Thats possibly true, since this here:

34 x e s => f(x) e s
U Spec, 3

depends on stuff before line 30.
But we only know for sure whether your
Dedekind -> Peano proof works or not,

when the whole proof went through
regression. Meanwhile it might be subject
to evil shadows, according to your own

standards.

Dan Christensen schrieb am Donnerstag, 13. Januar 2022 um 18:38:39 UTC+1:
> On Thursday, January 13, 2022 at 10:46:21 AM UTC-5, Mostowski Collapse wrote:
>
> > Dan Christensen schrieb am Donnerstag, 13. Januar 2022 um 16:40:39 UTC+1:
> > > On Thursday, January 13, 2022 at 2:47:18 AM UTC-5, Mostowski Collapse wrote:
> > > > So you didn't do regression testing of your changes?
> > > > DC Proof is not a reliable to tool. It nowhere automatically
> > > > records in the generated HTML files the version of DC Proof.
> > > >
> > > > For example in the link
> > > > http://www.dcproof.com/ProofByInduction.html" rel="nofollow" target="_blank">http://www.dcproof.com/ProofByInduction.html
> > > > I find:
> > > >
> > > > Apply definition of n for f(x)
> > > >
> > > > 30 f(x) e n <=> f(x) e s & ALL(b):[Set(b)
> > > > & s1 e b
> > > > & ALL(c):[c e b & c e s => f(c) e b]
> > > > => f(x) e b]
> > > > U Spec, 11
> > > >
> > > > What is the f(x) e S before line 30?
> > > On line 1, f is defined to be a function on s. On line 28, we see that x in s. So, f(x) in s as on line 35.
> > >
> > > In none of the proofs I have posted here or at my blog do I assume that f(x) would be anything other than an element of a set, so the minor change to my Function Axiom presents no problem for my previous work. It just prevents a few wonky results. (Hee, hee!) And it makes the axiom a little easier to explain without overloading the function name. Non-programmers probably wouldn't get that f could be different but related things depending on the context.
> > But line 35 is after line 30. So you cannot use U Spec, 11.
> Lines 34 and 35 could easily be inserted BEFORE line 30 as would be required with my recent changes. Not a big deal. Like I said, in none of the proofs I have posted here or at my blog do I assume that f(x), for example, would be anything other than an element of a set
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com

On Thursday, January 13, 2022 at 1:19:30 PM UTC-5, Mostowski Collapse wrote:

> Dan Christensen schrieb am Donnerstag, 13. Januar 2022 um 18:38:39 UTC+1:
> > On Thursday, January 13, 2022 at 10:46:21 AM UTC-5, Mostowski Collapse wrote:
> >
> > > Dan Christensen schrieb am Donnerstag, 13. Januar 2022 um 16:40:39 UTC+1:
> > > > On Thursday, January 13, 2022 at 2:47:18 AM UTC-5, Mostowski Collapse wrote:
> > > > > So you didn't do regression testing of your changes?
> > > > > DC Proof is not a reliable to tool. It nowhere automatically
> > > > > records in the generated HTML files the version of DC Proof.
> > > > >
> > > > > For example in the link
> > > > > http://www.dcproof.com/ProofByInduction.html
> > > > > I find:
> > > > >
> > > > > Apply definition of n for f(x)
> > > > >
> > > > > 30 f(x) e n <=> f(x) e s & ALL(b):[Set(b)
> > > > > & s1 e b
> > > > > & ALL(c):[c e b & c e s => f(c) e b]
> > > > > => f(x) e b]
> > > > > U Spec, 11
> > > > >
> > > > > What is the f(x) e S before line 30?
> > > > On line 1, f is defined to be a function on s. On line 28, we see that x in s. So, f(x) in s as on line 35.
> > > >
> > > > In none of the proofs I have posted here or at my blog do I assume that f(x) would be anything other than an element of a set, so the minor change to my Function Axiom presents no problem for my previous work. It just prevents a few wonky results. (Hee, hee!) And it makes the axiom a little easier to explain without overloading the function name. Non-programmers probably wouldn't get that f could be different but related things depending on the context.
> > > But line 35 is after line 30. So you cannot use U Spec, 11.
> > Lines 34 and 35 could easily be inserted BEFORE line 30 as would be required with my recent changes. Not a big deal. Like I said, in none of the proofs I have posted here or at my blog do I assume that f(x), for example, would be anything other than an element of a set

