Abstract
We generalize the famous Tarski result by showing that: if X is a complete lattice, and f : X → X is an order-preserving mapping, then for all points x ∈ X, the limit superior and the limit inferior of the (possibly transfinite) sequence of iterations x, f(x), f2(x)..., fβ(x),... are fixed points of f. These limits are the sharp fixed-point bounds between which sufficiently large transfinite iterations are located.
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