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Monotone convergence theorem

The monotone convergence theorem states that any nondecreasing or increasing sequence which is bounded above converges[?]. Also, any nonincreasing or decreasing sequence which is bounded below converges.

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Jordanes

... and possibly bishop of Croton. In approximately 580, he wrote "De origine actibusque Getarum[?]" (The origin and deeds of the Goths), "De breviatione chronicorum" ...