Is there a vacant embed in the enhance of a vacant set?

The vacant set is a part of any kind of various other set.

The solution is of course. Yet there are numerous remarks that require to be made :

1. There is just one vacant set. So it is far better to claim that $A=B=\emptyset$ as opposed to claiming that "both $A$ and also $B$ are vacant sets", as the last wrongly recommends that there is greater than one. This is due to the fact that 2 collections are equivalent specifically if they have the very same components. So any kind of 2 vacant collections are equivalent, given that they have specifically the very same components (particularly, none).

2. I think by "context" you suggest that the enhance of $B$ is calculated relative to the "universal set." In the typical system of set concept, there can be no "universal set", as thinking its presence brings about troubles (Russell mystery). [Though, yes, it is common to broach a "universal set" as a means to mark what things we want. ]

The reason that $A$ is had in the enhance of $B$ is that $A$ (being the vacant set) is a part of any kind of set. This is due to the fact that we specify "$A$ is had in $C$" to suggest that any kind of component of $A$ is additionally a component of $C$. Currently, given that absolutely nothing is a component of $A$, this problem is pleased in this instance (one commonly claims that it is completely satisfied vacuously .)