I do not believe that there is non-negative real
number x such the x =/= |x|. Thats your crazy invention.

I was asking in this thread whether you agree:

"If two functions differ at some argument, then they differ"
ALL(f):ALL(g):[EXIST(a):[f(a)=/=g(a)] => f=/=g]

Dan Christensen schrieb am Dienstag, 5. April 2022 um 22:29:03 UTC+2:
> You are the one claiming that x =/= |x| for some non-negative real x.

Mostowski Collapse wrote:

> I was asking in this thread whether you agree:
> "If two functions differ at some argument, then they differ"
> ALL(f):ALL(g):[EXIST(a):[f(a)=/=g(a)] => f=/=g]
> Dan Christensen schrieb am Dienstag, 5. April 2022 um 22:29:03 UTC+2:
>> You are the one claiming that x =/= |x| for some non-negative real x.

He can't answer. But the nazis of "ukraine", the nazis of "polakia", the nazis of the switzarland and the nazis of america, helping them, will be concentrated in forced labour camps, building highways, bridges etc in russia. You nazis can't escape. We write 2022 and the nazis still making wars?? Get out of here.
That's the problem with the russians, they are not evil enough. The will never
bomb infrastructure, water, electricity, etc, staging fals flags as the nazis does.
And btw, without mother Russia, many of you wankers not even would be born. Neither you and your parents. Think about it.

Disgusting: How the Ukrainian Nazi/Nationalist Movement Post WW2 Was Bought by the CIA
https://www.veteranstoday.com/2022/04/05/disgusting-how-the-ukrainian-nazi-nationalist-movement-post-ww2-was-bought-by-the-cia/

Russia calls for international probe into US-led biolabs in Ukraine
https://www.veteranstoday.com/2022/04/06/russia-calls-for-international-probe-into-us-led-biolabs-in-ukraine/

“Fakes emerge throughout Ukraine crisis just to be debunked later”
https://www.veteranstoday.com/2022/04/06/fakes-emerge-throughout-ukraine-crisis-just-to-be-debunked-later/

German chemical behemoth warns of country’s “total collapse” if Russian oil, gas is cut off
https://www.thetruthseeker.co.uk/?p=251808

“Vaccines” are Genocide Bio Weapons
https://www.thetruthseeker.co.uk/?p=251830

On Wednesday, April 6, 2022 at 7:12:52 AM UTC-4, Willie Dukes wrote:
> Mostowski Collapse wrote:
>
> > I was asking in this thread whether you agree:
> > "If two functions differ at some argument, then they differ"
> > ALL(f):ALL(g):[EXIST(a):[f(a)=/=g(a)] => f=/=g]
> > Dan Christensen schrieb am Dienstag, 5. April 2022 um 22:29:03 UTC+2:
> >> You are the one claiming that x =/= |x| for some non-negative real x.
> He can't answer. But the nazis of "ukraine"...

You are forgetting: WAR OF AGRESSION = NAZI

Looks like there will be a good chance you and your boss will be appearing before the Nuremberg War Crimes Tribunal II. Just hope they don't send you to a prison in the USA or Russia. I'm told conditions are absolutely appalling there.

Dan Christensen wrote:

>> He can't answer. But the nazis of "ukraine"...
>
> You are forgetting: WAR OF AGRESSION = NAZI

Idiot, wars ARE aggression, but the nazi is you.

> Looks like there will be a good chance you and your boss will be
> appearing

Meanwhile a general or more caught in Marionopol if this is true.

Numerous Reports: U.S. Army General CAPTURED in Mariupol with AZOV Nazis!
https://www.thetruthseeker.co.uk/?p=251848

You are strange, for a nazi to be.

On Wednesday, April 6, 2022 at 2:09:54 PM UTC-4, Jabe Jukado wrote:
> Dan Christensen wrote:
>
> >> He can't answer. But the nazis of "ukraine"...
> >
> > You are forgetting: WAR OF AGRESSION = NAZI
> Idiot, wars ARE aggression, but the nazi is you.

Tell it to the judge Hr Goebbels.

It becomes evident that Dan-O-Matiks psychosis is
based on his age old confusion of "the" with "a".

He writes axioms like:

1 ALL(dom):ALL(cod):ALL(f):ALL(g):[Set(dom) & Set(cod) &
ALL(a):[a e dom => f(a) e cod] & ALL(a):[a e dom => g(a) e cod]
=> [f=g <=> ALL(a):[a e dom => f(a)=g(a)]]]
Axiom

But thinks about them in terms of:

1 ALL(f):ALL(g):THE(dom):THE(cod):[Set(dom) & Set(cod) &
ALL(a):[a e dom => f(a) e cod] & ALL(a):[a e dom => g(a) e cod]
=> [f=g <=> ALL(a):[a e dom => f(a)=g(a)]]]
Axiom

Just plain crazy....

