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In order theory, a branch of mathematics, the least fixed point of a function from a partially ordered set to itself is the fixed point which is less than each other fixed point, according to the order of the poset. A function need not have a least fixed point, but if it does then the least fixed point is unique.
For example, with the usual order on the real numbers, the least fixed point of the real function f = x is x = 0. In contrast, f = x + 1 has no fixed points at all, so has no least one, and f = x has infinitely many fixed points, but has no least one.
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