Hier is an example of a "discernibility" which is
related to the Terrence Tao and Bourbaki approach,
why the Terrence Tao and Bourbaki approac is

found in mathematical text books. How would you define:

is_surjective(f) ?

By using DC Proof subst, this would then lead to:

f=g, is_surfjective(f) => is_surjective(g)

And hence, also to:

is_surfjective(f), ~is_surjective(g) => f=\=g

But can we prove such an example of f=\=g
also without relying on DC Proof subst? Is
your equivalence relation an equality?

What if you would not define the operator
=, but an other operator ~, which doesn't have
DC Proof subst. Would this other operator

be an equivalence relation or is this axiom here turd
(I have change = to ~, question is whether your
~ is an equality or only an equivalence relation)

4. ALL(dom):ALL(cod):ALL(f1):ALL(f2):[Set(dom) & Set(cod)
& Function(f1,dom,cod) & Function(f2,dom,cod) <---- New
=> [f1~f2 <=> ALL(a):[a in dom => f1(a)=f2(a)]]]
Axiom

Dan Christensen schrieb am Donnerstag, 28. Juli 2022 um 11:02:33 UTC+2:
> See my reply just now to your identical posting at sci.logic
>
> Dan
> On Thursday, July 28, 2022 at 3:18:49 AM UTC-4, Mostowski Collapse wrote:
> > Against Dan O Matik nonsense claim "This definition says NOTHING
> > about the equality of pairs of functions with different domains.".
> > Wrong, an equality that satisfies 4), has inqueality:
> >
> [snip]

You really have the custom of talking nonsense
all day long, without using your brain.

More nonsense flowing in:
> Since they are functions with different codomains,
however, they are not comparable.

Youre DC Proof tells me something else, here
is a proof that they are comparable, and

in particular that we have:

6 ~f=g
Conclusion, 3

If you don't want this to happen, you need
to use another relation symbol in your function

Equality axiom. Here is the full proof:

-------------------- cut here ----------------

1 Surjective(f)
Axiom

2 ~Surjective(g)
Axiom

3 f=g
Premise

4 Surjective(g)
Substitute, 3, 1

5 Surjective(g) & ~Surjective(g)
Join, 4, 2

6 ~f=g
Conclusion, 3

-------------------- cut here ----------------

The same proof does also work with your nonsense
Surjective(_,_,_), same result. Doesn't matter whether its

unary Surjective(_) or your philosophy department
nonsense ternary Surjective(_,_,_):

6 ~f=g
Conclusion, 3

For a full proof see here:

-------------------- begin cut here ----------------

1 Surjective(f,dom,cod)
Axiom

2 ~Surjective(g,dom,cod)
Axiom

3 f=g
Premise

4 Surjective(g,dom,cod)
Substitute, 3, 1

5 ~Surjective(g,dom,cod) & Surjective(g,dom,cod)
Join, 2, 4

6 ~f=g
Conclusion, 3

-------------------- end cut here ----------------

Mostowski Collapse schrieb am Freitag, 29. Juli 2022 um 17:42:27 UTC+2:
> You really have the custom of talking nonsense
> all day long, without using your brain.
>
> More nonsense flowing in:
> > Since they are functions with different codomains,
> however, they are not comparable.
>
> Youre DC Proof tells me something else, here
> is a proof that they are comparable, and
>
> in particular that we have:
>
> 6 ~f=g
> Conclusion, 3
>
> If you don't want this to happen, you need
> to use another relation symbol in your function
>
> Equality axiom. Here is the full proof:
>
> -------------------- cut here ----------------
>
>
> 1 Surjective(f)
> Axiom
>
> 2 ~Surjective(g)
> Axiom
>
> 3 f=g
> Premise
>
> 4 Surjective(g)
> Substitute, 3, 1
>
> 5 Surjective(g) & ~Surjective(g)
> Join, 4, 2
>
> 6 ~f=g
> Conclusion, 3
>
> -------------------- cut here ----------------

