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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

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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, 28 May 2022 02:32 UTC

On Friday, May 27, 2022 at 12:49:04 PM UTC-4, Mostowski Collapse wrote:
> The bottom line is, we get Pressburger Arithmetic
> by these simple axioms:
> https://en.wikipedia.org/wiki/Presburger_arithmetic
>

Desperately trying to change the subject, to create a diversion from you failed arguments, Jan Burse? It seems you continue to desperately grasp at straws. Presburger's Axioms are simply a kind of toy version of Peano's Axioms. It is not a substitute or any kind of real alternative in number theory.

"Presburger arithmetic is much weaker than Peano arithmetic, which includes both addition and multiplication operations.... It cannot formalize concepts such as divisibility or primality, or, more generally, any number concept leading to multiplication of variables."
https://en.wikipedia.org/wiki/Presburger_arithmetic

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 - Sat, 28 May 2022 09:52 UTC

You should be able to prove it from Presburger arithmetic
only, thats quite easy, I sketched it already here:
https://groups.google.com/g/sci.logic/c/UABVyIeAlxc/m/O_kQbK6PAQAJ

Presburger arithmetic is Peano induction
plus addition. See here:

x + 0 = x
x + (y + 1) = (x + y) + 1
https://en.wikipedia.org/wiki/Presburger_arithmetic

No need to introduce multiplication which is not necessarely
multiplication on the natural numbers. Just use a+a in place of 2*a.

On the German Wikipedia of Presburger arithmetic,
they make Even as an example for Presburger arithmetic:

„ x ist gerade“ durch G ( x ) :⇔ ∃ z : z + z = x
https://de.wikipedia.org/wiki/Presburger-Arithmetik

Dan Christensen schrieb am Samstag, 28. Mai 2022 um 04:32:50 UTC+2:
> On Friday, May 27, 2022 at 12:49:04 PM UTC-4, Mostowski Collapse wrote:
> > The bottom line is, we get Pressburger Arithmetic
> > by these simple axioms:
> > https://en.wikipedia.org/wiki/Presburger_arithmetic
> >
> Desperately trying to change the subject, to create a diversion from you failed arguments, Jan Burse? It seems you continue to desperately grasp at straws. Presburger's Axioms are simply a kind of toy version of Peano's Axioms. It is not a substitute or any kind of real alternative in number theory.
>
> "Presburger arithmetic is much weaker than Peano arithmetic, which includes both addition and multiplication operations.... It cannot formalize concepts such as divisibility or primality, or, more generally, any number concept leading to multiplication of variables."
> https://en.wikipedia.org/wiki/Presburger_arithmetic
> 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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