Definition talk:Ordering on Extended Real Numbers

Antisymmetry
I may be missing something, Lord_Farin, but the "demand" for antisymmetry seems entirely useless and confusing. All we need is to set $\le_{\overline {\mathbb R}} = \le_{\mathbb R} \cup \left\{{ \left({ x, +\infty }\right) \mid x \in \overline{\mathbb R} }\right\} \cup \left\{{ \left({ -\infty, x }\right) \mid x \in \overline{\mathbb R} }\right\}$. That is, we just extend it; there's no need to "demand" anything. $\left({+\infty,-\infty}\right)$ isn't going to appear out of nowhere. --Dfeuer (talk) 16:52, 6 January 2013 (UTC)