> Thats possibly true, since this here:
>
> 34 x e s => f(x) e s
> U Spec, 3
>
> depends on stuff before line 30.
> But we only know for sure whether your
> Dedekind -> Peano proof works or not,
>
> when the whole proof went through
> regression. Meanwhile it might be subject
> to evil shadows

In every proof where I introduced a function f mapping set x to set y, I have ALL(a):[a in x => f(a) in y]. Unlike you, I have no interest in drawing logical inferences about a function with argument(s) outside of its domain of definition. So, I am certain that all of my proofs can be easily converted.

See for example, my test version of constructing the add function on N at https://www.dcproof.com/ConstructAdditionNew.htm (712 lines). There you will find 16 examples of specifying function images like f(x) in various U Spec statements.

Dan

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

We are still waiting for your Dedekind - Peano proof.
Looks like you have taken the path of WM again,
he also claimed he found an inconsistency in

ZFC; but it was never published. Now you post
proofs that arent any proofs in dcproof5.exe,
welcome to the Kingdom of Cranks.

Dan Christensen schrieb am Donnerstag, 13. Januar 2022 um 19:54:55 UTC+1:
> On Thursday, January 13, 2022 at 1:19:30 PM UTC-5, Mostowski Collapse wrote:
>
> > Dan Christensen schrieb am Donnerstag, 13. Januar 2022 um 18:38:39 UTC+1:
> > > On Thursday, January 13, 2022 at 10:46:21 AM UTC-5, Mostowski Collapse wrote:
> > >
> > > > Dan Christensen schrieb am Donnerstag, 13. Januar 2022 um 16:40:39 UTC+1:
> > > > > On Thursday, January 13, 2022 at 2:47:18 AM UTC-5, Mostowski Collapse wrote:
> > > > > > So you didn't do regression testing of your changes?
> > > > > > DC Proof is not a reliable to tool. It nowhere automatically
> > > > > > records in the generated HTML files the version of DC Proof.
> > > > > >
> > > > > > For example in the link
> > > > > > http://www.dcproof.com/ProofByInduction.html" rel="nofollow" target="_blank">http://www.dcproof.com/ProofByInduction.html
> > > > > > I find:
> > > > > >
> > > > > > Apply definition of n for f(x)
> > > > > >
> > > > > > 30 f(x) e n <=> f(x) e s & ALL(b):[Set(b)
> > > > > > & s1 e b
> > > > > > & ALL(c):[c e b & c e s => f(c) e b]
> > > > > > => f(x) e b]
> > > > > > U Spec, 11
> > > > > >
> > > > > > What is the f(x) e S before line 30?
> > > > > On line 1, f is defined to be a function on s. On line 28, we see that x in s. So, f(x) in s as on line 35.
> > > > >
> > > > > In none of the proofs I have posted here or at my blog do I assume that f(x) would be anything other than an element of a set, so the minor change to my Function Axiom presents no problem for my previous work. It just prevents a few wonky results. (Hee, hee!) And it makes the axiom a little easier to explain without overloading the function name. Non-programmers probably wouldn't get that f could be different but related things depending on the context.
> > > > But line 35 is after line 30. So you cannot use U Spec, 11.
> > > Lines 34 and 35 could easily be inserted BEFORE line 30 as would be required with my recent changes. Not a big deal. Like I said, in none of the proofs I have posted here or at my blog do I assume that f(x), for example, would be anything other than an element of a set
> > Thats possibly true, since this here:
> >
> > 34 x e s => f(x) e s
> > U Spec, 3
> >
> > depends on stuff before line 30.
> > But we only know for sure whether your
> > Dedekind -> Peano proof works or not,
> >
> > when the whole proof went through
> > regression. Meanwhile it might be subject
> > to evil shadows
> In every proof where I introduced a function f mapping set x to set y, I have ALL(a):[a in x => f(a) in y]. Unlike you, I have no interest in drawing logical inferences about a function with argument(s) outside of its domain of definition. So, I am certain that all of my proofs can be easily converted.
>
> See for example, my test version of constructing the add function on N at https://www.dcproof.com/ConstructAdditionNew.htm (712 lines). There you will find 16 examples of specifying function images like f(x) in various U Spec statements.
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com

