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Evaluate World Peace

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dasnake to dewdney-ita, dasnake

An Infinite Game. ~~ A real mathematician's game with a real mathematician's solution. A and B alternate choosing positive (>0) real numbers to form a decreasing sequence; they play forever. At the Trump of Doom they add up their choices (infinitely many) . If the sum is infinite or rational, A wins. Othewise B. How does it come out?