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Is there a calendrical error in Asimov's “The Last Trump”?

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31 1 In the short story "The Last Trump" by Isaac Asimov, there is a point where one of the characters explains that the year is calculated differently by various different cultures: "Nor is that all," Etheriel went on. "The year A.D. 1957 is the year 7464 of the Byzantine era, 5716 by the Jewish calendar. It is 2708 A.U.C., that is, the 2,708th year since the founding of Rome, if we adopt the Roman calendar. It is the year 1375 in the Mohammedan calendar, and the hundred eightieth year of the independence of the United States. The part that interests me is the Jewish calendar. The year 1957 was not actually 5716 according to the Jewish calendar. The Jewish calendar counts its years from the Jewish New Year (Rosh Hashanah) which occurs around September. Thus, every Jewish year overl...