**************************************
Breaking News: A new form of dark matter revealed
**************************************

Like Schrödingers cat, there are now proofs that
exist and don't exist. For example Dan Christensen claims t
hat he knows (for my ~(m e n) and s(m)=0 example):

~ALL(a):[a e n => ~s(a)=0]

But he cannot prove it. This is a sensation. We
have found Gollums dog!

On Friday, May 6, 2022 at 11:14:08 AM UTC-4, Mostowski Collapse (aka Jan Burse) wrote:
> **************************************
> Breaking News: A new form of dark matter revealed
> **************************************
>
> Like Schrödingers cat, there are now proofs that
> exist and don't exist. For example Dan Christensen claims t
> hat he knows (for my ~(m e n) and s(m)=0 example):
>
> ~ALL(a):[a e n => ~s(a)=0]
>

Poor Jan Burse here has painted himself into yet another corner.

He claims that the set of integers Z with a "successor function" s(x)=x+1 satisfies Peano's Axioms. Now, we have -1 in Z. Apply his definition, we hav so s(-1)=0. This violates Peano's 4th Axiom that 0 has no predecessor. This supposed "successor function" on Z also violates Peano's 5th Axiom (Induction). Hint: Assume N is a subset of Z and -1 in Z but not in N.

Peano's Axioms in DC Proof format where n = the set of natural numbers N:

1. 0 in n
Axiom

2. ALL(a):[a in n => s(a) in n]
Axiom

3. ALL(a):ALL(b):[a in n & b in n => [s(a)=s(b) => a=b]]
Axiom

4. ALL(a):[a in n => ~s(a)=0]
Axiom

5. ALL(a):[Set(a) & ALL(b):[b in a => b in n]
=> [0 in a & ALL(b):[b in a => s(b) in a]
=> ALL(b):[b in n => b in a]]]
Axiom

Dan

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

No I did not claim that the set Z satisfies the Peano Axioms,
in the sende that we would substitute N by Z.

Where did I say that? You are bat shit crazy…

Dan Christensen schrieb am Freitag, 6. Mai 2022 um 18:21:28 UTC+2:
> On Friday, May 6, 2022 at 11:14:08 AM UTC-4, Mostowski Collapse (aka Jan Burse) wrote:
> > **************************************
> > Breaking News: A new form of dark matter revealed
> > **************************************
> >
> > Like Schrödingers cat, there are now proofs that
> > exist and don't exist. For example Dan Christensen claims t
> > hat he knows (for my ~(m e n) and s(m)=0 example):
> >
> > ~ALL(a):[a e n => ~s(a)=0]
> >
> Poor Jan Burse here has painted himself into yet another corner.
>
> He claims that the set of integers Z with a "successor function" s(x)=x+1 satisfies Peano's Axioms. Now, we have -1 in Z. Apply his definition, we hav so s(-1)=0. This violates Peano's 4th Axiom that 0 has no predecessor. This supposed "successor function" on Z also violates Peano's 5th Axiom (Induction). Hint: Assume N is a subset of Z and -1 in Z but not in N.
>
> Peano's Axioms in DC Proof format where n = the set of natural numbers N:
>
> 1. 0 in n
> Axiom
>
> 2. ALL(a):[a in n => s(a) in n]
> Axiom
>
> 3. ALL(a):ALL(b):[a in n & b in n => [s(a)=s(b) => a=b]]
> Axiom
>
> 4. ALL(a):[a in n => ~s(a)=0]
> Axiom
>
> 5. ALL(a):[Set(a) & ALL(b):[b in a => b in n]
> => [0 in a & ALL(b):[b in a => s(b) in a]
> => ALL(b):[b in n => b in a]]]
> Axiom
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com

Because -1 is not in N, this axiom is still
true, even if s : Z -> Z, thats pretty clear:

4. ALL(a):[a in N => ~s(a)=0]
Axiom

Just substitute a = -1, and you get

-1 e N => ~s(-1)=0

Which is vacously true, because -1 e N is false.
https://en.m.wikipedia.org/wiki/Vacuous_truth

Whats wrong with you? Got it now dumbo?

