Re: Peano's Axioms from the Field Axioms alone?


"William Elliot" <marsh@xxxxxxxxxxxxxxxxxx> wrote in message
news:Pine.BSI.4.58.0602252307370.18983@xxxxxxxxxxxxxxxxxxxx
On Sat, 25 Feb 2006, Dan Christensen wrote:

I have been able to show that the equivalent all but one of Peano's
Axioms can be derived from the fields axioms -- namely that no natural
number has a successor of 1. See:

http://www.dcproof.com/PeanoFieldAxioms.html

No thanks, too tedious to read because of format and style.

[snip]

This is an HTML version of the proof. It shows all the details in one view,
admittedly not the best format for such a long proof. In my program, you can
look at a proof in various levels of detail. At the highest level view, this
proof displays only 7 statements. I don't think there is any way to
implement this functionality in widely accessible HTML document.


The above formal proof was generated using my DC Proof software, a
PC-based, interactive proof-checker. Free download at my website.

Mathematicians are smarter than computers. No computer has ever taken a
math class, passed an math exam, nor earned a degree in mathematics.
Turn them off, they're stupid and the more automated our society becomes,
the more depersonalized it becomes and the more we are controlled
thru technology.

[snip]

This program was not meant to replace professional mathematicians or even
aid them in their work. It is a learning aid to teach non-specialists about
the nature of formal logic and proof.

Dan
Download my DC Proof software at http://www.dcproof.com


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