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Since the fixed point of f is also a fixed point of (f^{n}), the fixed point of f is unique.
Finally, suppose that the set of fixed point of f is well ordered.
Z ∈ X n is a ϒ-fixed point of F if and only if Z is a fixed point of F ϒ (that is, F ϒ Z = Z ).
Thus x2nis a fixed point of f.
Then the obtained fixed point of F is unique.
Now assume that w is another fixed point of f.
Then ω is a fixed point of f.
So, x ∗ is a fixed point of f.
So, z is a fixed point of f.
We prove that fixed point of f is unique.
Moreover, 0 is the unique fixed point of f. □.
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