/sci/ - Science & Math

>>11991165
I found an old set theory question on stackexchange, and one of the answers seems really wrong, but I don't know enough about set theory to be sure. See pic related.
As far as I can tell, 5 should be false regardless of whether it is referring to a subset or a proper subset.
One of the guys answering says that it actually becomes true if the notation means "proper subset of," but isn't that just making the relationship *more* restrictive?
To my understanding, Y is not a subset, proper or otherwise, of Z, because the null set is not in Z (although the null set is a subset of Z.)
And when he says "the null set is contained in every set," isn't that wrong? I thought the null set is a *subset* of every set, but it's not *in* every set. Or in other words, the contents of the null set are in every set, but the null set itself is not.