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tech / sci.math / Re: DC Proof is the biggest teaching mistake

SubjectAuthor
* DC Proof is the biggest teaching mistakeMostowski Collapse
+* Re: DC Proof is the biggest teaching mistakeDan Christensen
|`* Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| +* Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |+* Re: DC Proof is the biggest teaching mistakeKip Foh
| ||`* Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| || +* Re: DC Proof is the biggest teaching mistakeMichael Moroney
| || |+- Re: DC Proof is the biggest teaching mistakeKip Foh
| || |`* Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| || | `- Re: DC Proof is the biggest teaching mistakeKip Foh
| || `- Re: DC Proof is the biggest teaching mistakeKip Foh
| |`* Re: DC Proof is the biggest teaching mistakeDan Christensen
| | `* Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |  `* Re: DC Proof is the biggest teaching mistakeDan Christensen
| |   `* Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |    `* Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |     +* Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |     |`* Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |     | `- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |     `* Re: DC Proof is the biggest teaching mistakeDan Christensen
| |      `* Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |       `* Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |        `* Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |         `* Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |          `* Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |           `* Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |            `* Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |             +- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |             +- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |             +- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |             +- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |             +- Re: DC Proof is the biggest teaching mistakeDan Christensen
| |             +- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |             +- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |             +- Re: DC Proof is the biggest teaching mistakeDan Christensen
| |             +- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |             +- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |             +- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |             +- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |             +- Re: DC Proof is the biggest teaching mistakeDan Christensen
| |             +- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |             +- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |             +- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |             +- Re: DC Proof is the biggest teaching mistakeDan Christensen
| |             +- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |             +- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |             +- Re: DC Proof is the biggest teaching mistakeDan Christensen
| |             +- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |             +- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |             +- Re: DC Proof is the biggest teaching mistakeDan Christensen
| |             +- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |             +- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |             +- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |             +- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |             +- Re: DC Proof is the biggest teaching mistakeDan Christensen
| |             +- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |             +- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |             +- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |             +- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |             +- Re: DC Proof is the biggest teaching mistakeDan Christensen
| |             +- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |             +- Re: DC Proof is the biggest teaching mistakeDan Christensen
| |             +- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |             +- Re: DC Proof is the biggest teaching mistakeDan Christensen
| |             +- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |             +- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |             +- Re: DC Proof is the biggest teaching mistakeDan Christensen
| |             +- Re: DC Proof is the biggest teaching mistakeDan Christensen
| |             +- Re: DC Proof is the biggest teaching mistakeDan Christensen
| |             +- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |             +- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| |             `- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
| `* Re: DC Proof is the biggest teaching mistakeKip Foh
|  `* Re: DC Proof is the biggest teaching mistakeMostowski Collapse
|   `* Re: DC Proof is the biggest teaching mistakeKip Foh
|    `* Re: DC Proof is the biggest teaching mistakeMostowski Collapse
|     `- Re: DC Proof is the biggest teaching mistakeKip Foh
+* Re: DC Proof is the biggest teaching mistakeMostowski Collapse
|+* Re: DC Proof is the biggest teaching mistakeMostowski Collapse
||+- Re: DC Proof is the biggest teaching mistakeDan Christensen
||`* Re: DC Proof is the biggest teaching mistakeDan Christensen
|| `* Re: DC Proof is the biggest teaching mistakeMostowski Collapse
||  +- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
||  `* Re: DC Proof is the biggest teaching mistakeDan Christensen
||   `* Re: DC Proof is the biggest teaching mistakeMostowski Collapse
||    `* Re: DC Proof is the biggest teaching mistakeMostowski Collapse
||     +- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
||     `* Re: DC Proof is the biggest teaching mistakeDan Christensen
||      `* Re: DC Proof is the biggest teaching mistakeMostowski Collapse
||       `* Re: DC Proof is the biggest teaching mistakeDan Christensen
||        `* Re: DC Proof is the biggest teaching mistakeMostowski Collapse
||         +- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
||         `* Re: DC Proof is the biggest teaching mistakeDan Christensen
||          `* Re: DC Proof is the biggest teaching mistakeMostowski Collapse
||           `- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
|`* Re: DC Proof is the biggest teaching mistakeScot Dino
| `* Re: DC Proof is the biggest teaching mistakeMostowski Collapse
|  `* Re: DC Proof is the biggest teaching mistakemitchr...@gmail.com
|   `- Re: DC Proof is the biggest teaching mistakeMostowski Collapse
+* Re: DC Proof is the biggest teaching mistakeMostowski Collapse
|`* Re: DC Proof is the biggest teaching mistakeDan Christensen
+* Re: DC Proof is the biggest teaching mistakeMostowski Collapse
+* Re: DC Proof is the biggest teaching mistakeMostowski Collapse
+* Re: DC Proof is the biggest teaching mistakeMostowski Collapse
+* Re: DC Proof is the biggest teaching mistakeMostowski Collapse
+* Re: DC Proof is the biggest teaching mistakeMostowski Collapse
`* Re: DC Proof is the biggest teaching mistakeMostowski Collapse

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Re: DC Proof is the biggest teaching mistake

<57188c28-7c97-4e5b-a4b5-8fc816b0f1c4n@googlegroups.com>

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Subject: Re: DC Proof is the biggest teaching mistake
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Mon, 2 May 2022 12:26 UTC

Here is an example which possibly goes also
wrong with bounded quantifiers, since bounded
quantifiers would only catch the input arguments

but not the output arguments of functions, when
there is function composition. But it still depends,
Dan Christensen should show us how he would

define division, this would be the example, and
the identity would be:

(x/y)/(z/t) = (x/z)/(y/t)

Doesn't work in the natural numbers, works in
the rational numbers, but there are counter examples
with only natural number arguments:

(100/25)/(8/4) = 4/2 = 2
(100/8)/(25/4) not possible in natural numbers
(100/8)/(25/4) possible in rational numbers =
(25/2) / (25/4) = 2