Mostowski Collapse schrieb am Freitag, 6. Mai 2022 um 18:38:56 UTC+2:
> No I did not claim that the set Z satisfies the Peano Axioms,
> in the sende that we would substitute N by Z.
>
> Where did I say that? You are bat shit crazy…
> Dan Christensen schrieb am Freitag, 6. Mai 2022 um 18:21:28 UTC+2:
> > On Friday, May 6, 2022 at 11:14:08 AM UTC-4, Mostowski Collapse (aka Jan Burse) wrote:
> > > **************************************
> > > Breaking News: A new form of dark matter revealed
> > > **************************************
> > >
> > > Like Schrödingers cat, there are now proofs that
> > > exist and don't exist. For example Dan Christensen claims t
> > > hat he knows (for my ~(m e n) and s(m)=0 example):
> > >
> > > ~ALL(a):[a e n => ~s(a)=0]
> > >
> > Poor Jan Burse here has painted himself into yet another corner.
> >
> > He claims that the set of integers Z with a "successor function" s(x)=x+1 satisfies Peano's Axioms. Now, we have -1 in Z. Apply his definition, we hav so s(-1)=0. This violates Peano's 4th Axiom that 0 has no predecessor. This supposed "successor function" on Z also violates Peano's 5th Axiom (Induction). Hint: Assume N is a subset of Z and -1 in Z but not in N.
> >
> > Peano's Axioms in DC Proof format where n = the set of natural numbers N:
> >
> > 1. 0 in n
> > Axiom
> >
> > 2. ALL(a):[a in n => s(a) in n]
> > Axiom
> >
> > 3. ALL(a):ALL(b):[a in n & b in n => [s(a)=s(b) => a=b]]
> > Axiom
> >
> > 4. ALL(a):[a in n => ~s(a)=0]
> > Axiom
> >
> > 5. ALL(a):[Set(a) & ALL(b):[b in a => b in n]
> > => [0 in a & ALL(b):[b in a => s(b) in a]
> > => ALL(b):[b in n => b in a]]]
> > Axiom
> > Dan
> >
> > Download my DC Proof 2.0 freeware at http://www.dcproof.com
> > Visit my Math Blog at http://www.dcproof.wordpress.com

Definition of vacously true:

In mathematics and logic, a vacuous truth is a conditional
or universal statement (a universal statement that can be converted
to a conditional statement) that is true because the antecedent
cannot be satisfied.
https://en.m.wikipedia.org/wiki/Vacuous_truth

All your „Peano Axioms“ are of the form ALL(a):[a e N => …]
so they are automatically vacously true for instantiations
with values outside of N.

The are vacously true, and not vacously false as you
think right now. Whats wrong with you?

