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tech / sci.math / Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)

SubjectAuthor
* Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)Mostowski Collapse
+- Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)Mostowski Collapse
+* Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)Dan Christensen
|`* Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)Mostowski Collapse
| `* Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)Dan Christensen
|  `* Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)Mostowski Collapse
|   `* Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)Dan Christensen
|    +- Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)Mostowski Collapse
|    `* Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)Mostowski Collapse
|     `- Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)Mostowski Collapse
`* Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)Codey Ogata
 `* Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)Mostowski Collapse
  +- Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)Mostowski Collapse
  `* Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)Billy Naito
   `* Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)Mostowski Collapse
    +* Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)Mostowski Collapse
    |`- Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)Mostowski Collapse
    `* Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)Dick Ibuka
     `* Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)Mostowski Collapse
      `- Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)Mostowski Collapse

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Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)

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Subject: Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Sun, 15 May 2022 07:46 UTC

You are promoting non-well defined definitions with your
UNDEFINED nonsense. Lets take a closer look at
even natural numbers, how do they look like?

According to Dan Christensen Case 1 type definition:
{ ... dark elements ..., 0, 2, 4, ..., ... dark elements ... }
For example Even(1/2) might or might not hold.

The Euclid understanding Case 2 type definition:
{0, 2, 4, ...}
Evan(1/2) is definitively false.

What is well defined, see here:

In mathematics, a well-defined expression or unambiguous
expression is an expression whose definition assigns it a
unique interpretation or value.
https://en.wikipedia.org/wiki/Well-defined_expression

> From the introduction:
> "Here, I will develop the exponentiation function on the natural numbers with 0^0 undefined

Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)

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Subject: Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Sun, 15 May 2022 07:48 UTC

Its even provable for the Case 2 type definition:

125 ALL(a):[~a ε n => ~Even(a)]
Conclusion, 114

Here is the full proof:

See here:
https://groups.google.com/g/sci.logic/c/gV50jEU6fvQ/m/ncKE65R2AgAJ

Mostowski Collapse schrieb am Sonntag, 15. Mai 2022 um 09:46:36 UTC+2:
> You are promoting non-well defined definitions with your
> UNDEFINED nonsense. Lets take a closer look at
> even natural numbers, how do they look like?
>
> According to Dan Christensen Case 1 type definition:
> { ... dark elements ..., 0, 2, 4, ..., ... dark elements ... }
> For example Even(1/2) might or might not hold.
>
> The Euclid understanding Case 2 type definition:
> {0, 2, 4, ...}
> Evan(1/2) is definitively false.
>
> What is well defined, see here:
>
> In mathematics, a well-defined expression or unambiguous
> expression is an expression whose definition assigns it a
> unique interpretation or value.
> https://en.wikipedia.org/wiki/Well-defined_expression
>
> > From the introduction:
> > "Here, I will develop the exponentiation function on the natural numbers with 0^0 undefined

Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)

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Subject: Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)
From: Dan_Chri...@sympatico.ca (Dan Christensen)
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 by: Dan Christensen - Sun, 15 May 2022 15:00 UTC

On Sunday, May 15, 2022 at 3:46:36 AM UTC-4, Mostowski Collapse wrote:
> You are promoting non-well defined definitions with your
> UNDEFINED nonsense.

In your example here, the standard definition of evenness on the natural numbers is applicable ONLY to the natural numbers, not, as you would have it, for everything in the universe:

ALL(a):[a in N => [Even(a) <=> EXIST(b):[b in n & a=2*b]]]

In words: For every natural number, we say that it is even if and only if it is a multiple of 2.

This definition cannot be applied for -1 or 1/2. In mathematics, you need to distinguish between the predicate Even(x) being false, and Even(x) being undefined.

Dan

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

Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)

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Subject: Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)
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 by: Mostowski Collapse - Sun, 15 May 2022 15:20 UTC

Whats the use case of your nonsense keeping Even open? You proved:
ALL(a):[a e n => [Even(a) => Odd(a+1)]]

You can only extend it to EvenZ and OddZ:
ALL(a):[a e n => [EvenZ(a) => OddZ(a+1)]]

But this works already not anymore:
ALL(a):[a e n => [EvenQ(a) => OddQ(a+1)]]

The problem is unlike the Peano axioms, which are ∀-Formulas,
they can indeed be satisfied by succN, succZ, succQ, succR, etc..
The even definition is a ∀ ∃ - Formula:

ALL(a):[a in N => [Even(a) <=> EXIST(b):[b in n & a=2*b]]]

And you have hard wired N in the EXIST subformula,
by hard wiring (b in n). So keeping even open is nonsense,
evenN, evenZ still work, but evenQ, evenR, etc.. dont work.