Mostowski Collapse schrieb am Montag, 2. Mai 2022 um 14:08:18 UTC+2:
> This is also a nice alternative add, just take the
> usual + : N x N -> N, and then define +' : N' x N' -> N'
> where we have, where ? is the sole "dark element":
>
> N' = N u {?}
>
> +' = + u { (?,a,b) | a e N', b something random from N' }
> u { (a,?,b) | a e N, b something random from N' }
>
> This shows somehow that add need not be something
> that makes "sense". i.e. what we usually know as
> plus operations.
>
> What is more difficult, is to find a formula that is
> unprovable, but that also has bounded quantifiers.
> This here has no bounded quantifiers:
> ALL(x):ALL(y):[add(x,y,0) => x=0 & y=0]
> I think something with bounded quantifiers might be
> also possible. Not 100% sure. Thats the joker that
> Dan Christensen always pulls to justify
>
> his nonsense.
> Fritz Feldhase schrieb am Montag, 2. Mai 2022 um 12:49:46 UTC+2:
> > What's the matter with this guy?

Re: DC Proof is the biggest teaching mistake

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Subject: Re: DC Proof is the biggest teaching mistake
From: Dan_Chri...@sympatico.ca (Dan Christensen)
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 by: Dan Christensen - Mon, 2 May 2022 14:01 UTC

On Monday, May 2, 2022 at 4:21:36 AM UTC-4, Mostowski Collapse wrote:

> So you are living in the land of confusion.
> Dan Christensen schrieb am Montag, 2. Mai 2022 um 00:47:29 UTC+2:
> > On Sunday, May 1, 2022 at 4:05:23 PM UTC-4, Mostowski Collapse wrote:
> > > Why can we not prove ALL(x):ALL(y):[add(x,y,0) => x=0 & y=0] ?
> > > Well there is an easy counter example, the addition for positive
> > > and negative integers, call it simply "plus":
> > >
> > > plus : Z x Z -> Z
> > >
> > Pay attention, Jan Burse. Why are you nattering on about integers?

> Because you made two category mistakes again. Because you
> told us you constructed the natural numbers addition
> Function. But your symbol "add" does not capture
>
> that. Its only a Half-Function. You only proved:
>
> EXIST(add):[ALL(a):ALL(b):[a e n & b e n => add(a,b) e n]
> Etc...
>
> But you should have proved, note the two differences:
>
> EXISTUNQUE(add):[add : n x n -> n]
> Etc...
>

Utter nonsense!

Dan

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

Re: DC Proof is the biggest teaching mistake

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Subject: Re: DC Proof is the biggest teaching mistake
From: Dan_Chri...@sympatico.ca (Dan Christensen)
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 by: Dan Christensen - Mon, 2 May 2022 14:32 UTC

On Monday, May 2, 2022 at 6:31:25 AM UTC-4, Fritz Feldhase wrote:
> On Monday, May 2, 2022 at 6:42:53 AM UTC+2, Dan Christensen wrote:
> > On Sunday, May 1, 2022 at 11:42:29 PM UTC-4, Fritz Feldhase wrote:
> > >
> > > Hint: One instance of "add" might just be the "function" plus, MC mentioned above (which is defined on Z x Z such that plus(-1, 1) = plus(0, 0) = 0). Your theorem does not exclude that possibillity. Actually, the following should be provable too:
> > >
> > [...] In the statement ALL(a):ALL(b):[a e n & b e n => add(a,b) e n], I have restricted both quantifiers to the set n (the natural numbers here)..
>
> Holy shit! You seem to think that
>
> An e IN: Phi[x]
>
> somehow "restricts" the "valitity" of Phi[x] to IN. What's the matter with you cranks?
>

Where do you get that idea? It just says that Phi(x) is true for every natural number x.

> Hint:
>
> An e IN: n = n.
>
> Does that mean, that ~(-1 = -1), or what?
> > The add function here is also unique:
> > ...
> > => ALL(a):ALL(b):[a e n & b e n => add(a,b)=add'(a,b)]]
> No, you silly idiot!
>
> This does not mean that "add" is unique.
>
> This only means that add(x) = add'(x) for all x in a certain set X

On the set n, in this case. What is your point?

>
> Can't you read and/or comprehend my posts?
>

Many of them are indeed quite incomprehensible.

> For example, ALL(a):ALL(b):[a e n & b e n => add(a,b)=plus(a,b)]] will hold too. BUT and =/= plus.
> Hint:
> > > the following should be provable too:
> > >
> > > ALL(a):ALL(b):[a e n & b e n => plus(a,b) e n]
> > > & ALL(a):[a e n => plus(a,0)=a]
> > > & ALL(a):ALL(b):[a e n & b e n => plus(a,s(b))=s(plus(a,b))]
> > >
> > > where plus is the function MC mentioned above.
> > >
> > > But in this case: EXIST(x):EXIST(y):[plus(x,y)=0 & ~(x=0 & y=0)]
> > >
> > > Your present treatment of functions in the context of DC Proof is inferior, dumbo.
> > >
> > > Hint: Defining functions "recursively" works because of the theorem (schema)
> > >
> > > E!f(function(f) & f(0) = a & An(n e IN -> f(n+1) = ...f(n)...))
> > >
> > > Where
> > >
> > > f(0) = a
> > > f(n+1) = ...f(n)...
> > >
> > > are "the defining equations".
> > >
> > I am not simply defining the add function on N, I am proving its existence

> If you say so. BUT

> > > In a formal treatment we would have to "introduce" the new constant (which denotes the function we want to define) explicitely.
> > >
> > I do so on line 668 applying existential specification to previous line:
> >
> > 668. ALL(a1):ALL(a2):ALL(b):[(a1,a2) e n2 & b e n
> > => [addf(a1,a2)=b <=> (a1,a2,b) e add]]
> > E Spec, 667

> "add" isn't a CONSTANT
>

It is the graph of the required function, a set of ordered triples of natural numbers. fadd is the required function operator which was introduced by existential specification on this line. It is defined in terms of n and add. Informally You could think of it as a constant.
> after all your theorem reads:
> EXIST(add):[ALL(a):ALL(b):[a e n & b e n => add(a,b) e n]
> & ALL(a):[a e n => add(a,0)=a]
> & ALL(a):ALL(b):[a e n & b e n => add(a,s(b))=s(add(a,b))]]

Yes. Here add is a bound variable. Nothing wrong with that. Deal with it.

