User talk:Abcxyz/Sandbox/Real Numbers/Real Addition is Closed

Regarding $1/2$
If we're building the reals from the rationals, we probably want to have made some basic definitions within and proved some basic properties about the rationals first, such as the fact that there is a rational $2>0$, and thus a rational $1/2 > 0$, and that $1/2 + 1/2 = 1$. Can't we factor such basic facts about the rationals out of this proof about the reals? Or are you trying to improve efficiency by holding off on all such until the reals are constructed? --Dfeuer (talk) 03:56, 24 January 2013 (UTC)


 * I'll see when I'm done doing all this stuff. --abcxyz (talk) 04:01, 24 January 2013 (UTC)