In Q this here flips:

~EXIST(a):[a ε n & 2*a=1]

A proper way to do an open even, Case 1 and Case 2, would be:

Case 1: With Parameter D to solve ∀ ∃ - Formula Problem
ALL(a):[a in D => [Even(D,a) <=> EXIST(b):[b in D & a=2*b]]]

Case 2: With Parameter D to solve ∀ ∃ - Formula Problem
ALL(a):[Even(D,a) <=> a e D & EXIST(b):[b in D & a=2*b]]]

But with parameter case 2 is still better, since it is well defined.

Dan Christensen schrieb am Sonntag, 15. Mai 2022 um 17:00:11 UTC+2:
> On Sunday, May 15, 2022 at 3:46:36 AM UTC-4, Mostowski Collapse wrote:
> > You are promoting non-well defined definitions with your
> > UNDEFINED nonsense.
> In your example here, the standard definition of evenness on the natural numbers is applicable ONLY to the natural numbers, not, as you would have it, for everything in the universe:
>
> ALL(a):[a in N => [Even(a) <=> EXIST(b):[b in n & a=2*b]]]
>
> In words: For every natural number, we say that it is even if and only if it is a multiple of 2.
>
> This definition cannot be applied for -1 or 1/2. In mathematics, you need to distinguish between the predicate Even(x) being false, and Even(x) being undefined.
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com

Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)

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Subject: Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)
From: Dan_Chri...@sympatico.ca (Dan Christensen)
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 by: Dan Christensen - Sun, 15 May 2022 15:47 UTC

On Sunday, May 15, 2022 at 11:20:07 AM UTC-4, Mostowski Collapse wrote:
> Whats the use case of your nonsense keeping Even open? You proved:
> ALL(a):[a e n => [Even(a) => Odd(a+1)]]
>
> You can only extend it to EvenZ and OddZ:
> ALL(a):[a e n => [EvenZ(a) => OddZ(a+1)]]
>
> But this works already not anymore:
> ALL(a):[a e n => [EvenQ(a) => OddQ(a+1)]]
>

Makes no sense.

The standard definition again: For every natural number, we say it is even if and only if it is a multiple of 2? On what basis do you reject it? That it can't be applied to a fish or a bicycle? Only to 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

Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)

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Subject: Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Sun, 15 May 2022 15:54 UTC

Yes, I agree. Keeping even open makes no sense in a ∀ ∃ - Theory.
Ever seen a natural number that is not the double of a rational number?

EvenQ = Q
OddQ = {}

So what you proved:

ALL(a):[a e n => [Even(a) => Odd(a+1)]]
https://dcproof.com/EvenNextOdd.htm

Doesnt work for Q. So keeping Even(1/2) UNDEFINED makes
no sense. In general keeping predicates open for ∀ ∃ - Theories

is not very useful.

Dan Christensen schrieb am Sonntag, 15. Mai 2022 um 17:47:10 UTC+2:
> On Sunday, May 15, 2022 at 11:20:07 AM UTC-4, Mostowski Collapse wrote:
> > Whats the use case of your nonsense keeping Even open? You proved:
> > ALL(a):[a e n => [Even(a) => Odd(a+1)]]
> >
> > You can only extend it to EvenZ and OddZ:
> > ALL(a):[a e n => [EvenZ(a) => OddZ(a+1)]]
> >
> > But this works already not anymore:
> > ALL(a):[a e n => [EvenQ(a) => OddQ(a+1)]]
> >
> Makes no sense.
>
> The standard definition again: For every natural number, we say it is even if and only if it is a multiple of 2? On what basis do you reject it? That it can't be applied to a fish or a bicycle? Only to 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

Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)

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Subject: Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)
From: Dan_Chri...@sympatico.ca (Dan Christensen)
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 by: Dan Christensen - Sun, 15 May 2022 16:34 UTC

On Sunday, May 15, 2022 at 11:55:04 AM UTC-4, Mostowski Collapse wrote:

> Dan Christensen schrieb am Sonntag, 15. Mai 2022 um 17:47:10 UTC+2:
> > On Sunday, May 15, 2022 at 11:20:07 AM UTC-4, Mostowski Collapse wrote:
> > > Whats the use case of your nonsense keeping Even open? You proved:
> > > ALL(a):[a e n => [Even(a) => Odd(a+1)]]
> > >
> > > You can only extend it to EvenZ and OddZ:
> > > ALL(a):[a e n => [EvenZ(a) => OddZ(a+1)]]
> > >
> > > But this works already not anymore:
> > > ALL(a):[a e n => [EvenQ(a) => OddQ(a+1)]]
> > >
> > Makes no sense.
> >
> > The standard definition again: For every natural number, we say it is even if and only if it is a multiple of 2? On what basis do you reject it? That it can't be applied to a fish or a bicycle? Only to natural numbers?

> Yes, I agree. Keeping even open makes no sense in a ∀ ∃ - Theory.
> Ever seen a natural number that is not the double of a rational number?
>
> EvenQ = Q
> OddQ = {}
>
> So what you proved:
> ALL(a):[a e n => [Even(a) => Odd(a+1)]]
> https://dcproof.com/EvenNextOdd.htm
>
> Doesnt work for Q.

