1 + 1 + 1 + 1 + · · ·
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High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! in which the two infinite sums agree within the region in which they both converge (the complex numbers with real part greater than one), the second sum provides an analytic continuation of the zeta function to the complex numbers with positive real part, and the limit of the second sum as s goes to zero is -1/2. In this sense 1 + 1 + 1 + 1 + · · · = (0) = 1 2. Emilio Elizalde presents an anecdote on attitudes toward the series: In a short period of less than a year, two distinguished physicists, A. Slavnov…mehr

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High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! in which the two infinite sums agree within the region in which they both converge (the complex numbers with real part greater than one), the second sum provides an analytic continuation of the zeta function to the complex numbers with positive real part, and the limit of the second sum as s goes to zero is -1/2. In this sense 1 + 1 + 1 + 1 + · · · = (0) = 1 2. Emilio Elizalde presents an anecdote on attitudes toward the series: In a short period of less than a year, two distinguished physicists, A. Slavnov and F. Yndurain, gave seminars in Barcelona, about different subjects. It was remarkable that, in both presentations, at some point the speaker addressed the audience with these words: 'As everybody knows, 1 + 1 + 1 + · · · = 1 2'. Implying maybe: If you do not know this, it is no use to continue listening.