Mostowski Collapse schrieb am Freitag, 6. Mai 2022 um 18:43:10 UTC+2:
> Because -1 is not in N, this axiom is still
> true, even if s : Z -> Z, thats pretty clear:
>
> 4. ALL(a):[a in N => ~s(a)=0]
> Axiom
>
> Just substitute a = -1, and you get
>
> -1 e N => ~s(-1)=0
>
> Which is vacously true, because -1 e N is false.
> https://en.m.wikipedia.org/wiki/Vacuous_truth
>
> Whats wrong with you? Got it now dumbo?
> Mostowski Collapse schrieb am Freitag, 6. Mai 2022 um 18:38:56 UTC+2:
> > No I did not claim that the set Z satisfies the Peano Axioms,
> > in the sende that we would substitute N by Z.
> >
> > Where did I say that? You are bat shit crazy…
> > Dan Christensen schrieb am Freitag, 6. Mai 2022 um 18:21:28 UTC+2:
> > > On Friday, May 6, 2022 at 11:14:08 AM UTC-4, Mostowski Collapse (aka Jan Burse) wrote:
> > > > **************************************
> > > > Breaking News: A new form of dark matter revealed
> > > > **************************************
> > > >
> > > > Like Schrödingers cat, there are now proofs that
> > > > exist and don't exist. For example Dan Christensen claims t
> > > > hat he knows (for my ~(m e n) and s(m)=0 example):
> > > >
> > > > ~ALL(a):[a e n => ~s(a)=0]
> > > >
> > > Poor Jan Burse here has painted himself into yet another corner.
> > >
> > > He claims that the set of integers Z with a "successor function" s(x)=x+1 satisfies Peano's Axioms. Now, we have -1 in Z. Apply his definition, we hav so s(-1)=0. This violates Peano's 4th Axiom that 0 has no predecessor. This supposed "successor function" on Z also violates Peano's 5th Axiom (Induction). Hint: Assume N is a subset of Z and -1 in Z but not in N.
> > >
> > > Peano's Axioms in DC Proof format where n = the set of natural numbers N:
> > >
> > > 1. 0 in n
> > > Axiom
> > >
> > > 2. ALL(a):[a in n => s(a) in n]
> > > Axiom
> > >
> > > 3. ALL(a):ALL(b):[a in n & b in n => [s(a)=s(b) => a=b]]
> > > Axiom
> > >
> > > 4. ALL(a):[a in n => ~s(a)=0]
> > > Axiom
> > >
> > > 5. ALL(a):[Set(a) & ALL(b):[b in a => b in n]
> > > => [0 in a & ALL(b):[b in a => s(b) in a]
> > > => ALL(b):[b in n => b in a]]]
> > > Axiom
> > > Dan
> > >
> > > Download my DC Proof 2.0 freeware at http://www.dcproof.com
> > > Visit my Math Blog at http://www.dcproof.wordpress.com

On Friday, May 6, 2022 at 12:38:56 PM UTC-4, Mostowski Collapse wrote:
> No I did not claim that the set Z satisfies the Peano Axioms,
> in the sende that we would substitute N by Z.
>
> Where did I say that? You are bat shit crazy…

Nice climbdown, crank boy! HA, HA, HA!!!

Dan

I wrote this like a thousend times. Your Peano Axioms,
nothing changed concerning N, are satisfied by:

succZ : Z -> Z
succQ : Q -> Q
succR : R -> R
succC : C -> C

Where C are the complex numbers. If you set s = succX.
In general they are satisfied by any:

s : A -> B

When s | N = succN.

Dan Christensen schrieb am Freitag, 6. Mai 2022 um 18:56:43 UTC+2:
> On Friday, May 6, 2022 at 12:38:56 PM UTC-4, Mostowski Collapse wrote:
> > No I did not claim that the set Z satisfies the Peano Axioms,
> > in the sende that we would substitute N by Z.
> >
> > Where did I say that? You are bat shit crazy…
> Nice climbdown, crank boy! HA, HA, HA!!!
>
> Dan

The notation f | A means f restricted to A.
Set theoretically it means:

f | A = { (x,y) | (x,y) e f & x e A }

Then s | N = succN, because succN | N = succN,
expresses the idea that s agrees with succN

on the domain N.

Mostowski Collapse schrieb am Freitag, 6. Mai 2022 um 19:04:18 UTC+2:
> I wrote this like a thousend times. Your Peano Axioms,
> nothing changed concerning N, are satisfied by:
>
> succZ : Z -> Z
> succQ : Q -> Q
> succR : R -> R
> succC : C -> C
>
> Where C are the complex numbers. If you set s = succX.
> In general they are satisfied by any:
>
> s : A -> B
>
> When s | N = succN.
> Dan Christensen schrieb am Freitag, 6. Mai 2022 um 18:56:43 UTC+2:
> > On Friday, May 6, 2022 at 12:38:56 PM UTC-4, Mostowski Collapse wrote:
> > > No I did not claim that the set Z satisfies the Peano Axioms,
> > > in the sende that we would substitute N by Z.
> > >
> > > Where did I say that? You are bat shit crazy…
> > Nice climbdown, crank boy! HA, HA, HA!!!
> >
> > Dan

Mostowski Collapse wrote:

> No I did not claim that the set Z satisfies the Peano Axioms,
> in the sende that we would substitute N by Z.
>
> Where did I say that? You are bat shit crazy…
>
> Dan Christensen schrieb am Freitag, 6. Mai 2022 um 18:21:28 UTC+2:

the "ukrainian" nazis openly committing *war_crimes*. Fuck you both.

