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Topic: Need help deriving Peano Axioms from the reals
Replies: 15   Last Post: Jun 7, 2012 10:59 AM

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David Hartley

Posts: 440
Registered: 12/13/04
Re: Need help deriving Peano Axioms from the reals
Posted: Jun 2, 2012 3:26 AM
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In message
<5783f7cd-4f36-417f-8354-bf6a0c75e6dd@e20g2000vbm.googlegroups.com>, Dan
Christensen <Dan_Christensen@sympatico.ca> writes
>Something like that would work if there was some explicit link between
>the field and order axioms. (The order axioms are usually given in
>terms of positiveness, as in my proof, or in terms of various algebraic
>rules, e.g. trichotomy.) How is this usually handled? I can't find
>anything about this point on-line. It seems to me that ordering needs
>to be defined in terms of addition. Or is there some clever little
>lemma that is eluding me?



You have explicit links: "pos + pos = pos" and "pos * pos = pos".

Either 1 or -1 is positive, but (-1)*(-1) = 1 ...

--
David Hartley



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