> > > This step is usually omitted in math, there we usually just/already use the new constant (denoting the function) when stating the "defining equations".
> > >
> > > As you can see E!f plays an important role here. Now
> > >
> > > E!f(Phi(f)) <-> Ef(Phi[f]) & AfAg(Phi[f] & Phi[g] -> f = g).
> > >
> > > So ultimately we need an appropriate treatment (definition) of function equality (to ensure uniqueness).
> > >

> > Wrong. It is NOT necessary.

> No, not wrong.

> > See the above link where the uniqueness of the add function on N is proven.
> No, you didn't do so

Perhaps you were looking at the wrong link? Here is that again: https://dcproof.com/AdditionOnNUnique.htm

There I prove:

ALL(add):ALL(add'):[ALL(a):ALL(b):[a e n & b e n => add(a,b) e n]
& ALL(a):[a e n => add(a,0)=a]
& ALL(a):ALL(b):[a e n & b e n => add(a,s(b))=s(add(a,b))]

& ALL(a):ALL(b):[a e n & b e n => add'(a,b) e n]
& ALL(a):[a e n => add'(a,0)=a]
& ALL(a):ALL(b):[a e n & b e n => add'(a,s(b))=s(add'(a,b))]

=> ALL(a):ALL(b):[a e n & b e n => add(a,b)=add'(a,b)]]

Only 84 lines -- short for a formal proof. Note that every quantifier is restricted to the set of natural numbers.

Dan

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

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Subject: Re: DC Proof is the biggest teaching mistake
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Mon, 2 May 2022 15:48 UTC

I agree, you proved utter nonsense, as usual.

Dan Christensen schrieb am Montag, 2. Mai 2022 um 16:01:12 UTC+2:
> On Monday, May 2, 2022 at 4:21:36 AM UTC-4, Mostowski Collapse wrote:
>
> > So you are living in the land of confusion.
> > Dan Christensen schrieb am Montag, 2. Mai 2022 um 00:47:29 UTC+2:
> > > On Sunday, May 1, 2022 at 4:05:23 PM UTC-4, Mostowski Collapse wrote:
> > > > Why can we not prove ALL(x):ALL(y):[add(x,y,0) => x=0 & y=0] ?
> > > > Well there is an easy counter example, the addition for positive
> > > > and negative integers, call it simply "plus":
> > > >
> > > > plus : Z x Z -> Z
> > > >
> > > Pay attention, Jan Burse. Why are you nattering on about integers?
>
> > Because you made two category mistakes again. Because you
> > told us you constructed the natural numbers addition
> > Function. But your symbol "add" does not capture
> >
> > that. Its only a Half-Function. You only proved:
> >
> > EXIST(add):[ALL(a):ALL(b):[a e n & b e n => add(a,b) e n]
> > Etc...
> >
> > But you should have proved, note the two differences:
> >
> > EXISTUNQUE(add):[add : n x n -> n]
> > Etc...
> >
> Utter nonsense!
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com

Re: DC Proof is the biggest teaching mistake

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Subject: Re: DC Proof is the biggest teaching mistake
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Thu, 5 May 2022 21:51 UTC

Cocaine is a hell of a drug. A moment of silence
for Dan Christensen. Spot the error:

Dan Christensen schrieb am Donnerstag, 5. Mai 2022 um 23:30:20 UTC+2:
> None of these supposed "successor functions" satisfy Peano's
Axioms. In each case, there exists x in the respective set such
that x+1=0. This effectively violates the 4th Peano Axiom that
S(x)=/=0. Deal with it, Jan Burse. Just admit you were wrong.
https://groups.google.com/g/sci.math/c/sYkWEHylBAA/m/2ENocyfZAgAJ

I nowhere said I change n, so there is no variation in
the "respective set". The respective set is always n,
since the axiom reads as follows:

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

I only change s, not n. Whats wrong with you?
How does s = succQ make the above axiom false?

Re: DC Proof is the biggest teaching mistake

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Subject: Re: DC Proof is the biggest teaching mistake
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Fri, 6 May 2022 08:02 UTC

Ok, lets make the problem dumbo compatible, so
that crazy Dan Christensen also understands it.
Can you prove the alleged axiom violation:

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

in set theory and natural deduction, from these axioms here:

1. Your "Peano Axioms"
2. New Axiom: ~(-1 e n)
3. New Axiom: s(-1) = 0

Just curious, how would you prove it? Please show
us a formal DC Proof, so that it is a computer
verified proof, and not some halucination.

Thanks in advance.

Mostowski Collapse schrieb am Donnerstag, 5. Mai 2022 um 23:51:07 UTC+2:
> Cocaine is a hell of a drug. A moment of silence
> for Dan Christensen. Spot the error:
>
> Dan Christensen schrieb am Donnerstag, 5. Mai 2022 um 23:30:20 UTC+2:
> > None of these supposed "successor functions" satisfy Peano's
> Axioms. In each case, there exists x in the respective set such
> that x+1=0. This effectively violates the 4th Peano Axiom that
> S(x)=/=0. Deal with it, Jan Burse. Just admit you were wrong.
> https://groups.google.com/g/sci.math/c/sYkWEHylBAA/m/2ENocyfZAgAJ
>
> I nowhere said I change n, so there is no variation in
> the "respective set". The respective set is always n,
> since the axiom reads as follows:
>
> ALL(a):[a e n => ~s(a)=0]
>
> I only change s, not n. Whats wrong with you?
> How does s = succQ make the above axiom false?

Re: DC Proof is the biggest teaching mistake

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 by: Wesi Matsuya - Fri, 6 May 2022 10:13 UTC

Mostowski Collapse wrote:

> Cocaine is a hell of a drug. A moment of silence for Dan Christensen.
> Spot the error:

it's a nazi drug. Tell that the nazi zelenske, a *half_birth_certificate*
slavic russian talking puppet on cocaine. The *half_birth_certificate* is
an imbecile, fighting a "war" with no army, even the nazis left him alone.

