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Mathematical satisfaction
A belongs to A, then 1/( 1-a) belongs to A.

2 belongs to a

1/( 1-2) belongs to a.

-1 belongs to a.

1/[1-(-1)] belongs to a.

1/2 belongs to a.

There are two other elements in A-1 and 1/2.

If there are only 1 x elements in a,

Then 1/( 1-x) belongs to a.

So x = 1/( 1-x)

x( 1-x)= 1

This unary quadratic equation has no real roots.

So there is no solution.

So a can't contain only one element.