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tech / sci.math / Re: DC Proof challenge: Zorn's Lemma, how formalize it?

SubjectAuthor
* Re: DC Proof challenge: Zorn's Lemma, how formalize it?Mostowski Collapse
+* Re: DC Proof challenge: Zorn's Lemma, how formalize it?Dan Christensen
|`* Re: DC Proof challenge: Zorn's Lemma, how formalize it?Heath Soma
| `* Re: DC Proof challenge: Zorn's Lemma, how formalize it?Dan Christensen
|  `* Re: DC Proof challenge: Zorn's Lemma, how formalize it?Robt Kuno
|   `* Re: DC Proof challenge: Zorn's Lemma, how formalize it?Dan Christensen
|    `- Re: DC Proof challenge: Zorn's Lemma, how formalize it?Keven Togo
+- Re: DC Proof challenge: Zorn's Lemma, how formalize it?Dan Christensen
`* Re: DC Proof challenge: Zorn's Lemma, how formalize it?Mostowski Collapse
 `* Re: DC Proof challenge: Zorn's Lemma, how formalize it?Dan Christensen
  +* Re: DC Proof challenge: Zorn's Lemma, how formalize it?Mostowski Collapse
  |`- Re: DC Proof challenge: Zorn's Lemma, how formalize it?Dan Christensen
  `* Re: DC Proof challenge: Zorn's Lemma, how formalize it?Nilo Kiski
   `- Re: DC Proof challenge: Zorn's Lemma, how formalize it?Dan Christensen

1
Re: DC Proof challenge: Zorn's Lemma, how formalize it?

<9167e86f-1df5-493a-b427-66f3e3b7d168n@googlegroups.com>

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Subject: Re: DC Proof challenge: Zorn's Lemma, how formalize it?
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Wed, 18 May 2022 00:15 UTC

Its now almost 1000 days, and we still dont know whether
the real numbers can be ordered:

Every ordered field is a formally real field, i.e., 0 cannot be
written as a sum of nonzero squares. Conversely, every formally
real field can be equipped with a compatible total order, that will
turn it into an ordered field. (This order need not be uniquely determined.)
The proof uses Zorn's lemma.
https://en.wikipedia.org/wiki/Ordered_field#Which_fields_can_be_ordered?

Mostowski Collapse schrieb am Mittwoch, 23. September 2020 um 13:16:22 UTC+2:
> So whats the plan for proving Zorn's Lemma
> in DC Proof? Translate FOL to DC Proof?
>
> How do you think a FOL ZFC theorem is
> to be realized in DC Proof?

Re: DC Proof challenge: Zorn's Lemma, how formalize it?

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Subject: Re: DC Proof challenge: Zorn's Lemma, how formalize it?
From: Dan_Chri...@sympatico.ca (Dan Christensen)
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 by: Dan Christensen - Wed, 18 May 2022 01:03 UTC

On Tuesday, May 17, 2022 at 8:15:30 PM UTC-4, Mostowski Collapse wrote:

> Mostowski Collapse schrieb am Mittwoch, 23. September 2020 um 13:16:22 UTC+2:
> > So whats the plan for proving Zorn's Lemma
> > in DC Proof? Translate FOL to DC Proof?
> >
> > How do you think a FOL ZFC theorem is
> > to be realized in DC Proof?

> Its now almost 1000 days, and we still dont know whether
> the real numbers can be ordered:
>
> Every ordered field is a formally real field, i.e., 0 cannot be
> written as a sum of nonzero squares. Conversely, every formally
> real field can be equipped with a compatible total order, that will
> turn it into an ordered field. (This order need not be uniquely determined.)
> The proof uses Zorn's lemma.
> https://en.wikipedia.org/wiki/Ordered_field#Which_fields_can_be_ordered?

I'm having too much kicking your butt on the simple stuff, Jan Burse. Every student can relate to these fundamental issues. No one will care if I produce a 4000 line formal proof of Zorn's Lemma. If they need an example of power of DC Proof, I need only refer them to my proof of Cantor-Bernstein-Schroeder at my blog.

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 challenge: Zorn's Lemma, how formalize it?

