Talk:Meet is Associative

The "expand" comment is mystifying, as there is no indication anywhere in this page about "partial operation" or "total operation". Unless I've missed a crucial point, an operation on a set is defined as being total. There is nothing in the definition of "meet" which suggests partialness. And as a semilattice has been defined, as a semigroup with extra conditions, that guarantees that meet is closed, total and associative already.

Is there a need to take a more abstract view on semilattices so as to allow non-associative, non-total operations? --prime mover (talk) 10:18, 4 January 2013 (UTC)


 * The generalization I aim at is similar to what I wrote for Meet Precedes Operands. I intended to drop the condition of a meet semilattice, and simply talk about elements admitting meets, rather than imposing that all meets exist. It's just that as soon as one of the two things is defined, the other is, too, and they're equal.
 * It is true that currently there is no reference on PW regarding "partial operations", but in time, I think there will be some source covered that introduces this notion or s.t. similar. The operation of "meet" is more general than its occurrence in "meet semilattice"; that's all I'm trying to convey.
 * Note that it is not by definition the case that a meet semilattice is in fact a semilattice. This fact will be proved on Meet Semilattice is Semilattice and that page is guaranteed to invoke this result.
 * Finally, it is indeed the case that the "partial algebraic structure" (or whatever) $(S, \wedge)$ will be commutative, associative, and idempotent, but $\wedge$ needn't be defined on all of $S \times S$. I added the note to emphasize this option for generalization. I would however rather not continue calling this more general thing a meet semilattice; such remains reserved for what is currently up. --Lord_Farin (talk) 10:34, 4 January 2013 (UTC)