User talk:Abcxyz/Sandbox/Real Numbers/Identity for Real Addition

To my mind, the axiomatic definition should stand a bit separately, in a sense. There are two things that need to be proven: This theorem is part of the first thing. --Dfeuer (talk) 00:56, 24 January 2013 (UTC)
 * The various constructions of the reals satisfy the axiomatic definition.
 * Any two constructions satisfying the axioms are isomorphic as ordered fields.


 * Yes, I know those need to be proven. Just be patient; I'm working towards them.
 * What do you mean by "the axiomatic definition should stand a bit separately, in a sense"? --abcxyz (talk) 03:10, 24 January 2013 (UTC)


 * I mean that the axiomatic definition is not a separate construction, per se, but rather what all the constructions are aiming to attain. Having each of the theorems proving constructions satisfy the axioms include a section proving that something satisfying the axioms satisfies the axioms seems a bit odd. --Dfeuer (talk) 03:26, 24 January 2013 (UTC)


 * There has been a discussion about concepts with multiple definitions on the main talk page (if you haven't seen it). I'm not sure what the best way to do it is. And yes, I'm not even sure what the purpose of all that is, but there are actually quite a few pages (e.g. Rational Addition is Closed, Rational Addition is Associative, etc.) which do that. Maybe, if I can get a handle as to what the purpose of those pages is, I might have a better idea about how to address this issue. --abcxyz (talk) 03:46, 24 January 2013 (UTC)