THE: Is his mind reading quantifier.

So Dan Christensen still does not
believe that you cannot infer:

f : X -> X <=> ALL(a):[a in X => f(a) in X]

Easy counter example f = {(1,1),(2,2)} and X={1}, it
satisfies ALL(a):[a in X => f(a) in X], but it does not
satisfy f : X -> X, since dom(f)={1,2} =/= X.

Dan Christensen schrieb am Montag, 18. April 2022 um 19:26:50 UTC+2:
> > Hence "f: X --> X" means "f is a function with domain X and codomain X."
> You can also infer this from: ALL(a):[a in x => f(a) in x].
> Ultimately, it must come to this even with your "set theoretic" approach.

On Monday, April 18, 2022 at 4:32:28 PM UTC-4, Mostowski Collapse (aka Jan Burse) wrote:
> So Dan Christensen still does not
> believe that you cannot infer:
>
> f : X -> X <=> ALL(a):[a in X => f(a) in X]
>
> Easy counter example f = {(1,1),(2,2)} and X={1}, it
> satisfies ALL(a):[a in X => f(a) in X], but it does not
> satisfy f : X -> X, since dom(f)={1,2} =/= X.
>

No "counter-example" here, Jan Burse. If X = {1}, then ALL(a):[a in X => f(a) in X] and f: X --> X mean the same thing.

Maybe you didn't know, but {1} =/= {1, 2}. We are not talking about your mystical "dark elements" here, Jan Burse.

Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com

On Tuesday, April 19, 2022 at 6:13:53 AM UTC+2, Dan Christensen wrote:
> On Monday, April 18, 2022 at 4:32:28 PM UTC-4, Mostowski Collapse (aka Jan Burse) wrote:
> >
> > So Dan Christensen still does not believe that [one] cannot infer:
> >
> > f : X -> X <=> ALL(a):[a in X => f(a) in X]
> >
> > Easy counter example f = {(1,1),(2,2)} and X={1}, it
> > satisfies ALL(a):[a in X => f(a) in X], but it does not
> > satisfy f : X -> X, since dom(f)={1,2} =/= X.
> >
> No "counter-example" here, Jan Burse. If X = {1}, then <bla bla bla>

Holy shit. You are in the same category as WM, JG and AP now, Dan.

Hint: JB/MC defined a function f: {1, 2} -> {1, 2}.

Now Ax(x e {1} -> f(x) e {1}), but f: {1} --> {1} does not hold, since f is NOT a function from {1} to {1} (by definition).

The biggest problem, he denies his own U Spec inference rule:

Dan Christensen schrieb am Donnerstag, 21. April 2022 um 16:30:36 UTC+2:
> > the ad hoc axiom can prove g ~ h with g(-1/2)=1/2 & h(-1/2)=1/2,
> Another domain? Make up your mind, Jan Burse!

Thats just like Putin, no we didn't invade Ukraine. Balant denial.

Fritz Feldhase schrieb am Dienstag, 19. April 2022 um 06:50:21 UTC+2:
> On Tuesday, April 19, 2022 at 6:13:53 AM UTC+2, Dan Christensen wrote:
> > On Monday, April 18, 2022 at 4:32:28 PM UTC-4, Mostowski Collapse (aka Jan Burse) wrote:
> > >
> > > So Dan Christensen still does not believe that [one] cannot infer:
> > >
> > > f : X -> X <=> ALL(a):[a in X => f(a) in X]
> > >
> > > Easy counter example f = {(1,1),(2,2)} and X={1}, it
> > > satisfies ALL(a):[a in X => f(a) in X], but it does not
> > > satisfy f : X -> X, since dom(f)={1,2} =/= X.
> > >
> > No "counter-example" here, Jan Burse. If X = {1}, then <bla bla bla>
>
> Holy shit. You are in the same category as WM, JG and AP now, Dan.
>
> Hint: JB/MC defined a function f: {1, 2} -> {1, 2}.
>
> Now Ax(x e {1} -> f(x) e {1}), but f: {1} --> {1} does not hold, since f is NOT a function from {1} to {1} (by definition).

On Tuesday, April 19, 2022 at 12:13:53 AM UTC-4, Dan Christensen wrote:
> On Monday, April 18, 2022 at 4:32:28 PM UTC-4, Mostowski Collapse (aka Jan Burse) wrote:
> > So Dan Christensen still does not
> > believe that you cannot infer:
> >
> > f : X -> X <=> ALL(a):[a in X => f(a) in X]
> >

The arrow notation is not built into DC Proof. If I want to formally state that f is a function mapping the elements of set x to the elements of set y, I would write:

ALL(a):[a in x => f(a) in y]

I would only use f: x --> y as an informal abbreviation.

Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com

But ALL(a):[a in x => f(a) in y] and f : x -> y are not
logical equivalent. So your are not allowed to replace
the later by the former in all circumstances.

Dan Christensen schrieb am Donnerstag, 21. April 2022 um 19:07:10 UTC+2:
> On Tuesday, April 19, 2022 at 12:13:53 AM UTC-4, Dan Christensen wrote:
> > On Monday, April 18, 2022 at 4:32:28 PM UTC-4, Mostowski Collapse (aka Jan Burse) wrote:
> > > So Dan Christensen still does not
> > > believe that you cannot infer:
> > >
> > > f : X -> X <=> ALL(a):[a in X => f(a) in X]
> > >
> The arrow notation is not built into DC Proof. If I want to formally state that f is a function mapping the elements of set x to the elements of set y, I would write:
>
> ALL(a):[a in x => f(a) in y]
>
> I would only use f: x --> y as an informal abbreviation.
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com

Mostowski Collapse wrote:

> But ALL(a):[a in x => f(a) in y] and f : x -> y are not logical
> equivalent. So your are not allowed to replace
> the later by the former in all circumstances.

here's your nazis you are starving for. Beating children, disgusting sons
of the bitches. Strange your govt is not allying with Russia removing
these nazis wherever they are. There are shitholes countries, *knowingly*
arming the nazis with hard weaponry. The new *_bio_weapon_labs_* nazis.

Proof of Ukrainian Neo-Nazi Satanism and Underground Biolabs. Is Putin at
War With The NWO https://www.bitchute.com/video/Wj54U4w9JbeP/

Dan Christensen wrote:

> The arrow notation is not built into DC Proof. If I want to formally
> state that f is a function mapping the elements of set x to the elements
> of set y, I would write: ALL(a):[a in x => f(a) in y]

you look like a nazi. Here are your nazis, you are starving for. Beating
children, disgusting sons of the bitches. Strange your govt is not allying
with Russia removing these nazis wherever they are. There are shitholes
countries, *knowingly* arming the nazis with hard weaponry. The new
*_bio_weapon_labs_* nazis.

Proof of Ukrainian Neo-Nazi Satanism and Underground Biolabs. Is Putin at
War With The NWO https://www.bitchute.com/video/Wj54U4w9JbeP/

Thank you micro penis, for displaying the morron you are,
this is quite some recurring laugh. BTW they found a dead
mouse in a Putler copter:

Marvelous Russian "Flying Tank"
https://www.youtube.com/watch?v=z7G8RKJBH1w

Don't know whether fake or real... LoL

Sam Kaloxylos schrieb am Donnerstag, 21. April 2022 um 22:50:45 UTC+2:
> Proof of Ukrainian Neo-Nazi Satanism and Underground Biolabs. Is Putin at
> War With The NWO https://www.bitchute.com/video/Wj54U4w9JbeP/

LoL, **demilitarized** Ka-52 "Alligator"

Mostowski Collapse schrieb am Donnerstag, 21. April 2022 um 23:19:22 UTC+2:
> Thank you micro penis, for displaying the morron you are,
> this is quite some recurring laugh. BTW they found a dead
> mouse in a Putler copter:
>
> Marvelous Russian "Flying Tank"
> https://www.youtube.com/watch?v=z7G8RKJBH1w
>
> Don't know whether fake or real... LoL
> Sam Kaloxylos schrieb am Donnerstag, 21. April 2022 um 22:50:45 UTC+2:
> > Proof of Ukrainian Neo-Nazi Satanism and Underground Biolabs. Is Putin at
> > War With The NWO https://www.bitchute.com/video/Wj54U4w9JbeP/

Mostowski Collapse wrote:

> this is quite some recurring laugh. BTW they found a dead mouse in a
> Putler copter:

You don't undrestand engilsh. You, *fake_money* shithole nazi countries,
turned anglo-saxon santa clauss "christianity" overnight, are to be
dismissed. And so, the russian army are treating humanly these satanists.

*_"those_nazi_should_be_shot,_and_that_would_be_merciful"_*.

*_our_govt_are_paying_for_that,_and_want_to_make_ukraine_big_israel_*

Proof of Ukrainian Neo-Nazi Satanism and Underground Biolabs. Is Putin
at War With The NWO https://www.bitchute.com/video/Wj54U4w9JbeP/

micro penis got also some function axiom wrong...