Oops, no, the ternary Surjective(_,_,_) could be the
loophole why Dan-O-Matik refuses to abandon it.
In the example there is cod1 and cod2 causing

something to be not Surjective(_,_,_).
When we have, with cod1=\=cod2:

1 Surjective(f,dom,cod1)
Axiom

2 ~Surjective(g,dom,cod2)
Axiom

We cannot anymore derive ~f=g. Exept when
we can force the proof to use:

Surjective(f) <=> EXIST(dom):EXIST(cod):Surjective(f,dom,cod)

But ~Surjective(g,dom,cod2) does not imply
~EXIST(dom):EXIST(cod):Surjective(g,dom,cod)
this would be a fallacy. If we would have

this property on the other hand:

EXISTUNIQUE(dom):EXISTUNIQUE(cod):Function(f,dom,cod)

We could define:

Surjective(f) <=> EXIST(dom):EXIST(cod):(Function(f,dom,cod) & Surjective(f,dom,cod))

And we could do our thing, since we would also have:

Surjective(f) <=> ALL(dom):ALL(cod):(Function(f,dom,cod) => Surjective(f,dom,cod))

Mostowski Collapse schrieb am Freitag, 29. Juli 2022 um 17:46:56 UTC+2:
> The same proof does also work with your nonsense
> Surjective(_,_,_), same result. Doesn't matter whether its
>
> unary Surjective(_) or your philosophy department
> nonsense ternary Surjective(_,_,_):
>
> 6 ~f=g
> Conclusion, 3
>
> For a full proof see here:
>
> -------------------- begin cut here ----------------
>
> 1 Surjective(f,dom,cod)
> Axiom
>
> 2 ~Surjective(g,dom,cod)
> Axiom
>
> 3 f=g
> Premise
>
> 4 Surjective(g,dom,cod)
> Substitute, 3, 1
>
> 5 ~Surjective(g,dom,cod) & Surjective(g,dom,cod)
> Join, 2, 4
>
> 6 ~f=g
> Conclusion, 3
>
> -------------------- end cut here ----------------
> Mostowski Collapse schrieb am Freitag, 29. Juli 2022 um 17:42:27 UTC+2:
> > You really have the custom of talking nonsense
> > all day long, without using your brain.
> >
> > More nonsense flowing in:
> > > Since they are functions with different codomains,
> > however, they are not comparable.
> >
> > Youre DC Proof tells me something else, here
> > is a proof that they are comparable, and
> >
> > in particular that we have:
> >
> > 6 ~f=g
> > Conclusion, 3
> >
> > If you don't want this to happen, you need
> > to use another relation symbol in your function
> >
> > Equality axiom. Here is the full proof:
> >
> > -------------------- cut here ----------------
> >
> >
> > 1 Surjective(f)
> > Axiom
> >
> > 2 ~Surjective(g)
> > Axiom
> >
> > 3 f=g
> > Premise
> >
> > 4 Surjective(g)
> > Substitute, 3, 1
> >
> > 5 Surjective(g) & ~Surjective(g)
> > Join, 4, 2
> >
> > 6 ~f=g
> > Conclusion, 3
> >
> > -------------------- cut here ----------------

Mostowski Collapse wrote:

> You really have the custom of talking nonsense all day long, without
> using your brain.
>
> More nonsense flowing in:
>> Since they are functions with different codomains,
> however, they are not comparable.

amazing stupid this nazi, he is using *different codomains* same sentence.
What an idiot.

here is the lying cocaine zelenske say he is exporting grains from Odesa.
The proofs shows he is not exporting anything, but Russia.

https://www.marinetraffic.com/en/ais/home/centerx:33.8/centery:45.1/zoom:7

these khakhole khazars are not even looking at proofs before pushing it
like shit in mainstream media.

everybody with a good heart should take a screenshot of the activity,
every day. I am wondering why Russia is not ending these lying nazis a bit
faster.

i did nazi this coming such a question,
but I guess because they suck, just like
micro penis aka luigi is a cock sucker?