Ukrainian military won't take Russian prisoners
https://www.bitchute.com/video/EVz1HEwOJOUg/

what is your name, Jan Bursolaski?

Mostowski Collapse wrote:

> I wrote this like a thousend times. Your Peano Axioms,
> nothing changed concerning N, are satisfied by:
> succZ : Z -> Z succQ : Q -> Q succR : R -> R succC : C -> C
>
> Dan Christensen schrieb am Freitag, 6. Mai 2022 um 18:56:43 UTC+2:

I rather was to say, the "ukrainian" nazis openly committing *war_crimes*.
And they still can't find the nazi in nazi "ukraine". Fuck you both.

Ukrainian military won't take Russian prisoners
https://www.bitchute.com/video/EVz1HEwOJOUg/

what is your name, Jan Burselski?

Kids don't do drugs, bitchute cocaine is a hell of a drug.
Not only that, your rosetta gets wide and red.

Reese Page schrieb:
> I dont want to live in this world anymore,
> I am an italian comrad and my ass hurts
> from beeing fucked by Putin.

Nice aquarium with Moskva submarine:
https://twitter.com/KLiitti/status/1522895652287655939/photo/1

Are these some Nazi fish nearby?

Mostowski Collapse schrieb:
>
> Kids don't do drugs, bitchute cocaine is a hell of a drug.
> Not only that, your rosetta gets wide and red.
>
> Reese Page schrieb:
> > I dont want to live in this world anymore,
> > I am an italian comrad and my ass hurts
> > from beeing fucked by Putin.

Mostowski Collapse wrote:

> Nice aquarium with Moskva submarine:
> https://twitter.com/KLiitti/status/1522895652287655939/photo/1
>
> Are these some Nazi fish nearby?
>
> Mostowski Collapse schrieb:
>>

this nazi bitch, Janeko Burseskij, as soon he wakes up, a twitter dick is sucked up.
How predictable. You are an idiot.

People are starving and Biden sending new $150 million weapons to Ukraine without democratic vote.
https://www.presstv.ir/Detail/2022/05/06/681635/Biden-sending-new--150-million-weapons-to-Ukraine

Russia destroyed US, Europe huge military stockpile in Kharkiv
https://www.presstv.ir/Detail/2022/05/07/681658/Ukraine-conflict-Russia-military-stockpile-Kharkiv-

North Korea tests giant ballistic missile ahead of Biden's visit to Seoul
https://www.presstv.ir/Detail/2022/05/07/681660/N-Korea-fires-2nd-missile-in-3-days-ignoring-US-nuke-warning

Ha Ha, micro penis aka Luigi, the only idiot
who doesn't understand whats the game right now.
The game is of course to make Ukraine a
second Afghanistan for Russia.

Nothing with nukes, only 10 years more
grueling war. Actually the war started already
in 2014 or before? So its already around 8
or more years?

You have just too much bitchute cocaine
in your veins, slowdown comrad.

LMAO!

Emmet Shibanuma schrieb am Samstag, 7. Mai 2022 um 15:32:50 UTC+2:
> I dont want to live in this world anymore,
> I am an italian comrad and my ass hurts
> from beeing fucked by Putin.

