Definition talk:Bounded Lattice/Definition 1

Personally I think we should pull out the stuff about an ordered set and say in this definition that a bounded lattice is a lattice that's bounded above and below, and in the other definition that it's a lattice for which $\vee$ and $\wedge$ have identities (as we already do there). --Dfeuer (talk) 21:32, 21 January 2013 (UTC)


 * This definition was formulated with care. Contrast Definition:Lattice/Definition 1. This is the motivating definition of a (bounded) lattice and as such should be retained in current form. If you are not convinced see Definition:Empty Infimum and Definition:Empty Supremum. --Lord_Farin (talk) 22:06, 21 January 2013 (UTC)


 * I see what you're doing there NOW, but to my way of thinking it's much more nitpicky and definition-sensitive than "lattice with upper and lower bounds". It also doesn't build in such a pleasantly modular way on top of lattice. I'm not saying it shouldn't be included, but I'd prefer to see it bumped down to definition #3. In either case, we will need to have a definition #3. --Dfeuer (talk) 22:18, 21 January 2013 (UTC)


 * I agree that there is a need for another definition (even though that definition involves little more than mentioning the connection between empty infima cq. suprema and smallest cq. greatest elements). I disagree that this definition needs to be on another place than 1. It is historically, and in view of Definition:Complete Lattice, the motivating definition. Perhaps we needn't even bother with another definition and can suffice with a remark that this is the same as what you suggest by virtue of said correspondence (i.e., two links to respective results). How about that? (Discussion may arise as to whether that should be inside the include tags; I'm indifferent.) --Lord_Farin (talk) 22:24, 21 January 2013 (UTC)


 * I feel pretty strongly that we need to include the modular (lattice+bounded) definition, because I like modular. If you want to put it later, go ahead. Speaking of which, I need to add a definition of totally ordered field so as to practice what I preach. -Dfeuer (talk) 22:47, 21 January 2013 (UTC)

I see what you mean now, that this is the intersection of two definitions about ordered sets. Feel free to add it, then. It may aid some to grasp this concept faster. Admittedly the area is far from complete, because there are so many, only subtly different definitions that would ideally be covered. --Lord_Farin (talk) 22:53, 21 January 2013 (UTC)

Definition 1.5 needs to be added to Equivalence of Definitions of Bounded Lattice. --Lord_Farin (talk) 08:24, 22 January 2013 (UTC)