Civin Santini schrieb:
> I am wondering why Russia is not ending these lying nazis a bit faster.
>

Mostowski Collapse wrote:

> i did nazi this coming such a question, but I guess because they suck,
> just like micro penis aka luigi is a cock sucker?

ou cant suck a cock, impossible. You are a nazi idiot. Your country is a
*fake_money* shithole, not even existent in a few years.

the lying khazar cocaine zelenske is saying Odesa is exporting grains. The
reality shows he's a lying khazar bitch. He eats pig and other oddities.

https://www.marinetraffic.com/en/ais/home/centerx:33.8/centery:45.1/zoom:7

you nazis are a lying bitch.

Yeah, don't eat pig if you are muslim.

Brock Rocca schrieb am Freitag, 29. Juli 2022 um 18:43:32 UTC+2:
> Mostowski Collapse wrote:
>
>
> > i did nazi this coming such a question, but I guess because they suck,
> > just like micro penis aka luigi is a cock sucker?
> ou cant suck a cock, impossible. You are a nazi idiot. Your country is a
> *fake_money* shithole, not even existent in a few years.
>
> the lying khazar cocaine zelenske is saying Odesa is exporting grains. The
> reality shows he's a lying khazar bitch. He eats pig and other oddities.
> https://www.marinetraffic.com/en/ais/home/centerx:33.8/centery:45.1/zoom:7
> you nazis are a lying bitch.

Mostowski Collapse wrote:

> Yeah, don't eat pig if you are muslim.

not about muslims, you stinking nazi khazar. You should not eat pig, as
khazar. You lying stinking pig. Dr. Brock Rocca is consistent. You, NOT.
You are fucking nazi khazar. Your time is coming on the manifold.

> Brock Rocca schrieb am Freitag, 29. Juli 2022 um 18:43:32 UTC+2:
>> Mostowski Collapse wrote:
>>
>>
>> > i did nazi this coming such a question, but I guess because they
>> > suck,
>> > just like micro penis aka luigi is a cock sucker?
>> ou cant suck a cock, impossible. You are a nazi idiot. Your country is
>> a *fake_money* shithole, not even existent in a few years.
>>
>> the lying khazar cocaine zelenske is saying Odesa is exporting grains.
>> The reality shows he's a lying khazar bitch. He eats pig and other
>> oddities.
>> https://www.marinetraffic.com/en/ais/home/centerx:33.8/centery:45.1/
zoom:7
>> you nazis are a lying bitch.

Yeah you shouldnt eat pork if you are vegetarian.

Tory Napoliello schrieb am Freitag, 29. Juli 2022 um 20:28:37 UTC+2:
> Mostowski Collapse wrote:
>
> > Yeah, don't eat pig if you are muslim.
> not about muslims, you stinking nazi khazar. You should not eat pig, as
> khazar. You lying stinking pig. Dr. Brock Rocca is consistent. You, NOT.
> You are fucking nazi khazar. Your time is coming on the manifold.
> > Brock Rocca schrieb am Freitag, 29. Juli 2022 um 18:43:32 UTC+2:
> >> Mostowski Collapse wrote:
> >>
> >>
> >> > i did nazi this coming such a question, but I guess because they
> >> > suck,
> >> > just like micro penis aka luigi is a cock sucker?
> >> ou cant suck a cock, impossible. You are a nazi idiot. Your country is
> >> a *fake_money* shithole, not even existent in a few years.
> >>
> >> the lying khazar cocaine zelenske is saying Odesa is exporting grains.
> >> The reality shows he's a lying khazar bitch. He eats pig and other
> >> oddities.
> >> https://www.marinetraffic.com/en/ais/home/centerx:33.8/centery:45.1/
> zoom:7
> >> you nazis are a lying bitch.