This article is more than 4 months old
Ukraine could be ‘next Afghanistan’ for Russia if it invades, US senator warns
https://www.theguardian.com/world/2021/dec/04/biden-putin-call-ukraine-russia-white-house

Mostowski Collapse schrieb am Samstag, 7. Mai 2022 um 15:37:18 UTC+2:
> Ha Ha, micro penis aka Luigi, the only idiot
> who doesn't understand whats the game right now.
> The game is of course to make Ukraine a
> second Afghanistan for Russia.
>
> Nothing with nukes, only 10 years more
> grueling war. Actually the war started already
> in 2014 or before? So its already around 8
> or more years?
>
> You have just too much bitchute cocaine
> in your veins, slowdown comrad.
>
> LMAO!
> Emmet Shibanuma schrieb am Samstag, 7. Mai 2022 um 15:32:50 UTC+2:
> > I dont want to live in this world anymore,
> > I am an italian comrad and my ass hurts
> > from beeing fucked by Putin.

Mostowski Collapse wrote:

> This article is more than 4 months old Ukraine could be ‘next
> Afghanistan’ for Russia if it invades, US senator warns

You read 4 months old articles, which country are you?? When will your
country construct such magnificent buildings, can you use a math modelling
tool?

https://cdni.russiatoday.com/files/2022.05/l/62753b4085f54049e92af89d.jpg

After Dan Christensen has claimed that:

subst( s, succZ, ALL(a):[a e n => ~s(a)=0] ) =\= ALL(a):[a e n => ~succZ(a)=0]

He thinks it gives ALL(a):[a e z => ~succZ(a)=0],
I am expecting Dan Christensen will soon talk about
ellipses that are oval, just like AP brain farto.

Hail DC 💩 Poop 💩, brain confusion guaranteed.

Mostowski Collapse schrieb am Freitag, 6. Mai 2022 um 19:08:52 UTC+2:
> The notation f | A means f restricted to A.
> Set theoretically it means:
>
> f | A = { (x,y) | (x,y) e f & x e A }
>
> Then s | N = succN, because succN | N = succN,
> expresses the idea that s agrees with succN
>
> on the domain N.
> Mostowski Collapse schrieb am Freitag, 6. Mai 2022 um 19:04:18 UTC+2:
> > I wrote this like a thousend times. Your Peano Axioms,
> > nothing changed concerning N, are satisfied by:
> >
> > succZ : Z -> Z
> > succQ : Q -> Q
> > succR : R -> R
> > succC : C -> C
> >
> > Where C are the complex numbers. If you set s = succX.
> > In general they are satisfied by any:
> >
> > s : A -> B
> >
> > When s | N = succN.
> > Dan Christensen schrieb am Freitag, 6. Mai 2022 um 18:56:43 UTC+2:
> > > On Friday, May 6, 2022 at 12:38:56 PM UTC-4, Mostowski Collapse wrote:
> > > > No I did not claim that the set Z satisfies the Peano Axioms,
> > > > in the sende that we would substitute N by Z.
> > > >
> > > > Where did I say that? You are bat shit crazy…
> > > Nice climbdown, crank boy! HA, HA, HA!!!
> > >
> > > Dan

Why use Wonky nonsense called „ basic arithmetic (line 1-14) “ as here for Even:
https://dcproof.com/EvenNextOdd.htm

Why not use Presburger arithmetic:
https://de.m.wikipedia.org/wiki/Presburger-Arithmetik

You can then define:
Even(x) <=> EXISTS(y):[y+y=x]

And the prove:
Even(x) & Even(y) => Even(x+y)

Basically anything made from eliminable definitions and +
is either provable or refutable, since Presburger is complete.

Not incomplete as your Wonky „ basic arithmetic (line 1-14) “

You can also extend Presburger Arithmetic by notation:

n * x = x + … + x
\ n-times /

You can then more conveniently write:

Even(x) <=> EXISTS(y):[2*y=x]

But you wouldnt introduce arbitrary multiplication,
only a short hand n * x for x + … + x.