<880e9363-b0b0-4078-9a5d-d258300717cen@googlegroups.com>

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Subject: Re: DC Proof challenge: Zorn's Lemma, how formalize it?
From: Dan_Chri...@sympatico.ca (Dan Christensen)
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 by: Dan Christensen - Wed, 18 May 2022 01:55 UTC

On Tuesday, May 17, 2022 at 8:15:30 PM UTC-4, Mostowski Collapse wrote:

> Mostowski Collapse schrieb am Mittwoch, 23. September 2020 um 13:16:22 UTC+2:
> > So whats the plan for proving Zorn's Lemma
> > in DC Proof? Translate FOL to DC Proof?
> >
> > How do you think a FOL ZFC theorem is
> > to be realized in DC Proof?

> Its now almost 1000 days, and we still dont know whether
> the real numbers can be ordered:
>
> Every ordered field is a formally real field, i.e., 0 cannot be
> written as a sum of nonzero squares. Conversely, every formally
> real field can be equipped with a compatible total order, that will
> turn it into an ordered field. (This order need not be uniquely determined.)
> The proof uses Zorn's lemma.
> https://en.wikipedia.org/wiki/Ordered_field#Which_fields_can_be_ordered?

I'm having too much fun kicking your butt on the simple stuff, Jan Burse. Every student can relate to these fundamental issues. No one will care if I produce a 4000 line formal proof of Zorn's Lemma or whatever. If they need an example of power of DC Proof, I need only refer them to my proof of Cantor-Bernstein-Schroeder at my blog.

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 challenge: Zorn's Lemma, how formalize it?

<t63f28$152p$3@gioia.aioe.org>

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From: oes...@ahotmhos.as (Heath Soma)
Newsgroups: sci.math
Subject: Re: DC Proof challenge: Zorn's Lemma, how formalize it?
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Date: Wed, 18 May 2022 18:48:41 -0000 (UTC)
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 by: Heath Soma - Wed, 18 May 2022 18:48 UTC

Dan Christensen wrote:

>> uses Zorn's lemma.
>> https://en.wikipedia.org/wiki/Ordered_field#Which_fields_can_be_ordered?
>
> I'm having too much kicking your butt on the simple stuff, Jan Burse.
> Every student can relate to these fundamental issues. No one will care if
> I produce a 4000 line formal proof of Zorn's Lemma. If they need an
> example of power of DC Proof, I need only refer them to my proof of
> Cantor-Bernstein-Schroeder at my blog.

inconsistent.

Re: DC Proof challenge: Zorn's Lemma, how formalize it?

<2052ebb1-8b4d-4fc9-baa5-757ca7df08e1n@googlegroups.com>

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Subject: Re: DC Proof challenge: Zorn's Lemma, how formalize it?
From: Dan_Chri...@sympatico.ca (Dan Christensen)
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 by: Dan Christensen - Wed, 18 May 2022 19:17 UTC

On Wednesday, May 18, 2022 at 2:48:51 PM UTC-4, Heath Soma wrote:
> Dan Christensen wrote:
>
> >> uses Zorn's lemma.
> >> https://en.wikipedia.org/wiki/Ordered_field#Which_fields_can_be_ordered?
> >
> > I'm having too much kicking your butt on the simple stuff, Jan Burse.
> > Every student can relate to these fundamental issues. No one will care if
> > I produce a 4000 line formal proof of Zorn's Lemma. If they need an
> > example of power of DC Proof, I need only refer them to my proof of
> > Cantor-Bernstein-Schroeder at my blog.

> inconsistent.

If you want to be taken seriously, you will have to elaborate. Otherwise...

Dan

Re: DC Proof challenge: Zorn's Lemma, how formalize it?

<t63q8u$8ck$2@gioia.aioe.org>

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From: nuu...@kbobrnob.oo (Robt Kuno)
Newsgroups: sci.math
Subject: Re: DC Proof challenge: Zorn's Lemma, how formalize it?
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Date: Wed, 18 May 2022 21:59:59 -0000 (UTC)
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 by: Robt Kuno - Wed, 18 May 2022 21:59 UTC

Dan Christensen wrote:

>> > I'm having too much kicking your butt on the simple stuff, Jan Burse.
>> > Every student can relate to these fundamental issues. No one will
>> > care if I produce a 4000 line formal proof of Zorn's Lemma. If they
>> > need an example of power of DC Proof, I need only refer them to my
>> > proof of Cantor-Bernstein-Schroeder at my blog.
>
>> inconsistent.
>
> If you want to be taken seriously, you will have to elaborate.
> Otherwise...

impossible. It's inconsistent. You can't expect inconsistencies to be
elaborated.

