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What is power set of power set of an empty set?
It is the set comprising the following 4 elements:phi,{phi},{{phi}} and{phi, {phi}}
What is power sets in mathematics?
If tiu have a set S, its power set is the set of all subsets of S (including the null set and itself).
Is empty set a power set?
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 ∅.
Define the power set of a given set?
1,2,3,4,5,
Is it possible for a finite set to have the same cardinality as its power set?
No. If the cardinality of a finite set is N, then that of its power set is 2N. These cannot be equal for any non-negative integer N.