Re: DC Proof is the biggest teaching mistake

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Subject: Re: DC Proof is the biggest teaching mistake
From: Dan_Chri...@sympatico.ca (Dan Christensen)
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 by: Dan Christensen - Fri, 6 May 2022 14:25 UTC

See my reply to you just now on this topic in another thread here.

Dan

On Friday, May 6, 2022 at 4:02:16 AM UTC-4, Mostowski Collapse wrote:
> Ok, lets make the problem dumbo compatible, so
> that crazy Dan Christensen also understands it.
> Can you prove the alleged axiom violation:
>
> ~ALL(a):[a e n => ~s(a)=0]
>
> in set theory and natural deduction, from these axioms here:
>
> 1. Your "Peano Axioms"
> 2. New Axiom: ~(-1 e n)
> 3. New Axiom: s(-1) = 0
>
> Just curious, how would you prove it? Please show
> us a formal DC Proof, so that it is a computer
> verified proof, and not some halucination.
>
> Thanks in advance.
> Mostowski Collapse schrieb am Donnerstag, 5. Mai 2022 um 23:51:07 UTC+2:
> > Cocaine is a hell of a drug. A moment of silence
> > for Dan Christensen. Spot the error:
> >
> > Dan Christensen schrieb am Donnerstag, 5. Mai 2022 um 23:30:20 UTC+2:
> > > None of these supposed "successor functions" satisfy Peano's
> > Axioms. In each case, there exists x in the respective set such
> > that x+1=0. This effectively violates the 4th Peano Axiom that
> > S(x)=/=0. Deal with it, Jan Burse. Just admit you were wrong.
> > https://groups.google.com/g/sci.math/c/sYkWEHylBAA/m/2ENocyfZAgAJ
> >
> > I nowhere said I change n, so there is no variation in
> > the "respective set". The respective set is always n,
> > since the axiom reads as follows:
> >
> > ALL(a):[a e n => ~s(a)=0]
> >
> > I only change s, not n. Whats wrong with you?
> > How does s = succQ make the above axiom false?

Re: DC Proof is the biggest teaching mistake

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Subject: Re: DC Proof is the biggest teaching mistake
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Fri, 6 May 2022 14:36 UTC

There is no response on other thread....

Dan Christensen schrieb am Freitag, 6. Mai 2022 um 16:25:18 UTC+2:
> See my reply to you just now on this topic in another thread here.
>
> Dan
> On Friday, May 6, 2022 at 4:02:16 AM UTC-4, Mostowski Collapse wrote:
> > Ok, lets make the problem dumbo compatible, so
> > that crazy Dan Christensen also understands it.
> > Can you prove the alleged axiom violation:
> >
> > ~ALL(a):[a e n => ~s(a)=0]
> >
> > in set theory and natural deduction, from these axioms here:
> >
> > 1. Your "Peano Axioms"
> > 2. New Axiom: ~(-1 e n)
> > 3. New Axiom: s(-1) = 0
> >
> > Just curious, how would you prove it? Please show
> > us a formal DC Proof, so that it is a computer
> > verified proof, and not some halucination.
> >
> > Thanks in advance.
> > Mostowski Collapse schrieb am Donnerstag, 5. Mai 2022 um 23:51:07 UTC+2:
> > > Cocaine is a hell of a drug. A moment of silence
> > > for Dan Christensen. Spot the error:
> > >
> > > Dan Christensen schrieb am Donnerstag, 5. Mai 2022 um 23:30:20 UTC+2:
> > > > None of these supposed "successor functions" satisfy Peano's
> > > Axioms. In each case, there exists x in the respective set such
> > > that x+1=0. This effectively violates the 4th Peano Axiom that
> > > S(x)=/=0. Deal with it, Jan Burse. Just admit you were wrong.
> > > https://groups.google.com/g/sci.math/c/sYkWEHylBAA/m/2ENocyfZAgAJ
> > >
> > > I nowhere said I change n, so there is no variation in
> > > the "respective set". The respective set is always n,
> > > since the axiom reads as follows:
> > >
> > > ALL(a):[a e n => ~s(a)=0]
> > >
> > > I only change s, not n. Whats wrong with you?
> > > How does s = succQ make the above axiom false?

Re: DC Proof is the biggest teaching mistake

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Subject: Re: DC Proof is the biggest teaching mistake
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Fri, 6 May 2022 15:04 UTC

if you cannot write minus one -1 in DC Proof,
you can also use the constant m, maybe this
is easier for you:

Can you prove the alleged axiom violation:

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

in set theory and natural deduction, from these axioms here:

1. Your "Peano Axioms"
2. New Axiom: ~(m e n)
3. New Axiom: s(m) = 0

0 might be the first element in n. But what prevents
m outside of n, being the predecessor of 0. Can
you please tell us, via some proof?

