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Topic: An alternative Axiom of Infinity?
Replies: 41   Last Post: Feb 8, 2014 7:48 PM

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Dan Christensen

Posts: 1,699
Registered: 7/9/08
Re: An alternative Axiom of Infinity?
Posted: Feb 3, 2014 3:09 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Monday, February 3, 2014 2:39:50 PM UTC-5, Peter Percival wrote:
> Dan Christensen wrote:
>

> > On Monday, February 3, 2014 1:34:56 PM UTC-5, Peter Percival wrote:
>
> >> Dan Christensen wrote:
>
> >>
>
> >>> On Monday, February 3, 2014 1:00:14 PM UTC-5, Peter Percival
>
> >>> wrote:
>
> >>
>
> >>>> Dan Christensen wrote:
>
>
>

> >>>>> As I have told you elsewhere today, ZF theorists use '2' and
>
> >>>>> '3' as convenient abbreviations for '{{}, {{}}}' and '{{},
>
> >>>>> {{}}}, {{}, {{}}}}' respectively.
>
>
>

> >>>> Only those who choose the von Neumann definition. Zermelo
>
> >>>> didn't.
>
>
>

> >>> Again, as I also said there, get with the times, Peter. That was
>
> >>> 106 years ago! Time to move on.
>
>
>

> >> And yet you quote with approval Cauchy (1789 - 1857) on 0^0.
>
> >
>
> > Only because his recommendation is still widely used to today. Ask
>
> > just about any educated person. On the other hand, as far as I know,
>
> > your out-dated definition of the ZF successor function is now no more
>
> > than a historical curiosity.
>
>
>
> I haven't defined anything. I've just been trying to point out to you
>
> that the von Neumann ordinals (or any others) are an add-ons to ZF not
>
> an unchallengeable part of it.
>


Be that as it may, these days, the standard ZF Axiom of Infinity uses a the successor function S(x)={x,{x}}.

But even if you use the original definition of 106 years ago, you get wonky results like 2 is an element of 3.


Dan
Download my DC Proof 2.0 software at http://www.dcproof.com
Visit my new math blog at http://www.dcproof.wordpress.com


Date Subject Author
2/1/14
Read An alternative Axiom of Infinity?
Dan Christensen
2/1/14
Read Re: An alternative Axiom of Infinity?
Peter Percival
2/1/14
Read Re: An alternative Axiom of Infinity?
Dan Christensen
2/1/14
Read Re: An alternative Axiom of Infinity?
Peter Percival
2/1/14
Read Re: An alternative Axiom of Infinity?
Peter Percival
2/1/14
Read Re: An alternative Axiom of Infinity?
Dan Christensen
2/1/14
Read Re: An alternative Axiom of Infinity?
Peter Percival
2/1/14
Read Re: An alternative Axiom of Infinity?
Dan Christensen
2/1/14
Read Re: An alternative Axiom of Infinity?
Peter Percival
2/1/14
Read Re: An alternative Axiom of Infinity?
Peter Percival
2/1/14
Read Re: An alternative Axiom of Infinity?
Dan Christensen
2/4/14
Read Re: An alternative Axiom of Infinity?
Peter Percival
2/1/14
Read Re: An alternative Axiom of Infinity?
Dan Christensen
2/2/14
Read Re: An alternative Axiom of Infinity?
Shmuel (Seymour J.) Metz
2/3/14
Read Re: An alternative Axiom of Infinity?
Dan Christensen
2/3/14
Read Re: An alternative Axiom of Infinity?
Peter Percival
2/3/14
Read Re: An alternative Axiom of Infinity?
Dan Christensen
2/3/14
Read Re: An alternative Axiom of Infinity?
Peter Percival
2/3/14
Read Re: An alternative Axiom of Infinity?
Dan Christensen
2/3/14
Read Re: An alternative Axiom of Infinity?
Peter Percival
2/3/14
Read Re: An alternative Axiom of Infinity?
Dan Christensen
2/3/14
Read Re: An alternative Axiom of Infinity?
Peter Percival
2/3/14
Read Re: An alternative Axiom of Infinity?
Dan Christensen
2/3/14
Read Re: An alternative Axiom of Infinity?
Peter Percival
2/3/14
Read Re: An alternative Axiom of Infinity?
Dan Christensen
2/3/14
Read Re: An alternative Axiom of Infinity?
Peter Percival
2/3/14
Read Re: An alternative Axiom of Infinity?
Dan Christensen
2/4/14
Read Re: An alternative Axiom of Infinity?
Peter Percival
2/4/14
Read Re: An alternative Axiom of Infinity?
Dan Christensen
2/4/14
Read Re: An alternative Axiom of Infinity?
Peter Percival
2/4/14
Read Re: An alternative Axiom of Infinity?
Dan Christensen
2/4/14
Read Re: An alternative Axiom of Infinity?
Peter Percival
2/4/14
Read Re: An alternative Axiom of Infinity?
Dan Christensen
2/4/14
Read Re: An alternative Axiom of Infinity?
Peter Percival
2/4/14
Read Re: An alternative Axiom of Infinity?
Dan Christensen
2/8/14
Read Re: An alternative Axiom of Infinity?
Shmuel (Seymour J.) Metz
2/1/14
Read Re: An alternative Axiom of Infinity?
THE COLONEL
2/1/14
Read Re: An alternative Axiom of Infinity?
Dan Christensen
2/3/14
Read Re: An alternative Axiom of Infinity?
Joon Gibson
2/4/14
Read Re: An alternative Axiom of Infinity?
Dan Christensen
2/2/14
Read Re: An alternative Axiom of Infinity?
Dan Christensen
2/3/14
Read Re: An alternative Axiom of Infinity? FORMAL PROOF
Dan Christensen

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