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tech / sci.math / Re: WM Farm

SubjectAuthor
* WM FarmWilliam
+- Re: WM FarmChris M. Thomasson
+- Re: WM FarmGreg Cunt
`* Re: WM FarmDan Christensen
 `* Re: WM FarmGreg Cunt
  `* Re: WM FarmDan Christensen
   `- Re: WM FarmGreg Cunt

1
WM Farm

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Subject: WM Farm
From: wpihug...@gmail.com (William)
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 by: William - Mon, 16 Aug 2021 21:51 UTC

All elements are equal, but some are more equal than others

Re: WM Farm

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From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: sci.math
Subject: Re: WM Farm
Date: Mon, 16 Aug 2021 15:20:11 -0700
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 by: Chris M. Thomasson - Mon, 16 Aug 2021 22:20 UTC

On 8/16/2021 2:51 PM, William wrote:
> All elements are equal, but some are more equal than others
>

LOL!

Re: WM Farm

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Subject: Re: WM Farm
From: franz.fr...@gmail.com (Greg Cunt)
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 by: Greg Cunt - Mon, 16 Aug 2021 22:34 UTC

On Monday, August 16, 2021 at 11:52:01 PM UTC+2, William wrote:

> All elements are equal, but some are more equal than others

Well, actually "'Not equal' and 'equal can mean the same.” (WM, sci..math, 2016/06/09)

Re: WM Farm

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Subject: Re: WM Farm
From: Dan_Chri...@sympatico.ca (Dan Christensen)
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 by: Dan Christensen - Tue, 17 Aug 2021 02:33 UTC

On Monday, August 16, 2021 at 5:52:01 PM UTC-4, William wrote:
> All elements are equal, but some are more equal than others

Some time ago, WM proposed an alternative to Peano's Axioms. Unfortunately, he could not even prove that 1=/=2 in that system. I guess you could take that to mean that all numbers may be equal.

Dan

Re: WM Farm

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Subject: Re: WM Farm
From: franz.fr...@gmail.com (Greg Cunt)
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 by: Greg Cunt - Tue, 17 Aug 2021 11:05 UTC

On Tuesday, August 17, 2021 at 4:33:34 AM UTC+2, Dan Christensen wrote:
> On Monday, August 16, 2021 at 5:52:01 PM UTC-4, William wrote:
> >
> > All elements are equal, but some are more equal than others
> >
> Some time ago, WM proposed an alternative to Peano's Axioms. Unfortunately, he could not even prove that 1 =/= 2 in that system. I guess you could take that to mean that all numbers may be equal.

Actually, it's not even certrain that IN is not empty in his "alternative" system. (But if IN = {}, then there wouldn't be elements in IN which are more equal. So let's - for the sake of the argument - assume that IN =/= {}.)

Re: WM Farm

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Subject: Re: WM Farm
From: Dan_Chri...@sympatico.ca (Dan Christensen)
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 by: Dan Christensen - Wed, 18 Aug 2021 20:34 UTC

On Tuesday, August 17, 2021 at 7:05:26 AM UTC-4, Greg Cunt wrote:
> On Tuesday, August 17, 2021 at 4:33:34 AM UTC+2, Dan Christensen wrote:
> > On Monday, August 16, 2021 at 5:52:01 PM UTC-4, William wrote:
> > >
> > > All elements are equal, but some are more equal than others
> > >
> > Some time ago, WM proposed an alternative to Peano's Axioms. Unfortunately, he could not even prove that 1 =/= 2 in that system. I guess you could take that to mean that all numbers may be equal.
>
> Actually, it's not even certrain that IN is not empty in his "alternative" system. (But if IN = {}, then there wouldn't be elements in IN which are more equal. So let's - for the sake of the argument - assume that IN =/= {}.)

IIRC, he postulated the existence of an element 1 of some set. He did not, however, rule out the possibility of that set being the singleton {1}. Needless to say, this "innovation" did not go very far.

Dan

Re: WM Farm

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Subject: Re: WM Farm
From: franz.fr...@gmail.com (Greg Cunt)
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 by: Greg Cunt - Wed, 18 Aug 2021 21:25 UTC

On Wednesday, August 18, 2021 at 10:35:06 PM UTC+2, Dan Christensen wrote:

> IIRC, he postulated the existence of an element 1 of some set.

Yeah, depends on the interpretation of his "axiom system".

Instead of (the usual axioms)

1.) 1 e IN

and

2.) n e IN -> n+1 e IN

he states

1.) 1 e M

2.) n e M -> n+1 e M .

So it depends on the "status" of "M". Is it a variable?

If so, these two axioms would claim that each and every set is a "successor set". Complete nonsense, of course.

Is it a constant? In this case one might expect the term "IN" instead of "M"...

In short: His "axiom system" is a COMPLETE mess.

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