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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?

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    The empty set? There's nothing to it...2011-01-30

1 Answers 1

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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.

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    hmmm...maybe you're right (you have more experience). I think I must be projecting my own internal feelings when first learning it, that I felt I understood it when I translated the single $\emptyset$ sign to curly braces.2011-01-31