Pay attention, Jan Burse. It is a theorem about the natural numbers.

> So keeping Even(1/2) UNDEFINED makes
> no sense.

It makes sense on the natural numbers, the subject of the theorem.

> In general keeping predicates open for ∀ ∃ - Theories
>
> is not very useful.

On the contrary, you must be able to distinguish cases of Even(x) being false and Even(x) being undefined. This is impossible with your wonky definition, Jan Burse. Deal with it. Just admit you were wrong. You are looking like a fool here. A true crank.

Dan

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

Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)

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Subject: Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Sun, 15 May 2022 17:28 UTC

I wouldn't say so. You cannot make more theorems
with your axioms, that Euclid cannot do. For example:

fish e pond
-------------------------------------------
Even(fish) <=> ~Odd(fish))

bicycle e street
-----------------------------------------------------------
=> (~Even(bicycle) <=> Odd(bicycle))

Thats provable from your axioms here:
https://dcproof.com/EvenNextOdd.htm

Even fish, odd bicycle, etc..? How weird is that?

Here is a proof:

1 ALL(a):[Odd(a) <=> ~Even(a)]
Axiom

2 fish ε pond
Axiom

3 Odd(fish) <=> ~Even(fish)
U Spec, 1

4 [Odd(fish) => ~Even(fish)] & [~Even(fish) => Odd(fish)]
Iff-And, 3

5 Odd(fish) => ~Even(fish)
Split, 4

6 ~Even(fish) => Odd(fish)
Split, 4

7 ~~Even(fish) => ~Odd(fish)
Contra, 5

8 ~Odd(fish) => ~~Even(fish)
Contra, 6

9 Even(fish) => ~Odd(fish)
Rem DNeg, 7

10 ~Odd(fish) => Even(fish)
Rem DNeg, 8

11 [Even(fish) => ~Odd(fish)]
& [~Odd(fish) => Even(fish)]
Join, 9, 10

12 Even(fish) <=> ~Odd(fish)
Iff-And, 11

Dan Christensen schrieb am Sonntag, 15. Mai 2022 um 18:34:27 UTC+2:
> On Sunday, May 15, 2022 at 11:55:04 AM UTC-4, Mostowski Collapse wrote:
>
> > Dan Christensen schrieb am Sonntag, 15. Mai 2022 um 17:47:10 UTC+2:
> > > On Sunday, May 15, 2022 at 11:20:07 AM UTC-4, Mostowski Collapse wrote:
> > > > Whats the use case of your nonsense keeping Even open? You proved:
> > > > ALL(a):[a e n => [Even(a) => Odd(a+1)]]
> > > >
> > > > You can only extend it to EvenZ and OddZ:
> > > > ALL(a):[a e n => [EvenZ(a) => OddZ(a+1)]]
> > > >
> > > > But this works already not anymore:
> > > > ALL(a):[a e n => [EvenQ(a) => OddQ(a+1)]]
> > > >
> > > Makes no sense.
> > >
> > > The standard definition again: For every natural number, we say it is even if and only if it is a multiple of 2? On what basis do you reject it? That it can't be applied to a fish or a bicycle? Only to natural numbers?
> > Yes, I agree. Keeping even open makes no sense in a ∀ ∃ - Theory.
> > Ever seen a natural number that is not the double of a rational number?
> >
> > EvenQ = Q
> > OddQ = {}
> >
> > So what you proved:
> > ALL(a):[a e n => [Even(a) => Odd(a+1)]]
> > https://dcproof.com/EvenNextOdd.htm
> >
> > Doesnt work for Q.
> Pay attention, Jan Burse. It is a theorem about the natural numbers.
> > So keeping Even(1/2) UNDEFINED makes
> > no sense.
> It makes sense on the natural numbers, the subject of the theorem.
> > In general keeping predicates open for ∀ ∃ - Theories
> >
> > is not very useful.
> On the contrary, you must be able to distinguish cases of Even(x) being false and Even(x) being undefined. This is impossible with your wonky definition, Jan Burse. Deal with it. Just admit you were wrong. You are looking like a fool here. A true crank.
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com

Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)

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Subject: Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Sun, 15 May 2022 17:30 UTC

I wouldn't say so. You can make more theorems
with your axioms, that Euclid cannot do. For example:

fish e pond
-------------------------------------------
Even(fish) <=> ~Odd(fish))

bicycle e street
-----------------------------------------------------------
=> (~Even(bicycle) <=> Odd(bicycle))

Thats provable from your axioms here:
https://dcproof.com/EvenNextOdd.htm

Even fish, odd bicycle, etc..? How weird is that?

