Definition talk:Lower Bound

Are there terms for similar notions applying to general endorelations?

• $\forall b \in S: a \mathrel{\mathcal R} b$
• $\forall b \in S: a \ne b \implies a \mathrel{\mathcal R} b$
• $\forall b \in S: a \ne b \iff a \mathrel{\mathcal R} b$

There doesn't seem to be anything about the actual meat of the definition that requires an ordering. --Dfeuer (talk) 05:31, 22 January 2013 (UTC)