Talk:Empty domain

Membership

“an empty set having no members”. When exactly can the empty set have members?

Empty conjuction vs. Empty disjunction

"An analogous case is the trivial truth of the empty conjunction and falsehood of the empty disjunction ...". Neither of them is well-formed formula. Can we speak about their turth?

Okay, allow us to talk about non-wff, what is the difference (in form) between an empty conjuction and an empty disjunction? It seems to me that they are both empty formula. If there is no difference in form but they are different in semantic, isn't it really strange?

Further, the way the truth conditions stated is a bit strange. It excludes discussion for empty conjunction (disjunction). Tomlee2060 (talk) 02:06, 13 May 2008 (UTC)

An empty conjunction would not actually be a formula, you're right. It's what you get by starting with the shorthand notation $\bigwedge _{i=1}^{k}\phi _{i}$ and setting k to 0. An empty disjunction is similar. So here there is already information about whether a conjecuntion or disjunction is intended. This is entirely parallel to an empty sum in algebra, which is not a term, but a special case of summation notation. — Carl (CBM · talk) 11:04, 13 May 2008 (UTC)