Brandon Scott

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Consider the following series: 1 – 1 + 1 – 1 + 1 – 1 + 1 – 1 + 1 – . . . . It’s not so hard to show that this series sums to zero. After all, (1 – 1) + (1 – 1) + (1 – 1) + (1 – 1) + (1 – 1) + (1 – 1) + . . . is the same thing as 0 + 0 + 0 + 0 + 0 + 0 + . . . which clearly sums to zero. But beware! Group the series in a different way: 1 + (–1 + 1) + (–1 + 1) + (–1 + 1) + (–1 + 1) + (–1 + 1) + . . . is the same thing as 1 + 0 + 0 + 0 + 0 + 0 + . . . which clearly sums to one. The same infinite sum of zeros can equal 0 and 1 at the same time. An Italian priest, Father Guido Grandi, even used this ...more
Zero: The Biography of a Dangerous Idea
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