LoL

Mostowski Collapse schrieb am Freitag, 6. Mai 2022 um 16:36:26 UTC+2:
> There is no response on other thread....
> Dan Christensen schrieb am Freitag, 6. Mai 2022 um 16:25:18 UTC+2:
> > See my reply to you just now on this topic in another thread here.
> >
> > Dan
> > On Friday, May 6, 2022 at 4:02:16 AM UTC-4, Mostowski Collapse wrote:
> > > Ok, lets make the problem dumbo compatible, so
> > > that crazy Dan Christensen also understands it.
> > > Can you prove the alleged axiom violation:
> > >
> > > ~ALL(a):[a e n => ~s(a)=0]
> > >
> > > in set theory and natural deduction, from these axioms here:
> > >
> > > 1. Your "Peano Axioms"
> > > 2. New Axiom: ~(-1 e n)
> > > 3. New Axiom: s(-1) = 0
> > >
> > > Just curious, how would you prove it? Please show
> > > us a formal DC Proof, so that it is a computer
> > > verified proof, and not some halucination.
> > >
> > > Thanks in advance.
> > > Mostowski Collapse schrieb am Donnerstag, 5. Mai 2022 um 23:51:07 UTC+2:
> > > > Cocaine is a hell of a drug. A moment of silence
> > > > for Dan Christensen. Spot the error:
> > > >
> > > > Dan Christensen schrieb am Donnerstag, 5. Mai 2022 um 23:30:20 UTC+2:
> > > > > None of these supposed "successor functions" satisfy Peano's
> > > > Axioms. In each case, there exists x in the respective set such
> > > > that x+1=0. This effectively violates the 4th Peano Axiom that
> > > > S(x)=/=0. Deal with it, Jan Burse. Just admit you were wrong.
> > > > https://groups.google.com/g/sci.math/c/sYkWEHylBAA/m/2ENocyfZAgAJ
> > > >
> > > > I nowhere said I change n, so there is no variation in
> > > > the "respective set". The respective set is always n,
> > > > since the axiom reads as follows:
> > > >
> > > > ALL(a):[a e n => ~s(a)=0]
> > > >
> > > > I only change s, not n. Whats wrong with you?
> > > > How does s = succQ make the above axiom false?

Re: DC Proof is the biggest teaching mistake

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Subject: Re: DC Proof is the biggest teaching mistake
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 by: Mostowski Collapse - Wed, 11 May 2022 13:44 UTC

Its almost 80 days since ruSSia invaded the
Ukraine, and Dan Christensen can still not

define Even/Odd so that he can prove,
disjoint partitioning of n:

Challenge 1:
ALL(a):[a e n <=> [Even(a) v Odd(a)]]

Challenge 2:
ALL(a):[a e {} <=> [Even(a) & Odd(a)]]

LoL

Re: DC Proof is the biggest teaching mistake

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Subject: Re: DC Proof is the biggest teaching mistake
From: Dan_Chri...@sympatico.ca (Dan Christensen)
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 by: Dan Christensen - Wed, 11 May 2022 15:36 UTC

On Friday, May 6, 2022 at 11:04:27 AM UTC-4, Mostowski Collapse wrote:
> if you cannot write minus one -1 in DC Proof,

Use underscore: _1 = minus one

I didn't want to overload the "-" symbol (for subtraction).

> you can also use the constant m, maybe this
> is easier for you:
> Can you prove the alleged axiom violation:
>
> ~ALL(a):[a e n => ~s(a)=0]
>

Huh? Prove that one of Peano's Axiom is false??? I don't think so.

> in set theory and natural deduction, from these axioms here:
>
> 1. Your "Peano Axioms"
> 2. New Axiom: ~(m e n)
> 3. New Axiom: s(m) = 0
>
> 0 might be the first element in n. But what prevents
> m outside of n, being the predecessor of 0.

You can only apply Peano's Axioms for the natural numbers (not for m in this case).

Dan

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

Re: DC Proof is the biggest teaching mistake

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Subject: Re: DC Proof is the biggest teaching mistake
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 by: Mostowski Collapse - Wed, 11 May 2022 16:14 UTC

You can prove ~ALL(a):[a e n => ~s(a)=0] from:

1. Your "Peano Axioms"
2. New Axiom: (m e n)
3. New Axiom: s(m) = 0

But you cannot prove ~ALL(a):[a e n => ~s(a)=0] from
this where 3. is flipped:

1. Your "Peano Axioms"
2. New Axiom: ~(m e n)
3. New Axiom: s(m) = 0

Which condradicts your claim that s(-1)=0 necessarely
makes ~ALL(a):[a e n => ~s(a)=0].

You repeatedly say s(-1)=0 is not possible in your
Peano axioms, but by all means it is possible.

Dan Christensen schrieb am Mittwoch, 11. Mai 2022 um 17:36:08 UTC+2:
> On Friday, May 6, 2022 at 11:04:27 AM UTC-4, Mostowski Collapse wrote:
> > if you cannot write minus one -1 in DC Proof,
> Use underscore: _1 = minus one
>
> I didn't want to overload the "-" symbol (for subtraction).
> > you can also use the constant m, maybe this
> > is easier for you:
> > Can you prove the alleged axiom violation:
> >
> > ~ALL(a):[a e n => ~s(a)=0]
> >
> Huh? Prove that one of Peano's Axiom is false??? I don't think so.
> > in set theory and natural deduction, from these axioms here:
> >
> > 1. Your "Peano Axioms"
> > 2. New Axiom: ~(m e n)
> > 3. New Axiom: s(m) = 0
> >
> > 0 might be the first element in n. But what prevents
> > m outside of n, being the predecessor of 0.
> You can only apply Peano's Axioms for the natural numbers (not for m in this case).
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com

Re: DC Proof is the biggest teaching mistake

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Subject: Re: DC Proof is the biggest teaching mistake
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 by: Cecil Nitta - Wed, 11 May 2022 20:43 UTC

Dan Christensen wrote:

> On Friday, May 6, 2022 at 11:04:27 AM UTC-4, Mostowski Collapse wrote:
>> if you cannot write minus one -1 in DC Proof,
>
> Use underscore: _1 = minus one
> I didn't want to overload the "-" symbol (for subtraction).

lol, clearly "coded" in visual basic by an idiot. Listen up, nasa was
funded by the nazis.

