Definition talk:Complement (Lattice Theory)

This definition specifies $\top$ and $\bot$ as identities of $\vee$ and $\wedge$, but these also have identities as greatest and least elements. In a sense, the bounded lattice structure is $(S,\wedge,\vee,\preceq,\bot,\top)$, but that's getting into a lot of typing, so I'm not sure if that is or isn't the way to go. --Dfeuer (talk) 00:22, 22 January 2013 (UTC)

Then again, we went with the four-piece approach to unify the order-theoretic and algebraic approaches to lattices, so maybe six-piece bounded lattices and seven-piece complemented ones would be okay? It looks wretched. --Dfeuer (talk) 00:25, 22 January 2013 (UTC)

OK, I think I figured it out! If we define the "top" and "bottom" of a bounded lattice, we can just use those terms in this definition. --Dfeuer (talk) 01:06, 22 January 2013 (UTC)