Is empty set a power set?

Answer 1

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 ∅.