Re: DC Proof is the biggest teaching mistake

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Subject: Re: DC Proof is the biggest teaching mistake
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 by: Mostowski Collapse - Wed, 11 May 2022 22:04 UTC

-1 is quite handy, since ~(-1 e n).
These 3 are not provable from your definition, but
they are provable from the standard definition:

∀a(¬Na → ¬Ea)
∀a(¬Na → ¬Oa)
∀a(Na ↔ (Ea ∨ Oa))

Legend:
Na = a e n
Ea = Even(a)
Oa = Odd(a)

See countermodels here to your definition:

Counter Model 1:
(∀a(Na → (Ea ↔ Da)) ∧ ∀a(Oa ↔ ¬Ea)))) → ∀a(¬Na → ¬Ea) is invalid.
Universe of Discourse: { 0,2,4,..., 1,3,4,..., -1}
N: { 0,2,4,..., 1,3,4,... }
E: { 0,2,4,..., -1 }
O: { 1,3,4,... }
D: { 0,2,4,... }

Counter Model 2: similar
Counter Model 3: similar

Mostowski Collapse schrieb am Mittwoch, 11. Mai 2022 um 18:14:31 UTC+2:
> You can prove ~ALL(a):[a e n => ~s(a)=0] from:
>
> 1. Your "Peano Axioms"
> 2. New Axiom: (m e n)
> 3. New Axiom: s(m) = 0
> But you cannot prove ~ALL(a):[a e n => ~s(a)=0] from
> this where 3. is flipped:
> 1. Your "Peano Axioms"
> 2. New Axiom: ~(m e n)
> 3. New Axiom: s(m) = 0
> Which condradicts your claim that s(-1)=0 necessarely
> makes ~ALL(a):[a e n => ~s(a)=0].
>
> You repeatedly say s(-1)=0 is not possible in your
> Peano axioms, but by all means it is possible.

Re: DC Proof is the biggest teaching mistake

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Subject: Re: DC Proof is the biggest teaching mistake
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Wed, 11 May 2022 22:06 UTC

Do you have problems with vacuously true again.
Confusing it with vacuously false?

If you deny that they are not provable, then
please show us a proof of the following:

∀a(¬Na → ¬Ea)
∀a(¬Na → ¬Oa)
∀a(Na ↔ (Ea ∨ Oa))

From your nonsense:

∀a(Na → (Ea ↔ Da)) ∧ ∀a(Oa ↔ ¬Ea)

Legend:
Da = EXIST(b):[b in N & a=2*b]

Mostowski Collapse schrieb am Donnerstag, 12. Mai 2022 um 00:04:57 UTC+2:
> -1 is quite handy, since ~(-1 e n).
> These 3 are not provable from your definition, but
> they are provable from the standard definition:
>
> ∀a(¬Na → ¬Ea)
> ∀a(¬Na → ¬Oa)
> ∀a(Na ↔ (Ea ∨ Oa))
>
> Legend:
> Na = a e n
> Ea = Even(a)
> Oa = Odd(a)
>
> See countermodels here to your definition:
>
> Counter Model 1:
> (∀a(Na → (Ea ↔ Da)) ∧ ∀a(Oa ↔ ¬Ea)))) → ∀a(¬Na → ¬Ea) is invalid.
> Universe of Discourse: { 0,2,4,..., 1,3,4,..., -1}
> N: { 0,2,4,..., 1,3,4,... }
> E: { 0,2,4,..., -1 }
> O: { 1,3,4,... }
> D: { 0,2,4,... }
>
> Counter Model 2: similar
> Counter Model 3: similar
> Mostowski Collapse schrieb am Mittwoch, 11. Mai 2022 um 18:14:31 UTC+2:
> > You can prove ~ALL(a):[a e n => ~s(a)=0] from:
> >
> > 1. Your "Peano Axioms"
> > 2. New Axiom: (m e n)
> > 3. New Axiom: s(m) = 0
> > But you cannot prove ~ALL(a):[a e n => ~s(a)=0] from
> > this where 3. is flipped:
> > 1. Your "Peano Axioms"
> > 2. New Axiom: ~(m e n)
> > 3. New Axiom: s(m) = 0
> > Which condradicts your claim that s(-1)=0 necessarely
> > makes ~ALL(a):[a e n => ~s(a)=0].
> >
> > You repeatedly say s(-1)=0 is not possible in your
> > Peano axioms, but by all means it is possible.

Re: DC Proof is the biggest teaching mistake

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Subject: Re: DC Proof is the biggest teaching mistake
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 by: Mostowski Collapse - Wed, 11 May 2022 22:58 UTC

So Dan Christensen has still problems with Euclids even
and odd natural numbers. He is still bat shit crazy
and high as a kite. Woa!

Dan Christensen schrieb am Donnerstag, 12. Mai 2022 um 00:35:26 UTC+2:
> So, everything that is isn't a natural number is both
not even and not odd. How wonky is that?
https://groups.google.com/g/sci.logic/c/gV50jEU6fvQ/m/ASEgcINuAQAJ

Try this syphilis brain:

Every one that isn't a russian is neither a femal russian
nor a male russian.

Do you see why its not wonky?

Mostowski Collapse schrieb am Donnerstag, 12. Mai 2022 um 00:06:28 UTC+2:
> Do you have problems with vacuously true again.
> Confusing it with vacuously false?
>
> If you deny that they are not provable, then
> please show us a proof of the following:
> ∀a(¬Na → ¬Ea)
> ∀a(¬Na → ¬Oa)
> ∀a(Na ↔ (Ea ∨ Oa))
> From your nonsense:
>
> ∀a(Na → (Ea ↔ Da)) ∧ ∀a(Oa ↔ ¬Ea)
>
> Legend:
> Da = EXIST(b):[b in N & a=2*b]
> Mostowski Collapse schrieb am Donnerstag, 12. Mai 2022 um 00:04:57 UTC+2:
> > -1 is quite handy, since ~(-1 e n).
> > These 3 are not provable from your definition, but
> > they are provable from the standard definition:
> >
> > ∀a(¬Na → ¬Ea)
> > ∀a(¬Na → ¬Oa)
> > ∀a(Na ↔ (Ea ∨ Oa))
> >
> > Legend:
> > Na = a e n
> > Ea = Even(a)
> > Oa = Odd(a)
> >
> > See countermodels here to your definition:
> >
> > Counter Model 1:
> > (∀a(Na → (Ea ↔ Da)) ∧ ∀a(Oa ↔ ¬Ea)))) → ∀a(¬Na → ¬Ea) is invalid.
> > Universe of Discourse: { 0,2,4,..., 1,3,4,..., -1}
> > N: { 0,2,4,..., 1,3,4,... }
> > E: { 0,2,4,..., -1 }
> > O: { 1,3,4,... }
> > D: { 0,2,4,... }
> >
> > Counter Model 2: similar
> > Counter Model 3: similar
> > Mostowski Collapse schrieb am Mittwoch, 11. Mai 2022 um 18:14:31 UTC+2:
> > > You can prove ~ALL(a):[a e n => ~s(a)=0] from:
> > >
> > > 1. Your "Peano Axioms"
> > > 2. New Axiom: (m e n)
> > > 3. New Axiom: s(m) = 0
> > > But you cannot prove ~ALL(a):[a e n => ~s(a)=0] from
> > > this where 3. is flipped:
> > > 1. Your "Peano Axioms"
> > > 2. New Axiom: ~(m e n)
> > > 3. New Axiom: s(m) = 0
> > > Which condradicts your claim that s(-1)=0 necessarely
> > > makes ~ALL(a):[a e n => ~s(a)=0].
> > >
> > > You repeatedly say s(-1)=0 is not possible in your
> > > Peano axioms, but by all means it is possible.