Sam Kaloxylos schrieb am Donnerstag, 21. April 2022 um 23:45:45 UTC+2:
> Mostowski Collapse wrote:
>
> > this is quite some recurring laugh. BTW they found a dead mouse in a
> > Putler copter:
> You don't undrestand engilsh. You, *fake_money* shithole nazi countries,
> turned anglo-saxon santa clauss "christianity" overnight, are to be
> dismissed. And so, the russian army are treating humanly these satanists.
>
> *_"those_nazi_should_be_shot,_and_that_would_be_merciful"_*.
>
> *_our_govt_are_paying_for_that,_and_want_to_make_ukraine_big_israel_*
> Proof of Ukrainian Neo-Nazi Satanism and Underground Biolabs. Is Putin
> at War With The NWO https://www.bitchute.com/video/Wj54U4w9JbeP/

Are you a gator? No!
But DC Proof looks dead, so I come over and investigate.
But that makes you an investigator.

Why isn’t gator attacking you?!?!
https://www.youtube.com/watch?v=3nTbQlZsQv0

Mostowski Collapse wrote:

> Are you a gator? No!
> But DC Proof looks dead, so I come over and investigate.
> But that makes you an investigator.

You are an idiot. A stupid nazi. Proofs:

Die Wahrheit über den Schauspieler Selenski der Euch in den dritten
Weltkrieg führen will🤮 https://www.bitchute.com/video/qCCl5XnOCTP6/

Ding Dong Vaseline. Thats a good match for micro penis.

LoL

Dong Vassilikos schrieb am Sonntag, 24. April 2022 um 23:19:39 UTC+2:
> Mostowski Collapse wrote:
>
> > Are you a gator? No!
> > But DC Proof looks dead, so I come over and investigate.
> > But that makes you an investigator.
> You are an idiot. A stupid nazi. Proofs:
>
> Die Wahrheit über den Schauspieler Selenski der Euch in den dritten
> Weltkrieg führen will🤮 https://www.bitchute.com/video/qCCl5XnOCTP6/

Mostowski Collapse wrote:

> Ding Dong Vaseline. Thats a good match for micro penis. LoL
>
> Dong Vassilikos schrieb am Sonntag, 24. April 2022 um 23:19:39 UTC+2:
>> Mostowski Collapse wrote:
>>
>> > Are you a gator? No!
>> > But DC Proof looks dead, so I come over and investigate.
>> > But that makes you an investigator.
>> You are an idiot. A stupid nazi. Proofs:
>>
>> Die Wahrheit über den Schauspieler Selenski der Euch in den dritten
>> Weltkrieg führen will🤮 https://www.bitchute.com/video/qCCl5XnOCTP6/

Also, you are stupid nazi "micro penises" obsessed pedophile.

What sits in the corner and cries all days, because
Selenski is not his homo partner? Its Luigi micro penis!

Maybe try Putler as your bed warmer ... Or Kyrill ...

Dong Vassilikos schrieb am Sonntag, 24. April 2022 um 23:51:37 UTC+2:
> Mostowski Collapse wrote:
>
> > Ding Dong Vaseline. Thats a good match for micro penis. LoL
> >
> > Dong Vassilikos schrieb am Sonntag, 24. April 2022 um 23:19:39 UTC+2:
> >> Mostowski Collapse wrote:
> >>
> >> > Are you a gator? No!
> >> > But DC Proof looks dead, so I come over and investigate.
> >> > But that makes you an investigator.
> >> You are an idiot. A stupid nazi. Proofs:
> >>
> >> Die Wahrheit über den Schauspieler Selenski der Euch in den dritten
> >> Weltkrieg führen will🤮 https://www.bitchute.com/video/qCCl5XnOCTP6/
> Also, you are stupid nazi "micro penises" obsessed pedophile.

Doesn't make any sense to prove existence of add/3 with 762 proof lines.
The problem is you have now Peano induction schema:

P(0) & ALL(x):[P(x+1) => P(x)]
------------------------------------------------
ALL(y):P(y)

You can prove it much shorter if you have such a schema. Thats
usually what they teach in University.

Dan Christensen schrieb am Samstag, 30. April 2022 um 22:39:44 UTC+2:
> This is how it is done: https://dcproof.com/ConstructAddFunction.htm

Corr.: Typo

> The problem is you have no Peano induction schema:
>
> P(0) & ALL(x):[P(x) => P(x+1)]
> ------------------------------------------------
> ALL(y):P(y)

Sorry, its already late...

Mostowski Collapse schrieb am Samstag, 30. April 2022 um 23:37:18 UTC+2:
> Doesn't make any sense to prove existence of add/3 with 762 proof lines.
> The problem is you have now Peano induction schema:
>
> P(0) & ALL(x):[P(x+1) => P(x)]
> ------------------------------------------------
> ALL(y):P(y)
>
> You can prove it much shorter if you have such a schema. Thats
> usually what they teach in University.
>
> Dan Christensen schrieb am Samstag, 30. April 2022 um 22:39:44 UTC+2:
> > This is how it is done: https://dcproof.com/ConstructAddFunction.htm