Re: DC Proof challenge: Zorn's Lemma, how formalize it?

<a8923940-fa13-4db2-9f4b-375907c696a6n@googlegroups.com>

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Subject: Re: DC Proof challenge: Zorn's Lemma, how formalize it?
From: Dan_Chri...@sympatico.ca (Dan Christensen)
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 by: Dan Christensen - Wed, 18 May 2022 22:15 UTC

On Wednesday, May 18, 2022 at 6:00:08 PM UTC-4, Robt Kuno wrote:
> Dan Christensen wrote:
>
> >> > I'm having too much kicking your butt on the simple stuff, Jan Burse.
> >> > Every student can relate to these fundamental issues. No one will
> >> > care if I produce a 4000 line formal proof of Zorn's Lemma. If they
> >> > need an example of power of DC Proof, I need only refer them to my
> >> > proof of Cantor-Bernstein-Schroeder at my blog.
> >
> >> inconsistent.
> >
> > If you want to be taken seriously, you will have to elaborate.
> > Otherwise...

> impossible. It's inconsistent. You can't expect inconsistencies to be
> elaborated.

Obviously YOU cannot elaborate. HA, HA, HA!!!! (xaxaxa!!!)

Re: DC Proof challenge: Zorn's Lemma, how formalize it?

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Subject: Re: DC Proof challenge: Zorn's Lemma, how formalize it?
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 by: Keven Togo - Wed, 18 May 2022 22:22 UTC

Dan Christensen wrote:

>> >> inconsistent.
>> >
>> > If you want to be taken seriously, you will have to elaborate.
>> > Otherwise...
>
>> impossible. It's inconsistent. You can't expect inconsistencies to be
>> elaborated.
>
> Obviously YOU cannot elaborate. HA, HA, HA!!!! (xaxaxa!!!)

do it yourself, but you don't know the difference between a suppose and a
proof requirement.

Re: DC Proof challenge: Zorn's Lemma, how formalize it?

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Subject: Re: DC Proof challenge: Zorn's Lemma, how formalize it?
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Wed, 18 May 2022 23:19 UTC

Still waiting, should we use this:

ALL(a):ALL(b):[a e n & b e n => [a<b <=> EXIST(c):[c e n & ~c=0 & a+c=b]]]
https://dcproof.com/EvenNextOdd.htm

To order the reals? The rest of the axioms except
for Nr. 10 are also satisfied by the reals.

Mostowski Collapse schrieb am Mittwoch, 18. Mai 2022 um 02:15:30 UTC+2:
> Its now almost 1000 days, and we still dont know whether
> the real numbers can be ordered:
>
> Every ordered field is a formally real field, i.e., 0 cannot be
> written as a sum of nonzero squares. Conversely, every formally
> real field can be equipped with a compatible total order, that will
> turn it into an ordered field. (This order need not be uniquely determined.)
> The proof uses Zorn's lemma.
> https://en.wikipedia.org/wiki/Ordered_field#Which_fields_can_be_ordered?
> Mostowski Collapse schrieb am Mittwoch, 23. September 2020 um 13:16:22 UTC+2:
> > So whats the plan for proving Zorn's Lemma
> > in DC Proof? Translate FOL to DC Proof?
> >
> > How do you think a FOL ZFC theorem is
> > to be realized in DC Proof?

Re: DC Proof challenge: Zorn's Lemma, how formalize it?

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Subject: Re: DC Proof challenge: Zorn's Lemma, how formalize it?
From: Dan_Chri...@sympatico.ca (Dan Christensen)
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 by: Dan Christensen - Thu, 19 May 2022 00:03 UTC

On Wednesday, May 18, 2022 at 7:19:10 PM UTC-4, Mostowski Collapse wrote:
> Still waiting, should we use this:
>
> ALL(a):ALL(b):[a e n & b e n => [a<b <=> EXIST(c):[c e n & ~c=0 & a+c=b]]]

Maybe you didn't know, but this is the formal definition of < on N (line 13). Used on line 50.

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 challenge: Zorn's Lemma, how formalize it?

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Subject: Re: DC Proof challenge: Zorn's Lemma, how formalize it?
From: burse...@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Thu, 19 May 2022 08:54 UTC

If and only if it were N, and not something else maybe.