Here is a proof:

1 ALL(a):[Odd(a) <=> ~Even(a)]
Axiom

2 fish ε pond
Axiom

3 Odd(fish) <=> ~Even(fish)
U Spec, 1

4 [Odd(fish) => ~Even(fish)] & [~Even(fish) => Odd(fish)]
Iff-And, 3

5 Odd(fish) => ~Even(fish)
Split, 4

6 ~Even(fish) => Odd(fish)
Split, 4

7 ~~Even(fish) => ~Odd(fish)
Contra, 5

8 ~Odd(fish) => ~~Even(fish)
Contra, 6

9 Even(fish) => ~Odd(fish)
Rem DNeg, 7

10 ~Odd(fish) => Even(fish)
Rem DNeg, 8

11 [Even(fish) => ~Odd(fish)]
& [~Odd(fish) => Even(fish)]
Join, 9, 10

12 Even(fish) <=> ~Odd(fish)
Iff-And, 11

Dan Christensen schrieb am Sonntag, 15. Mai 2022 um 18:34:27 UTC+2:
> On Sunday, May 15, 2022 at 11:55:04 AM UTC-4, Mostowski Collapse wrote:
>
> > Dan Christensen schrieb am Sonntag, 15. Mai 2022 um 17:47:10 UTC+2:
> > > On Sunday, May 15, 2022 at 11:20:07 AM UTC-4, Mostowski Collapse wrote:
> > > > Whats the use case of your nonsense keeping Even open? You proved:
> > > > ALL(a):[a e n => [Even(a) => Odd(a+1)]]
> > > >
> > > > You can only extend it to EvenZ and OddZ:
> > > > ALL(a):[a e n => [EvenZ(a) => OddZ(a+1)]]
> > > >
> > > > But this works already not anymore:
> > > > ALL(a):[a e n => [EvenQ(a) => OddQ(a+1)]]
> > > >
> > > Makes no sense.
> > >
> > > The standard definition again: For every natural number, we say it is even if and only if it is a multiple of 2? On what basis do you reject it? That it can't be applied to a fish or a bicycle? Only to natural numbers?
> > Yes, I agree. Keeping even open makes no sense in a ∀ ∃ - Theory.
> > Ever seen a natural number that is not the double of a rational number?
> >
> > EvenQ = Q
> > OddQ = {}
> >
> > So what you proved:
> > ALL(a):[a e n => [Even(a) => Odd(a+1)]]
> > https://dcproof.com/EvenNextOdd.htm
> >
> > Doesnt work for Q.
> Pay attention, Jan Burse. It is a theorem about the natural numbers.
> > So keeping Even(1/2) UNDEFINED makes
> > no sense.
> It makes sense on the natural numbers, the subject of the theorem.
> > In general keeping predicates open for ∀ ∃ - Theories
> >
> > is not very useful.
> On the contrary, you must be able to distinguish cases of Even(x) being false and Even(x) being undefined. This is impossible with your wonky definition, Jan Burse. Deal with it. Just admit you were wrong. You are looking like a fool here. A true crank.
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com

Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)

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Subject: Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Sun, 15 May 2022 17:36 UTC

In the Case 2 definition, in Euclid setting, you cannot
prove nonsense like this:

2 fish ε pond
Axiom

12 Even(fish) <=> ~Odd(fish)
Iff-And, 11

Unless you have pond = n also somewhere. On the
other hand Dan Christensen approach,
which is not a fault of Case 1 versus Case 2, but
yet another fault, can make such irrelevant

theorems. The modelling in:
https://dcproof.com/EvenNextOdd.htm

Lacks some relevance to n. There are better
ways to define a pair Even and Odd, with
keeping the relevance to the natural numbers
intact and not making blunder.

Its exactly a fault he critizes in other people,
but I guess he doesn't see it as a fault, since
he assumes ~UNDEFINED = UNDEFINED,
and then thinks everything is fine?

