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- W1038089917 abstract "Riemann’s theorem on conditionally–convergent series surprises a lot of people. Some people react to it by retreating to the view that only absolute convergence deserves to be taken seriously. I go the other way. What I take from it is that the ordinary notion of the convergence of a series is not so sacred, after all. That notion relates to one particular way of adding up a series, one of many. Depending on the circumstances, one of the other ways may be more appropriate or interesting. The idea that a series should add up in the usual way is just a prejudice. For instance, with the Fourier series of a continuous function, it is a fact that the series often fails to converge in the ordinary way, but we know that the Cesaro means always converge uniformly to the function." @default.
- W1038089917 created "2016-06-24" @default.
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- W1038089917 date "1990-01-01" @default.
- W1038089917 modified "2023-10-04" @default.
- W1038089917 title "A series of surprises" @default.
- W1038089917 hasPublicationYear "1990" @default.
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