Meanwhile for us non-vegans:

World’s OLDEST Restaurant!! SPANISH FOOD for 300 Years in Madrid, Spain!!
https://m.youtube.com/watch?v=iQIAtTJ9Sj4

Mostowski Collapse schrieb am Freitag, 29. Juli 2022 um 22:52:02 UTC+2:
> Yeah you shouldnt eat pork if you are vegetarian.
> Tory Napoliello schrieb am Freitag, 29. Juli 2022 um 20:28:37 UTC+2:
> > Mostowski Collapse wrote:
> >
> > > Yeah, don't eat pig if you are muslim.
> > not about muslims, you stinking nazi khazar. You should not eat pig, as
> > khazar. You lying stinking pig. Dr. Brock Rocca is consistent. You, NOT..
> > You are fucking nazi khazar. Your time is coming on the manifold.
> > > Brock Rocca schrieb am Freitag, 29. Juli 2022 um 18:43:32 UTC+2:
> > >> Mostowski Collapse wrote:
> > >>
> > >>
> > >> > i did nazi this coming such a question, but I guess because they
> > >> > suck,
> > >> > just like micro penis aka luigi is a cock sucker?
> > >> ou cant suck a cock, impossible. You are a nazi idiot. Your country is
> > >> a *fake_money* shithole, not even existent in a few years.
> > >>
> > >> the lying khazar cocaine zelenske is saying Odesa is exporting grains.
> > >> The reality shows he's a lying khazar bitch. He eats pig and other
> > >> oddities.
> > >> https://www.marinetraffic.com/en/ais/home/centerx:33.8/centery:45.1/
> > zoom:7
> > >> you nazis are a lying bitch.

In Bourbaki g = (G, A, B). You can extract dom and cod from
the function, because its an intrinsic parameter, its a property of g.
Same in Terrence Tao, its only verbally in the text, via anaphora.

But its basically the same as Bourbaki. But I guess even if you
try to do it nevertheless in DC Proof, i.e. an unary surjective(f),
you will possibly produce yet another nonsense, like this here:

- The Kind is bald and The King is not bald

I remember the Russells Definite Description thread,
when both French King is bald and French Kind is not
bald, became true, because Dan-O-Matik translated

it to ALL() something. How hillarious. I guess we will
experience more entertainment of this sort the next weeks.

Dan Christensen schrieb am Donnerstag, 28. Juli 2022 um 11:02:33 UTC+2:
> See my reply just now to your identical posting at sci.logic

Well it says:

~(f=g)

here:

6 ~f=g
Conclusion, 3

http://www.rubycap.ch/dcproof16_compare.html

So who is right? Your Equality Axiom who wants
f=g UNDEFIND or the rest of DC Poop who wants f=g FALSE.

LMAO!

Exercise: And why does this even happen? You
verifyed reflexivity, symmetry and transitivity for the
relation defined in your Axiom. What is missing?

I downloaded the new version dcproof17.exe. It has
built-in this equality axiom. It doesn't define Eq(f,g,dom,cod),
it defines f=g in DC Poop as follows:

1 ALL(dom):ALL(cod):ALL(f1):ALL(f2):[Set(dom) & Set(cod)
& Function(f1,dom,cod) & Function(f2,dom,cod)
=> [f1=f2 <=> ALL(a):[a ε dom => f1(a)=f2(a)]]]
Fn Equality

Similarly you don't need to define Surjective(f,dom,cod),
you can define Surjective(f) as follows:

2 ALL(dom):ALL(cod):ALL(f):[Set(dom) & Set(cod)
& Function(f,dom,cod)
=> [Surjective(f) <=> ALL(b):[b ε cod => EXIST(a):[a ε dom & f(a)=b]]]]
Axiom

Whats so difficult? Now you can easily prove:

Surjective(f)
~Surjective(g)

This is left as an exercise. This was part of THE EXERCISE .

