
Re: Need help deriving Peano Axioms from the reals
Posted:
Jun 2, 2012 3:26 AM


In message <5783f7cd4f36417f8354bf6a0c75e6dd@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 online. 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

