Dan: Yes, the empty set is a subset of any set. But am I mistaken in thinking that in order for the meet of the empty set to make sense, we need to specify the preordered set for which it is a subset of? For example, in the power set of some set \\(X\\) with inclusion as the preorder, the meet of the empty set is \\( X\\) but in \\(P(X)\cup\\{Y\\}\\) where \\(X\subset Y\\) and \\(X\not=Y\\), the meet of the empty set is then \\(Y\\)?

Basically, I'm wondering if it is necessary to specify the preorder set we're looking at when it comes to finding the meet of the empty set.