User talk:Abcxyz/Sandbox/Real Numbers

This is turning into a very commendable effort. Keep it up! --Lord_Farin (talk) 22:29, 22 January 2013 (UTC)

There's some circularity: in particular, proving that real numbers are closed because the real numbers form a field, etc. The proof that the real numbers form a field depends on the fact that the real numbers are closed. --prime mover (talk) 22:44, 22 January 2013 (UTC)

I was referring to the axiomatic definition of $\left({\R, +, \times, \le}\right)$. I forgot to mention which definition/construction of $\R$ was being used in each proof. --abcxyz (talk) 16:17, 23 January 2013 (UTC)