Re: DC Proof is the biggest teaching mistake

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Subject: Re: DC Proof is the biggest teaching mistake
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Wed, 11 May 2022 23:03 UTC

This sentence is even immune if we would consider
russian transsexuals as neither male or female, its
still a linguistic truth:

Every one that isn't a russian is neither a femal russian
nor a male russian.

LoL

Mostowski Collapse schrieb am Donnerstag, 12. Mai 2022 um 00:58:09 UTC+2:
> So Dan Christensen has still problems with Euclids even
> and odd natural numbers. He is still bat shit crazy
> and high as a kite. Woa!
>
> Dan Christensen schrieb am Donnerstag, 12. Mai 2022 um 00:35:26 UTC+2:
> > So, everything that is isn't a natural number is both
> not even and not odd. How wonky is that?
> https://groups.google.com/g/sci.logic/c/gV50jEU6fvQ/m/ASEgcINuAQAJ
>
> Try this syphilis brain:
>
> Every one that isn't a russian is neither a femal russian
> nor a male russian.
>
> Do you see why its not wonky?

Re: DC Proof is the biggest teaching mistake

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Subject: Re: DC Proof is the biggest teaching mistake
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Sat, 21 May 2022 17:16 UTC

Did nobody tell Dan Christensen in school that one is only
allowed to replace definitions by logically equivalent ones

and not by weaker axioms. If you do the later you only get
garbage. Like odd natural numbers where this is not provable:

/* not provable */
ALL(a):[a < 0 => ~Odd(a)]
https://dcproof.com/EvenNextOdd.htm

Re: DC Proof is the biggest teaching mistake

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Subject: Re: DC Proof is the biggest teaching mistake
From: Dan_Chri...@sympatico.ca (Dan Christensen)
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 by: Dan Christensen - Sat, 21 May 2022 19:18 UTC

On Saturday, May 21, 2022 at 1:16:50 PM UTC-4, Mostowski Collapse (Jan Burse) wrote:
> Did nobody tell Dan Christensen in school that one is only
> allowed to replace definitions by logically equivalent ones
>
> and not by weaker axioms. If you do the later you only get
> garbage. Like odd natural numbers where this is not provable:
>
> /* not provable */
> ALL(a):[a < 0 => ~Odd(a)]

Idiot! That should be: ALL(a):[a in N => [a < 0 => ...

When will you learn, Jan Burse? Whatever proposition you tack on here will be vacuously true because there no elements of N that are less than 0.

> https://dcproof.com/EvenNextOdd.htm

Poor Jan Burse still doesn't get it. He believes that it is possible to make logical inferences about functions outside of their domains of definition, i.e. where they are technically UNDEFINED! Some nonsense about "dark elements?"

Dan

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Subject: Re: DC Proof is the biggest teaching mistake
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Sat, 21 May 2022 21:58 UTC

It depends. In your file EvenNextOdd.htm, you should
write the following:

6 ALL(a):ALL(b):[a e d & b e d => a+b e d]
Axiom
Properties of +
7 ALL(a):ALL(b):[a e d & b e d => a+b=b+a]
Axiom
https://dcproof.com/EvenNextOdd.htm

Where is associativity? LoL
Where is all of Peano? LMAO!
Do you see the problem, or are you just too dumb?

You should not write n, if its not n. No mathematician
does that. Your axioms define some structure <D, +, ...>
but its not necessarely the structure <N, +, ...>

So the correct offending theorem would be anyway:

ALL(a):[a e d => [a < 0 => ~Odd(a)]]

Which makes it even more clear why its not provable.

Dan Christensen schrieb am Samstag, 21. Mai 2022 um 21:18:06 UTC+2:
> On Saturday, May 21, 2022 at 1:16:50 PM UTC-4, Mostowski Collapse (Jan Burse) wrote:
> > Did nobody tell Dan Christensen in school that one is only
> > allowed to replace definitions by logically equivalent ones
> >
> > and not by weaker axioms. If you do the later you only get
> > garbage. Like odd natural numbers where this is not provable:
> >
> > /* not provable */
> > ALL(a):[a < 0 => ~Odd(a)]
> Idiot! That should be: ALL(a):[a in N => [a < 0 => ...
>
> When will you learn, Jan Burse? Whatever proposition you tack on here will be vacuously true because there no elements of N that are less than 0.
>
> > https://dcproof.com/EvenNextOdd.htm
>
> Poor Jan Burse still doesn't get it. He believes that it is possible to make logical inferences about functions outside of their domains of definition, i.e. where they are technically UNDEFINED! Some nonsense about "dark elements?"
>
> Dan

Re: DC Proof is the biggest teaching mistake

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Subject: Re: DC Proof is the biggest teaching mistake
From: Dan_Chri...@sympatico.ca (Dan Christensen)
Injection-Date: Sun, 22 May 2022 03:09:32 +0000
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 by: Dan Christensen - Sun, 22 May 2022 03:09 UTC

On Saturday, May 21, 2022 at 5:58:35 PM UTC-4, Mostowski Collapse (Jan Burse) wrote:
> It depends. In your file https://dcproof.com/EvenNextOdd.htm , you should
> write the following:
>
> 6 ALL(a):ALL(b):[a e d & b e d => a+b e d]

It was correctly stated as:

ALL(a):ALL(b):[a e n & b e n => a+b e n]

where n = the set of natural numbers

Deal with it, Jan Burse.

