from my understanding,every set has at least two subsets; the null set and the original set itself.
My question is, what is the power set of the null set? Shouldn't it be just itself?
from my understanding,every set has at least two subsets; the null set and the original set itself.
My question is, what is the power set of the null set? Shouldn't it be just itself?
Every nonempty set has at least two distinct subsets, namely the empty set and the set itself.
However, the empty set has only one subset: itself.
Thus, the power set of the empty set has one element, namely the empty set. That is, $\mathcal{P}(\emptyset) = \{\emptyset\}$.
Notice that the set whose only element is the empty set, $\{\emptyset\}$, is not empty: a bag that has an empty bag inside is not, itself, empty. So the power set of the empty set is not the empty set.