LoL

Dan Christensen schrieb am Donnerstag, 19. Mai 2022 um 02:03:24 UTC+2:
> On Wednesday, May 18, 2022 at 7:19:10 PM UTC-4, Mostowski Collapse wrote:
> > Still waiting, should we use this:
> >
> > ALL(a):ALL(b):[a e n & b e n => [a<b <=> EXIST(c):[c e n & ~c=0 & a+c=b]]]
> Maybe you didn't know, but this is the formal definition of < on N (line 13). Used on line 50.
> 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 challenge: Zorn's Lemma, how formalize it?

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Subject: Re: DC Proof challenge: Zorn's Lemma, how formalize it?
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 by: Nilo Kiski - Thu, 19 May 2022 11:38 UTC

Dan Christensen wrote:

> On Wednesday, May 18, 2022 at 7:19:10 PM UTC-4, Mostowski Collapse
> wrote:
>> Still waiting, should we use this:
>> ALL(a):ALL(b):[a e n & b e n => [a<b <=> EXIST(c):[c e n & ~c=0 &
>> a+c=b]]]
>
> Maybe you didn't know, but this is the formal definition of < on N (line
> 13). Used on line 50.

you don't undrestand tensors, you putrid nazi excrement.

UK Column News 18th May 2022
https://www.ukcolumn.org/ukcolumn-news/uk-column-news-18th-may-2022

23:13 - The Word "Surrender" Is Out and "Evacuate" Is In, Sources:
*****************
Guardian AU Article: - https://bit.ly/38CxYb5
Ministry of Defence Channel: - https://bit.ly/3wBTLHT
Defence Intelligence Update 18th May: - https://bit.ly/3wmdPPN
Defence Intelligence Update 17th May: - https://bit.ly/3NnFfKC
Defence Intelligence Update 16th May: - https://bit.ly/3yL47Ir
AP Article: - https://bit.ly/38yGOXm
Defense Politics Asia: - https://bit.ly/3PvlYsA

49:26 - It's All Worth It Propaganda, Sources:
*****************
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DO Article: - https://bit.ly/38ChdwH
The AEI: - https://www.aei.org/
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57:26 - Effectively Spreading Information, Sources:
*****************
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Re: DC Proof challenge: Zorn's Lemma, how formalize it?

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Subject: Re: DC Proof challenge: Zorn's Lemma, how formalize it?
From: Dan_Chri...@sympatico.ca (Dan Christensen)
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 by: Dan Christensen - Thu, 19 May 2022 13:17 UTC

On Thursday, May 19, 2022 at 4:54:21 AM UTC-4, Mostowski Collapse (Jan Burse) wrote:

> Dan Christensen schrieb am Donnerstag, 19. Mai 2022 um 02:03:24 UTC+2:
> > On Wednesday, May 18, 2022 at 7:19:10 PM UTC-4, Mostowski Collapse wrote:
> > > Still waiting, should we use this:
> > >
> > > ALL(a):ALL(b):[a e n & b e n => [a<b <=> EXIST(c):[c e n & ~c=0 & a+c=b]]]
> > Maybe you didn't know, but this is the formal definition of < on N (line 13). Used on line 50.

> If and only if it were N, and not something else maybe.
>

Desperately trying to change the subject, Jan Burse? Can't blame you. You are getting your butt kicked here, but I made no claims about any numbers other than N.

Just admit you were wrong and move on. You are looking very crankish here.

Dan

Re: DC Proof challenge: Zorn's Lemma, how formalize it?

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Subject: Re: DC Proof challenge: Zorn's Lemma, how formalize it?
From: Dan_Chri...@sympatico.ca (Dan Christensen)
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 by: Dan Christensen - Thu, 19 May 2022 13:26 UTC

On Thursday, May 19, 2022 at 7:38:41 AM UTC-4, Nilo Kiski wrote:
> Dan Christensen wrote:
>
> > On Wednesday, May 18, 2022 at 7:19:10 PM UTC-4, Mostowski Collapse
> > wrote:
> >> Still waiting, should we use this:
> >> ALL(a):ALL(b):[a e n & b e n => [a<b <=> EXIST(c):[c e n & ~c=0 &
> >> a+c=b]]]
> >
> > Maybe you didn't know, but this is the formal definition of < on N (line
> > 13). Used on line 50.
> you don't undrestand tensors, you putrid nazi excrement.
>

WAR OF AGGRESSION = NAZI

You don't understand--maybe you do?--what a horrible position your Fuhrer has put your country in. You will take generations to recover. The sooner you start, the better.

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