Le samedi 24 mai 2014 09:45:37 UTC+9, xorxes a écrit :"lo selcmi be no da" works well as a description of the empty set in a universe of discourse in which there are only sets. (But then that is really the only universe of discourse in which one should mention sets at all, in my opinion.){lo selcmi be no da} is a standard definition of "empty set" of set theory.
In other words, {zo'e noi roda naku zo'u ke'a selcmi da}. We can think of a universe of discourse in which a spoon satisfies {ke'a selcmi no da}, but it means that the spoon is regarded as an empty set in that universe of discourse. An empty set is indeed a kind of set, {lo selcmi}. If we wanted to imply that a spoon is not a set, we could rather say that a spoon satisfies {ke'a selcmi zi'o}, in which the meaning of {selcmi} was changed by {zi'o}.
There's another problem with the "lo'i" definition. Can "lo selcmi be lo broda" be any set that has lo broda among its members, or is it the one and only set that has lo broda as its sole members? "cmima" only says that x1 is/are among the members of x2, does "selcmi" say that its x2 are all the members of its x1? Open question.You created a Lojban entry of {selcmi} in jbovlaste:It might have been modified by someone else, and is now defined as follows:{x1 selcmi x2} =ca'e {x1 se cmima ro lo me x2 me'u e no lo na me x2}That is to say, the meaning of {selcmi} is different from {se cmima}, and {lo selcmi be lo broda} is the one and only set that has lo broda as its sole members.
However, I would prefer that the meaning of {selcmi} is the same as {se cmima}, and that {A cmima A ce B} is implied by {A ce B selcmi A}.
In that case, {lo selcmi be lo broda} can be any set that has lo broda among its members. I am willing to add a comment on it, but I'm not sure if I should obey the definition of jbovlaste, or rather keep it as an open question.