> Axiom
> Properties of +
> 7 ALL(a):ALL(b):[a e d & b e d => a+b=b+a]

Wrong again, Jan Burse.

It is corrected stated as:

ALL(a):ALL(b):[a e n & b e n => a+b=b+a]

> Axiom
> https://dcproof.com/EvenNextOdd.htm
>
> Where is associativity? LoL

When will you learn, Jan Burse??? It wasn't required to prove the required results, so it was not listed. Geez yer dumb!

> Where is all of Peano?

As above, idiot! Do try to learn some math, 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

Re: DC Proof is the biggest teaching mistake

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Subject: Re: DC Proof is the biggest teaching mistake
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Sun, 22 May 2022 08:44 UTC

No mathematician is this careless as you are.

Trying to sell us your non-classical Even and Odd
is a result of a fallacy. You think Peano => Basics does
also imply Basics => Peano, thats why you use the name n,

which is not justified. You are subject to this fallacy:

Fallacy of the Commutation of Conditionals
https://www.logicallyfallacious.com/logicalfallacies/Commutation-of-Conditionals

If I am smart, then I can use DC Proof
Therefore, if I can use DC Proof, then I am smart.

Dan Christensen schrieb am Sonntag, 22. Mai 2022 um 05:09:37 UTC+2:
> On Saturday, May 21, 2022 at 5:58:35 PM UTC-4, Mostowski Collapse (Jan Burse) wrote:
> > It depends. In your file https://dcproof.com/EvenNextOdd.htm , you should
> > write the following:
> >
> > 6 ALL(a):ALL(b):[a e d & b e d => a+b e d]
> It was correctly stated as:
>
> ALL(a):ALL(b):[a e n & b e n => a+b e n]
>
> where n = the set of natural numbers
> Deal with it, Jan Burse.
> > Axiom
> > Properties of +
> > 7 ALL(a):ALL(b):[a e d & b e d => a+b=b+a]
> Wrong again, Jan Burse.
>
> It is corrected stated as:
>
> ALL(a):ALL(b):[a e n & b e n => a+b=b+a]
> > Axiom
> > https://dcproof.com/EvenNextOdd.htm
> >
> > Where is associativity? LoL
> When will you learn, Jan Burse??? It wasn't required to prove the required results, so it was not listed. Geez yer dumb!
> > Where is all of Peano?
> As above, idiot! Do try to learn some math, 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

Re: DC Proof is the biggest teaching mistake

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Subject: Re: DC Proof is the biggest teaching mistake
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Sun, 22 May 2022 09:23 UTC

Just like non-classical logics, like for example intuitionistic
logics, which does not have this here as a tautology:

/* law of excluded middle */
/* doesn't hold in intuitionistic logic */
A v ~A

Dan-O-Matiks non-classical Even and Odd do have a lot
of holes, one cannot prove the following:

/* doesn't hold in Dan-O-Matiks D */
Odd(A) & Odd(B) => A+B =\= 0

What are the claasical Even and Odds?

P.S.: Counter example to Odd(A) & Odd(B) => A+B =\= 0
is the structure F4. Just take A=1 and B=3:

+ 0 1 2 3
0 0 1 2 3
1 1 2 3 0
2 2 3 1 0
3 3 1 2 0

Mostowski Collapse schrieb am Sonntag, 22. Mai 2022 um 10:44:52 UTC+2:
> No mathematician is this careless as you are.
>
> Trying to sell us your non-classical Even and Odd
> is a result of a fallacy. You think Peano => Basics does
> also imply Basics => Peano, thats why you use the name n,
>
> which is not justified. You are subject to this fallacy:
>
> Fallacy of the Commutation of Conditionals
> https://www.logicallyfallacious.com/logicalfallacies/Commutation-of-Conditionals
>
> If I am smart, then I can use DC Proof
> Therefore, if I can use DC Proof, then I am smart.
> Dan Christensen schrieb am Sonntag, 22. Mai 2022 um 05:09:37 UTC+2:
> > On Saturday, May 21, 2022 at 5:58:35 PM UTC-4, Mostowski Collapse (Jan Burse) wrote:
> > > It depends. In your file https://dcproof.com/EvenNextOdd.htm , you should
> > > write the following:
> > >
> > > 6 ALL(a):ALL(b):[a e d & b e d => a+b e d]
> > It was correctly stated as:
> >
> > ALL(a):ALL(b):[a e n & b e n => a+b e n]
> >
> > where n = the set of natural numbers
> > Deal with it, Jan Burse.
> > > Axiom
> > > Properties of +
> > > 7 ALL(a):ALL(b):[a e d & b e d => a+b=b+a]
> > Wrong again, Jan Burse.
> >
> > It is corrected stated as:
> >
> > ALL(a):ALL(b):[a e n & b e n => a+b=b+a]
> > > Axiom
> > > https://dcproof.com/EvenNextOdd.htm
> > >
> > > Where is associativity? LoL
> > When will you learn, Jan Burse??? It wasn't required to prove the required results, so it was not listed. Geez yer dumb!
> > > Where is all of Peano?
> > As above, idiot! Do try to learn some math, 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

Re: DC Proof is the biggest teaching mistake

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Subject: Re: DC Proof is the biggest teaching mistake
From: Dan_Chri...@sympatico.ca (Dan Christensen)
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 by: Dan Christensen - Sun, 22 May 2022 19:04 UTC

On Sunday, May 22, 2022 at 4:44:52 AM UTC-4, Mostowski Collapse wrote:
> No mathematician is this careless as you are.
>
[snip]

None are as desperate as you, Jan Burse. Learn some math and just admit you were wrong and save yourself all this embarrassment.

Dan

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