
28.04.2022, 09:56:57 (gestern)
Of course you need to have the corresponding set theory in DC Proof first, to redo the proof in DC
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Dan Christensen
28.04.2022, 22:58:59 (vor 17 Stunden)
See my reply just now to your identical posting at sci.math. Dan On Thursday, April 28, 2022 at 3:47:
Profilbild von Mostowski Collapse
Mostowski Collapse
15:46 (vor 16 Minuten)
I think we could go with the answer by Asaf Karagila for some issue we have.. Asaf Karagila introduces
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Mostowski Collapse
ungelesen,
16:02 (jetzt)
an
Unfortunately Asaf Karagila is not a very expanded
answer. When he writes then "ask whether or not the range is
equal to the its codomain", we are a bit left with the

question what is range? And is it extrinsic or
intrinsic? And what about the codomain, where do
I find it? Anyway proving this one could answer

all questions:

ALL(f):EXIST(y):ALL(a):[f(a) e y]

P.S.: Also Dan Christensen uses a faux definition in
his question. Since wikipedia explicitly states that cod
is not what Dan Christensen writes: "The codomain set

is just the set of all its 2nd co-ordinates (ordinates)."
So there is a category in Dan Christensens question
since by co-domain we understand:

It is the set Y in the notation f: X → Y.

So maybe we have already an answer, the codomain
is extrinsic, and the range is intrinsic?

LoL

Mostowski Collapse schrieb am Freitag, 29. April 2022 um 15:45:00 UTC+2:
> I think we could go with the answer by Asaf Karagila for
> some issue we have. Asaf Karagila introduces some new
> terminology we might find useful:
>
> "Surjectivity is a relationship between a function and a
> set. It is an extrinsic property of a function, when the
> function is defined as a set of ordered pairs. Not an
> intrinsic one like injectivity is."
> https://math.stackexchange.com/a/4438437/1002973
>
> I think he has put the Bourbaki idea f = <F,X,Y> aside,
> and talks set theory, when he writes the above. Since in
> Bourbaki we have Y is intrinsic and not extrinsic:
>
> Y = π3(f) /* third projection from the triple <F,X,Y> */
>
> We might also use the term intrinsic and extrinsic
> to point out a lot of problems in Dan-O-Matiks treatment
> so far, for example in this here:
>
> ALL(a):[x e dom => f(a) e cod]
>
> Two extrinsic properties dom and cod are used. That
> dom is extrinsic is the more annoying thing, because
> dom is intrinsic in set theory:
>
> dom(f) := { x | EXIST(y):[(x,y) e f]
>
> Depending on the pairing function we can show that
> dom(f) exists as a set when f is a set already in Z
> or we might need ZF. Similar in set theory we can prove:
> ALL(f):EXIST(y):ALL(a):[f(a) e y]
> Fritz Feldhase schrieb am Freitag, 29. April 2022 um 00:09:23 UTC+2:
> > On Thursday, April 28, 2022 at 10:49:16 PM UTC+2, Dan Christensen wrote:
> >
> > > I guess wonky results like this are part of the reason so-called "mathematical" logic is <bla>
> >
> > Dan, you are an idiotic crank. Please, shut up!