On Sunday, August 14, 2022 at 4:00:57 AM UTC-4, Mostowski Collapse wrote:
> I downloaded the new version dcproof17.exe. It has
> built-in this equality axiom. It doesn't define Eq(f,g,dom,cod)

[snip]

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

Dan

Very good point Dany Boy:

Dan Christensen schrieb am Sonntag, 14. August 2022 um 15:32:12 UTC+2:
> The whole point of the Function Equality Axiom was to give meaning to f=g

And whats the point of a definition for Surjective(_)?

Dan Christensen schrieb am Sonntag, 14. August 2022 um 15:38:21 UTC+2:
> On Sunday, August 14, 2022 at 4:00:57 AM UTC-4, Mostowski Collapse wrote:
> > I downloaded the new version dcproof17.exe. It has
> > built-in this equality axiom. It doesn't define Eq(f,g,dom,cod)
> [snip]
>
> See my reply just now to identical posting at sci.logic.
>
> Dan

You can EASILY define Surjective(f) as follows:

2 ALL(dom):ALL(cod):ALL(f):[Set(dom) & Set(cod)
& Function(f,dom,cod)
=> [Surjective(f) <=> ALL(b):[b ε cod => EXIST(a):[a ε dom & f(a)=b]]]]
Axiom

Whats so difficult? Now you can easily prove:

Surjective(f)
~Surjective(g)

This is left as an exercise. This was part of THE EXERCISE .
You failed successfully this exercise. Bravo Dany Boy.

Mostowski Collapse schrieb am Sonntag, 14. August 2022 um 15:53:06 UTC+2:
> Very good point Dany Boy:
>
> Dan Christensen schrieb am Sonntag, 14. August 2022 um 15:32:12 UTC+2:
> > The whole point of the Function Equality Axiom was to give meaning to f=g
>
> And whats the point of a definition for Surjective(_)?
> Dan Christensen schrieb am Sonntag, 14. August 2022 um 15:38:21 UTC+2:
> > On Sunday, August 14, 2022 at 4:00:57 AM UTC-4, Mostowski Collapse wrote:
> > > I downloaded the new version dcproof17.exe. It has
> > > built-in this equality axiom. It doesn't define Eq(f,g,dom,cod)
> > [snip]
> >
> > See my reply just now to identical posting at sci.logic.
> >
> > Dan

On Sunday, August 14, 2022 at 9:55:00 AM UTC-4, Mostowski Collapse (Jan Burse) wrote:
> You can EASILY define Surjective(f) as follows:
> 2 ALL(dom):ALL(cod):ALL(f):[Set(dom) & Set(cod)
> & Function(f,dom,cod)
> => [Surjective(f) <=> ALL(b):[b ε cod => EXIST(a):[a ε dom & f(a)=b]]]]
> Axiom
>

You are grasping at straws, Jan Burse. Why would I adopt such an unconventional definition when there is nothing wrong with the standard one that I use? (See Tao)

BTW you can concoct all the wonky definitions you want, Jan Burse. As long as they are syntactically correct, DC Proof can probably handle them.

Dan

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

Dan Christensen wrote:

> On Sunday, August 14, 2022 at 4:00:57 AM UTC-4, Mostowski Collapse
> wrote:
>> I downloaded the new version dcproof17.exe. It has built-in this
>> equality axiom. It doesn't define Eq(f,g,dom,cod) [snip]
>
> See my reply just now to identical posting at sci.logic.

why on fuck would an imbecile like you post in sci.logic?? You have
nothing to do with logic, which is math, hence math and logic. You are a
nazi, you don't need logic. The logic to you nazis, goes out of the
window, automatically.

you capitalists are idiots. Not even knowing you are idiots.

On Sunday, August 14, 2022 at 12:33:50 PM UTC-4, Tadd Muraro wrote:
> Dan Christensen wrote:
>
> > On Sunday, August 14, 2022 at 4:00:57 AM UTC-4, Mostowski Collapse
> > wrote:
> >> I downloaded the new version dcproof17.exe. It has built-in this
> >> equality axiom. It doesn't define Eq(f,g,dom,cod) [snip]
> >
> > See my reply just now to identical posting at sci.logic.
> why on fuck would an imbecile like you post in sci.logic?? You have
> nothing to do with logic, which is math, hence math and logic. You are a
> nazi, you don't need logic. The logic to you nazis, goes out of the
> window, automatically.
>
> you capitalists are idiots. Not even knowing you are idiots.

