Best Answer

It is the set comprising the following 4 elements:

- phi,
- {phi},
- {{phi}} and
- {phi, {phi}}

Q: What is power set of power set of an empty set?

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To me, I believe that a power set is not empty. Here is my thought: ∅ ∊ P(A) where P(A) is the power set and A is the set. This implies: ∅ ⊆ A This means that A = ∅, but ∅ ∉ A. ∅ ∊ A if A = {∅} [It makes sense that ∅ ∊ {∅}]. Then, {∅} ⊆ A, so {∅} ∊ P(A) = {∅, {∅}}. That P(A) is not empty since it contains {∅} and ∅.

No. Let A = {a} (a singleton set) then P(A) = {a, 0} where 0 is the null (empty) set.

Yes,an empty set is the subset of every set. The subset of an empty set is only an empty set itself.

The empty set is a set that has no elements.

The only subset of an empty set is the empty set itself.

Related questions

To me, I believe that a power set is not empty. Here is my thought: ∅ ∊ P(A) where P(A) is the power set and A is the set. This implies: ∅ ⊆ A This means that A = ∅, but ∅ ∉ A. ∅ ∊ A if A = {∅} [It makes sense that ∅ ∊ {∅}]. Then, {∅} ⊆ A, so {∅} ∊ P(A) = {∅, {∅}}. That P(A) is not empty since it contains {∅} and ∅.

The power set of the empty has one member, which is the set whose member is the empty set . {phi} ( Actually the symbol for the empty set is the Norwegian letter O which resembles the Greek letter phi but is a different symbol )

An empty set is not a proper subset of an empty set.An empty set is not a proper subset of an empty set.An empty set is not a proper subset of an empty set.An empty set is not a proper subset of an empty set.

No. Let A = {a} (a singleton set) then P(A) = {a, 0} where 0 is the null (empty) set.

Yes it is. Everything in the empty set (which is nothing of course) is also in the empty set. If it's not in the empty set, it's not in the empty set. The empty set has no propersubsets, though, or subsets that are different from it.

Yes,an empty set is the subset of every set. The subset of an empty set is only an empty set itself.

The empty set is the set that contains no elements. (It is the empty set, not an empty set, because there is only one of them. It is a unique mathematical object.)

difinition of empty set

The empty set is a set that has no elements.

The only subset of an empty set is the empty set itself.

empty set is a set because its name indicate as it is the set.

It isn't. The empty set is a subset - but not a proper subset - of the empty set.