Mostowski Collapse schrieb am Mittwoch, 25. Mai 2022 um 10:45:41 UTC+2:
> Why use Wonky nonsense called „ basic arithmetic (line 1-14) “ as here for Even:
> https://dcproof.com/EvenNextOdd.htm
>
> Why not use Presburger arithmetic:
> https://de.m.wikipedia.org/wiki/Presburger-Arithmetik
>
> You can then define:
> Even(x) <=> EXISTS(y):[y+y=x]
>
> And the prove:
> Even(x) & Even(y) => Even(x+y)
>
> Basically anything made from eliminable definitions and +
> is either provable or refutable, since Presburger is complete.
>
> Not incomplete as your Wonky „ basic arithmetic (line 1-14) “

On Wednesday, May 25, 2022 at 4:45:41 AM UTC-4, Mostowski Collapse (Jan Burse) wrote:
> Why use Wonky nonsense called „ basic arithmetic (line 1-14) “ as here for Even:
> https://dcproof.com/EvenNextOdd.htm
>

Nothing wrong there, Jan Burse. Deal with it. Not like this:

> Why not use Presburger arithmetic:
> https://de.m.wikipedia.org/wiki/Presburger-Arithmetik
>
[snip]

Why would you do that unless you were simply avoiding admitting a silly mistake, Jan Burse?

Dan

This axiom is dubious:

9 ALL(a):ALL(b):ALL(c):[a e n & b e n & c e n => a*(b-c)=a*b-a*c]
Axiom

What if b < c ? From this

11 ALL(a):ALL(b):ALL(c):[a e n & b e n & c e n => [a-b=c <=> a=c+b]]
Axiom

it must be ~(b - c) e n.

How do you prove the Axiom 9 from Peano? You need to have
knowledge of * outside of n, since the argument b - c can be outside of n.

Your axioms are not provable from Peano, that the biggest
lie I have ever heard. You just pulled them out of your ass.

What one can define in Peano is for example this Peano subtraction:

a -.- b := Max(0, a - b)

Dan Christensen schrieb am Mittwoch, 25. Mai 2022 um 15:48:05 UTC+2:
> On Wednesday, May 25, 2022 at 4:45:41 AM UTC-4, Mostowski Collapse (Jan Burse) wrote:
> > Why use Wonky nonsense called „ basic arithmetic (line 1-14) “ as here for Even:
> > https://dcproof.com/EvenNextOdd.htm
> >
> Nothing wrong there, Jan Burse. Deal with it. Not like this:
> > Why not use Presburger arithmetic:
> > https://de.m.wikipedia.org/wiki/Presburger-Arithmetik
> >
> [snip]
>
> Why would you do that unless you were simply avoiding admitting a silly mistake, Jan Burse?
>
> Dan

This is sometimes called „truncated subtraction"
There is also special sign for it:
∸ denotes truncated subtraction

https://math.stackexchange.com/q/461719

Mostowski Collapse schrieb am Mittwoch, 25. Mai 2022 um 17:00:28 UTC+2:
> This axiom is dubious:
>
> 9 ALL(a):ALL(b):ALL(c):[a e n & b e n & c e n => a*(b-c)=a*b-a*c]
> Axiom
>
> What if b < c ? From this
>
> 11 ALL(a):ALL(b):ALL(c):[a e n & b e n & c e n => [a-b=c <=> a=c+b]]
> Axiom
>
> it must be ~(b - c) e n.
>
> How do you prove the Axiom 9 from Peano? You need to have
> knowledge of * outside of n, since the argument b - c can be outside of n..
>
> Your axioms are not provable from Peano, that the biggest
> lie I have ever heard. You just pulled them out of your ass.
>
> What one can define in Peano is for example this Peano subtraction:
>
> a -.- b := Max(0, a - b)
> Dan Christensen schrieb am Mittwoch, 25. Mai 2022 um 15:48:05 UTC+2:
> > On Wednesday, May 25, 2022 at 4:45:41 AM UTC-4, Mostowski Collapse (Jan Burse) wrote:
> > > Why use Wonky nonsense called „ basic arithmetic (line 1-14) “ as here for Even:
> > > https://dcproof.com/EvenNextOdd.htm
> > >
> > Nothing wrong there, Jan Burse. Deal with it. Not like this:
> > > Why not use Presburger arithmetic:
> > > https://de.m.wikipedia.org/wiki/Presburger-Arithmetik
> > >
> > [snip]
> >
> > Why would you do that unless you were simply avoiding admitting a silly mistake, Jan Burse?
> >
> > Dan