So, how is that genocidal war of conquest going, Nazi boy? That bad!

It cannot end well for you, Nazi boy. Escape while you can. You probably don't have enough hard currency to bribe the Chinese authorities. Maybe North Korea may let you in for free. You could probably stand to lose a few pounds sitting at a computer screen all day.

On Sunday, August 14, 2022 at 5:18:55 PM UTC+2, Dan Christensen wrote:
>
> Why would I adopt such an unconventional definition when there is nothing wrong with the standard one that I use? (See Tao)

Tao's definition is totally nonsensical.

On Sunday, August 14, 2022 at 10:43:01 PM UTC-4, Fritz Feldhase wrote:
> On Sunday, August 14, 2022 at 5:18:55 PM UTC+2, Dan Christensen wrote:
> >
> > Why would I adopt such an unconventional definition when there is nothing wrong with the standard one that I use? (See Tao)
> Tao's definition is totally nonsensical.

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

Dan

Well the task is to prove "literally":

Surjective(f)
~Surjective(g)

And not some other nonsense.
The word literally means word for word, verbatim.
I made this already clear here a few days ago:

Mostowski Collapse schrieb am Montag, 8. August 2022 um 23:38:01 UTC+2:
> What is so difficult to understand in the word " literally ", it means
> " word for word " / " verbatim ", the task is to prove this:
>
> Surjective(f)
> ~Surjective(g)
>
> word for word. And nothing else.
https://groups.google.com/g/sci.logic/c/QSfRj2g1ur8/m/EqceW2QNAQAJ

Dan Christensen schrieb am Montag, 15. August 2022 um 06:23:11 UTC+2:
> On Sunday, August 14, 2022 at 10:43:01 PM UTC-4, Fritz Feldhase wrote:
> > On Sunday, August 14, 2022 at 5:18:55 PM UTC+2, Dan Christensen wrote:
> > >
> > > Why would I adopt such an unconventional definition when there is nothing wrong with the standard one that I use? (See Tao)
> > Tao's definition is totally nonsensical.
> See my reply just now to your identical claim at sci.logic.
>
> Dan

On Monday, August 15, 2022 at 3:46:21 AM UTC-4, Mostowski Collapse wrote:
> Well the task is to prove "literally":
>
> Surjective(f)
> ~Surjective(g)
>

No, the task was to prove:

ALL(a):[a in x => EXIST(b):[b in x & f(b)=a]] (which can be abbreviated Surjective(f,x,x))

EXIST(a):[a in y & ALL(b):[b in x => ~g(b)=a]] (which can be abbreviated ~Surjective(g,x,y))

where f: {0} --> {0}, g: {0} --> {0,1} and f(0)=g(0)=0

It may be possible to squeeze in some unconventional unary predicate for surjectivity as you suggest, but can I see no advantage in it.

Dan

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

On Monday, August 15, 2022 at 3:46:21 AM UTC-4, Mostowski Collapse wrote:

> > Concoct all the wonky definitions you want, Jan Burse. DC Proof can probably handle them as long are they are syntactically correct.
> Well the task is to prove "literally":
>
> Surjective(f)
> ~Surjective(g)
>

No, the task was to prove:

ALL(a):[a in x => EXIST(b):[b in x & f(b)=a]] (which can be abbreviated Surjective(f,x,x))

EXIST(a):[a in y & ALL(b):[b in x => ~g(b)=a]] (which can be abbreviated ~Surjective(g,x,y))

where f: {0} --> {0}, g: {0} --> {0,1} and f(0)=g(0)=0

It may be possible to squeeze in some unconventional unary predicate for surjectivity as you suggest, but can I see no advantage in it.

Dan

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