Mostowski Collapse schrieb am Sonntag, 15. Mai 2022 um 19:30:24 UTC+2:
> I wouldn't say so. You can make more theorems
> with your axioms, that Euclid cannot do. For example:
>
> fish e pond
> -------------------------------------------
> Even(fish) <=> ~Odd(fish))
>
> bicycle e street
> -----------------------------------------------------------
> => (~Even(bicycle) <=> Odd(bicycle))
>
> Thats provable from your axioms here:
> https://dcproof.com/EvenNextOdd.htm
>
> Even fish, odd bicycle, etc..? How weird is that?
>
> Here is a proof:
>
> 1 ALL(a):[Odd(a) <=> ~Even(a)]
> Axiom
>
> 2 fish ε pond
> Axiom
>
> 3 Odd(fish) <=> ~Even(fish)
> U Spec, 1
>
> 4 [Odd(fish) => ~Even(fish)] & [~Even(fish) => Odd(fish)]
> Iff-And, 3
>
> 5 Odd(fish) => ~Even(fish)
> Split, 4
>
> 6 ~Even(fish) => Odd(fish)
> Split, 4
>
> 7 ~~Even(fish) => ~Odd(fish)
> Contra, 5
>
> 8 ~Odd(fish) => ~~Even(fish)
> Contra, 6
>
> 9 Even(fish) => ~Odd(fish)
> Rem DNeg, 7
>
> 10 ~Odd(fish) => Even(fish)
> Rem DNeg, 8
>
> 11 [Even(fish) => ~Odd(fish)]
> & [~Odd(fish) => Even(fish)]
> Join, 9, 10
>
> 12 Even(fish) <=> ~Odd(fish)
> Iff-And, 11
> Dan Christensen schrieb am Sonntag, 15. Mai 2022 um 18:34:27 UTC+2:
> > On Sunday, May 15, 2022 at 11:55:04 AM UTC-4, Mostowski Collapse wrote:
> >
> > > Dan Christensen schrieb am Sonntag, 15. Mai 2022 um 17:47:10 UTC+2:
> > > > On Sunday, May 15, 2022 at 11:20:07 AM UTC-4, Mostowski Collapse wrote:
> > > > > Whats the use case of your nonsense keeping Even open? You proved:
> > > > > ALL(a):[a e n => [Even(a) => Odd(a+1)]]
> > > > >
> > > > > You can only extend it to EvenZ and OddZ:
> > > > > ALL(a):[a e n => [EvenZ(a) => OddZ(a+1)]]
> > > > >
> > > > > But this works already not anymore:
> > > > > ALL(a):[a e n => [EvenQ(a) => OddQ(a+1)]]
> > > > >
> > > > Makes no sense.
> > > >
> > > > The standard definition again: For every natural number, we say it is even if and only if it is a multiple of 2? On what basis do you reject it? That it can't be applied to a fish or a bicycle? Only to natural numbers?
> > > Yes, I agree. Keeping even open makes no sense in a ∀ ∃ - Theory.
> > > Ever seen a natural number that is not the double of a rational number?
> > >
> > > EvenQ = Q
> > > OddQ = {}
> > >
> > > So what you proved:
> > > ALL(a):[a e n => [Even(a) => Odd(a+1)]]
> > > https://dcproof.com/EvenNextOdd.htm
> > >
> > > Doesnt work for Q.
> > Pay attention, Jan Burse. It is a theorem about the natural numbers.
> > > So keeping Even(1/2) UNDEFINED makes
> > > no sense.
> > It makes sense on the natural numbers, the subject of the theorem.
> > > In general keeping predicates open for ∀ ∃ - Theories
> > >
> > > is not very useful.
> > On the contrary, you must be able to distinguish cases of Even(x) being false and Even(x) being undefined. This is impossible with your wonky definition, Jan Burse. Deal with it. Just admit you were wrong. You are looking like a fool here. A true crank.
> > Dan
> >
> > Download my DC Proof 2.0 freeware at http://www.dcproof.com
> > Visit my Math Blog at http://www.dcproof.wordpress.com

Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)

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Subject: Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)
Date: Mon, 16 May 2022 10:13:09 -0000 (UTC)
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 by: Codey Ogata - Mon, 16 May 2022 10:13 UTC

Mostowski Collapse wrote:

> According to Dan Christensen Case 1 type definition:
> { ... dark elements ..., 0, 2, 4, ..., ... dark elements ... }
> For example Even(1/2) might or might not hold.
> The Euclid understanding Case 2 type definition:
> {0, 2, 4, ...} Evan(1/2) is definitively false.

so true so much indeed. Time to leave that _shithole_ named _switzarland_!
They steal your organs out *_B_E_F_O_R_E_* you are dead!! Amazing what
those *fake_money* can do with the citizens. How the fuck to live in that
shithole, are you humans??

Switzerland changes organ donation rules
60% of Swiss voters support new ‘presumed consent’ system
https://www.rt.com/news/555529-switzerland-organ-donor-referendum/

Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)

<e9c74784-4d52-4155-8dfb-69b8eefede56n@googlegroups.com>

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Subject: Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Mon, 16 May 2022 11:00 UTC

Ha Ha, micro penis aka Luigi, guess what:

Russia has a so-called opt-out system, under which all adult
citizens are presumed to have given consent to their organs
being donated after their death unless they sign a
notarized document stating otherwise.

An opt-out system has been in place for decades in Israel,
Singapore, and a number of European countries including Spain,
Europe's leader in organ transplantation.
https://www.rferl.org/a/russia-organ-harvesting-grieving-mother/27617168.html

Codey Ogata schrieb am Montag, 16. Mai 2022 um 12:13:23 UTC+2:
> Mostowski Collapse wrote:
>
> > According to Dan Christensen Case 1 type definition:
> > { ... dark elements ..., 0, 2, 4, ..., ... dark elements ... }
> > For example Even(1/2) might or might not hold.
> > The Euclid understanding Case 2 type definition:
> > {0, 2, 4, ...} Evan(1/2) is definitively false.
> so true so much indeed. Time to leave that _shithole_ named _switzarland_!
> They steal your organs out *_B_E_F_O_R_E_* you are dead!! Amazing what
> those *fake_money* can do with the citizens. How the fuck to live in that
> shithole, are you humans??
>
> Switzerland changes organ donation rules
> 60% of Swiss voters support new ‘presumed consent’ system
> https://www.rt.com/news/555529-switzerland-organ-donor-referendum/

Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)

<6055bf2d-da19-4dbe-9e1c-6b7a98875ab2n@googlegroups.com>

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Subject: Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Mon, 16 May 2022 11:07 UTC

BTW: formerly ruSSIa is now called east Ukaine:

Let's start online referendum :-)
https://twitter.com/CMCD048/status/1525953321755893761

LoL

Mostowski Collapse schrieb am Montag, 16. Mai 2022 um 13:00:30 UTC+2:
> Ha Ha, micro penis aka Luigi, guess what:
>
> Russia has a so-called opt-out system, under which all adult
> citizens are presumed to have given consent to their organs
> being donated after their death unless they sign a
> notarized document stating otherwise.
>
> An opt-out system has been in place for decades in Israel,
> Singapore, and a number of European countries including Spain,
> Europe's leader in organ transplantation.
> https://www.rferl.org/a/russia-organ-harvesting-grieving-mother/27617168.html
> Codey Ogata schrieb am Montag, 16. Mai 2022 um 12:13:23 UTC+2:
> > Mostowski Collapse wrote:
> >
> > > According to Dan Christensen Case 1 type definition:
> > > { ... dark elements ..., 0, 2, 4, ..., ... dark elements ... }
> > > For example Even(1/2) might or might not hold.
> > > The Euclid understanding Case 2 type definition:
> > > {0, 2, 4, ...} Evan(1/2) is definitively false.
> > so true so much indeed. Time to leave that _shithole_ named _switzarland_!
> > They steal your organs out *_B_E_F_O_R_E_* you are dead!! Amazing what
> > those *fake_money* can do with the citizens. How the fuck to live in that
> > shithole, are you humans??
> >
> > Switzerland changes organ donation rules
> > 60% of Swiss voters support new ‘presumed consent’ system
> > https://www.rt.com/news/555529-switzerland-organ-donor-referendum/

Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)

<t5tbr4$k6h$1@gioia.aioe.org>

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From: ltl...@oyiyllal.ti (Billy Naito)
Newsgroups: sci.math
Subject: Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)
Date: Mon, 16 May 2022 11:16:52 -0000 (UTC)
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 by: Billy Naito - Mon, 16 May 2022 11:16 UTC

Mostowski Collapse wrote:

> Ha Ha, micro penis aka Luigi, guess what:
> Russia has a so-called opt-out system, under which all adult citizens
> are presumed to have given consent to their organs being donated after
> their death unless they sign a notarized document stating otherwise.

hmm, this math imbecile isn't knowing he has to be alive when his organs
are stolen. I bet the big mathematicians around here, are not knowing this
simple thing.

"However, Frei claimed the result was skewed by people who are misinformed
about the organ donation procedure, and thinking of “cold bodies” in
freezers rather than brain-dead patients still on life support in ICU,
according to Swissinfo."

moreover, nazi "ukraine", known as *vanilla_ISIS*, is committing openly
*_severe_war_crimes_*, getting nobelized in return, with eurovision and
Nobel prize for "peace", loads of money and armament, cocaine etc etc and
etc, by the corrupt liberal capitalist "west", knowingly the facts, that
the nazi "ukraine" are inbreed terrorists.

Ukraine Military Committing War Crimes!
https://www.brighteon.com/ee7d2ff9-b855-4f01-85b1-73eeb06aa64f

*nazi_cocaine_Selenskyy* brazenly admits on Fox News that various Nazi
groups are incorporated into the Ukrainian Army, known as *vanilla_ISIS*!!
https://www.brighteon.com/bf69ac6f-b2ee-469f-a41a-d56237075d8e

Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)

<9e6af712-0fdb-42ef-a81b-0f4b8e302843n@googlegroups.com>

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Subject: Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Mon, 16 May 2022 12:32 UTC

You are already brain dead micro penis, I guess you are an
internet zombie without any organs, almost like an Egyptian
mummy, only with a keyboard and screen as extra.

LoL

BTW: There is was a famous Swiss death researcher:
https://en.m.wikipedia.org/wiki/Elisabeth_K%C3%BCbler-Ross

Unfortunately shes dead, so she wont look into your case of
internet zombie by brain death through bitchute cocaine.

Billy Naito schrieb am Montag, 16. Mai 2022 um 13:17:03 UTC+2:
> Mostowski Collapse wrote:
>
> > Ha Ha, micro penis aka Luigi, guess what:
> > Russia has a so-called opt-out system, under which all adult citizens
> > are presumed to have given consent to their organs being donated after
> > their death unless they sign a notarized document stating otherwise.
> hmm, this math imbecile isn't knowing he has to be alive when his organs
> are stolen. I bet the big mathematicians around here, are not knowing this
> simple thing.
>
> "However, Frei claimed the result was skewed by people who are misinformed
> about the organ donation procedure, and thinking of “cold bodies” in
> freezers rather than brain-dead patients still on life support in ICU,
> according to Swissinfo."

Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)

<16830405-04bb-4538-af35-db69f9a5ff43n@googlegroups.com>

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Subject: Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Mon, 16 May 2022 12:41 UTC

But mwith new neuroscience methods, there are certain
new ways to determine whether a patient is in coma or
brain dead? This article is from 2019:

January 29, 2019; 92 (5) SPECIAL ARTICLE
Brain death, the determination of brain death, and member
guidance for brain death accommodation requests
https://n.neurology.org/content/92/5/228

Maybe if a person does suse bitchute cocaine or
DC Proof with Dan Christensen definitions, we
can say this person is brain dead?

Mostowski Collapse schrieb am Montag, 16. Mai 2022 um 14:32:16 UTC+2:
> You are already brain dead micro penis, I guess you are an
> internet zombie without any organs, almost like an Egyptian
> mummy, only with a keyboard and screen as extra.
>
> LoL
>
>
> BTW: There is was a famous Swiss death researcher:
> https://en.m.wikipedia.org/wiki/Elisabeth_K%C3%BCbler-Ross
>
> Unfortunately shes dead, so she wont look into your case of
> internet zombie by brain death through bitchute cocaine.
> Billy Naito schrieb am Montag, 16. Mai 2022 um 13:17:03 UTC+2:
> > Mostowski Collapse wrote:
> >
> > > Ha Ha, micro penis aka Luigi, guess what:
> > > Russia has a so-called opt-out system, under which all adult citizens
> > > are presumed to have given consent to their organs being donated after
> > > their death unless they sign a notarized document stating otherwise.
> > hmm, this math imbecile isn't knowing he has to be alive when his organs
> > are stolen. I bet the big mathematicians around here, are not knowing this
> > simple thing.
> >
> > "However, Frei claimed the result was skewed by people who are misinformed
> > about the organ donation procedure, and thinking of “cold bodies” in
> > freezers rather than brain-dead patients still on life support in ICU,
> > according to Swissinfo."

Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)

<cfaeae8a-1087-4059-96c5-37e6fe5ce604n@googlegroups.com>

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Subject: Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Mon, 16 May 2022 12:54 UTC

Its quite possible that comrad micro penis aka luigi is
already brain death, since his posts are only incoherent
bowel movements. So maybe comrad micro prenis

was shelled a few years ago in Donbass and is
now some vegetable in some tuSSian orcSS poison
laboratory. Quite possible, he was talking about

downloading stuff via vaccines, so thats maybe
how he gets prepared. After all new medicinal
technology is quite amazing:

As a result, irreversibly brain-injured individuals could
have their physiologic existence sustained for
variable periods of time.
https://n.neurology.org/content/neurology/92/5/228.full.pdf

So all the ruSSian bots are brain dead mummies?

Mostowski Collapse schrieb am Montag, 16. Mai 2022 um 14:41:19 UTC+2:
> But mwith new neuroscience methods, there are certain
> new ways to determine whether a patient is in coma or
> brain dead? This article is from 2019:
>
> January 29, 2019; 92 (5) SPECIAL ARTICLE
> Brain death, the determination of brain death, and member
> guidance for brain death accommodation requests
> https://n.neurology.org/content/92/5/228
>
> Maybe if a person does suse bitchute cocaine or
> DC Proof with Dan Christensen definitions, we
> can say this person is brain dead?
> Mostowski Collapse schrieb am Montag, 16. Mai 2022 um 14:32:16 UTC+2:
> > You are already brain dead micro penis, I guess you are an
> > internet zombie without any organs, almost like an Egyptian
> > mummy, only with a keyboard and screen as extra.
> >
> > LoL
> >
> >
> > BTW: There is was a famous Swiss death researcher:
> > https://en.m.wikipedia.org/wiki/Elisabeth_K%C3%BCbler-Ross
> >
> > Unfortunately shes dead, so she wont look into your case of
> > internet zombie by brain death through bitchute cocaine.
> > Billy Naito schrieb am Montag, 16. Mai 2022 um 13:17:03 UTC+2:
> > > Mostowski Collapse wrote:
> > >
> > > > Ha Ha, micro penis aka Luigi, guess what:
> > > > Russia has a so-called opt-out system, under which all adult citizens
> > > > are presumed to have given consent to their organs being donated after
> > > > their death unless they sign a notarized document stating otherwise..
> > > hmm, this math imbecile isn't knowing he has to be alive when his organs
> > > are stolen. I bet the big mathematicians around here, are not knowing this
> > > simple thing.
> > >
> > > "However, Frei claimed the result was skewed by people who are misinformed
> > > about the organ donation procedure, and thinking of “cold bodies” in
> > > freezers rather than brain-dead patients still on life support in ICU,
> > > according to Swissinfo."

Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)

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From: iak...@ciidkcki.cd (Dick Ibuka)
Newsgroups: sci.math
Subject: Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)
Date: Mon, 16 May 2022 12:58:04 -0000 (UTC)
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 by: Dick Ibuka - Mon, 16 May 2022 12:58 UTC

Mostowski Collapse wrote:

> You are already brain dead micro penis, I guess you are an internet

You stinking "micro_penises" obsessed pedophile. Read the given *data*.
The switzarlenders are stupid and fooled by the corrupt government,
thinking they are to be dead when their organs, eyes, veins, etc are
stolen by the *_big_pharma_* once again.

You stupid braindead *fake_money* slavic nazi, turned anglo-saxon
overnight. Your organs, accordingly, can be stole right now. You are
fucking *braindead*, specified by the filter.

>> hmm, this math imbecile isn't knowing he has to be alive when his
>> organs are stolen. I bet the big mathematicians around here, are not
>> knowing this simple thing.
>>
>> "However, Frei claimed the result was skewed by people who are
>> misinformed about the organ donation procedure, and thinking of “cold
>> bodies” in freezers rather than brain-dead patients still on life
>> support in ICU, according to Swissinfo."

Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)

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Subject: Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Mon, 16 May 2022 13:17 UTC

Well big pharma will find more brain dead in Russia,
half of the population is brain dead from vodka.

"Russia has a so-called opt-out system, under which all adult
citizens are presumed to have given consent to their organs
being donated after their death unless they sign a
notarized document stating otherwise."
https://www.rferl.org/a/russia-organ-harvesting-grieving-mother/27617168.html

They even don't need freezers in siberia. Thats
why the Gulags are such a success.

Dick Ibuka schrieb am Montag, 16. Mai 2022 um 14:58:14 UTC+2:
> Mostowski Collapse wrote:
>
> > You are already brain dead micro penis, I guess you are an internet
> You stinking "micro_penises" obsessed pedophile. Read the given *data*.
> The switzarlenders are stupid and fooled by the corrupt government,
> thinking they are to be dead when their organs, eyes, veins, etc are
> stolen by the *_big_pharma_* once again.
>
> You stupid braindead *fake_money* slavic nazi, turned anglo-saxon
> overnight. Your organs, accordingly, can be stole right now. You are
> fucking *braindead*, specified by the filter.
> >> hmm, this math imbecile isn't knowing he has to be alive when his
> >> organs are stolen. I bet the big mathematicians around here, are not
> >> knowing this simple thing.
> >>
> >> "However, Frei claimed the result was skewed by people who are
> >> misinformed about the organ donation procedure, and thinking of “cold
> >> bodies” in freezers rather than brain-dead patients still on life
> >> support in ICU, according to Swissinfo."

Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)

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Subject: Re: Oh, the Ambiguity! 0^0 = ??? (Updated blog posting)
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Mon, 16 May 2022 13:30 UTC

Just go find the Russian Text and an English Translation of:

Order of the Ministry of Health of the Russian Federation dated
December 25, 2014 No. 908n “On the Procedure for Establishing
a Diagnosis of Human Brain Death”,
https://www.europeanproceedings.com/article/10.15405/epsbs.2021.02.02.54

Tell us your findings....

LMAO!

Mostowski Collapse schrieb am Montag, 16. Mai 2022 um 15:17:34 UTC+2:
> Well big pharma will find more brain dead in Russia,
> half of the population is brain dead from vodka.
> "Russia has a so-called opt-out system, under which all adult
> citizens are presumed to have given consent to their organs
> being donated after their death unless they sign a
> notarized document stating otherwise."
> https://www.rferl.org/a/russia-organ-harvesting-grieving-mother/27617168.html
>
> They even don't need freezers in siberia. Thats
> why the Gulags are such a success.
> Dick Ibuka schrieb am Montag, 16. Mai 2022 um 14:58:14 UTC+2:
> > Mostowski Collapse wrote:
> >
> > > You are already brain dead micro penis, I guess you are an internet
> > You stinking "micro_penises" obsessed pedophile. Read the given *data*.
> > The switzarlenders are stupid and fooled by the corrupt government,
> > thinking they are to be dead when their organs, eyes, veins, etc are
> > stolen by the *_big_pharma_* once again.
> >
> > You stupid braindead *fake_money* slavic nazi, turned anglo-saxon
> > overnight. Your organs, accordingly, can be stole right now. You are
> > fucking *braindead*, specified by the filter.
> > >> hmm, this math imbecile isn't knowing he has to be alive when his
> > >> organs are stolen. I bet the big mathematicians around here, are not
> > >> knowing this simple thing.
> > >>
> > >> "However, Frei claimed the result was skewed by people who are
> > >> misinformed about the organ donation procedure, and thinking of “cold
> > >> bodies” in freezers rather than brain-dead patients still on life
> > >> support in ICU, according to Swissinfo."

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