Let the elements of a set be real numbers and satisfy: 1.1 ∈ a; 2. If a ∈ a, then 1 / (1-A) ∈ a (1) If 2 ∈ a, try to find the set a (2) If a ∈ a, try to find the set a (3) Can set a be a single element set? If so, find the set. If not, explain the reason To correct the mistake, the title "1.1 ∈ a" should be "1 &; a".

Let the elements of a set be real numbers and satisfy: 1.1 ∈ a; 2. If a ∈ a, then 1 / (1-A) ∈ a (1) If 2 ∈ a, try to find the set a (2) If a ∈ a, try to find the set a (3) Can set a be a single element set? If so, find the set. If not, explain the reason To correct the mistake, the title "1.1 ∈ a" should be "1 &; a".

First of all, set elements can not be repeated; let's use this problem to set conditions: if a ∈ a, then 1 / (1-A) ∈ a {- 1,1 / 2,2} first of all, a is not equal to 1 / (1-A) (we can prove and judge the number of equations by ourselves), so, because a ∈ a, then 1 / (1-A) ∈ a, then (A-1) / a ∈ a, so a = {(A-1) / A, 1 / (1-A), a}