User talk:Lord Farin/Sandbox/Definition:Lattice

I think this is a good start, but I have two thoughts:
 * 1. Since the name "lattice" comes from its shape as an ordered structure, and the ordered structure is extremely easy to describe, I think that definition should come first.
 * Disagree - putting the constructivist approach first seems far more sensible, as it indicates how to build one of these things. Def 2 posits the existence of such a structure which already has those properties. --prime mover (talk) 16:31, 23 December 2012 (UTC)
 * Disagree with disagreement: commutative, associative, idempotent operations satisfying absorption laws aren't any more obviously constructable. --Dfeuer (talk) 16:53, 23 December 2012 (UTC)
 * Disagree with dis etc.: commutativity, associativity, idempotent operations satisfying absorption laws aren't even mentioned (except in the first definition they are explicitly shown). --prime mover (talk) 17:15, 23 December 2012 (UTC)
 * Aside from the absorption laws, which are stated but not named, the axioms are brought in through the definition of semilattice, and, through that, the definition of semigroup. --Dfeuer (talk) 18:05, 23 December 2012 (UTC)
 * Whatever. You're the boss. --prime mover (talk) 18:25, 23 December 2012 (UTC)
 * 2. I think it would be good to include (in addition) expanded definitions that don't rely on semilattice, join semilattice, and meet semilattice. --Dfeuer (talk) 16:21, 23 December 2012 (UTC)
 * Excellent idea. We probably want to put a page together called "Lattice Axioms" like we do with various other abstract algebraic concepts - one in progress now, as I type ... --prime mover (talk) 16:31, 23 December 2012 (UTC)