Comments by "L.W. Paradis" (@l.w.paradis2108) on "Парадокс Римана: π = бесконечность минус бесконечность" video.

  1. Bertrand Russell: "Anything can be deduced from a contradiction." A voice from the back of the room: "Zero equals one. Therefore, you are the Pope." BR: "All right. 0 = 1. Hence, 1 = 2. The Pope and I are two. Therefore, the Pope and I are one."
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  2. Perfect. Yes, you are the best.
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  3. I know people know, but just for the record: proof by contradiction. If rearranging the terms of a given infinite series leads to a contradiction, then rearranging the terms of that series is forbidden. Simple, but not satisfying. So, you study these series in depth and find that they either converge to a finite sum at the limit, or they do not. Etc. Everyone has known about the existence of convergent infinite series since 5th grade, if not before, perhaps without being aware of it: 1 ÷ 3 = 0.3333 . . . 0.3333 . . . = 3/10 + 3/100 + 3/1000 + 3/10,000 . . . . (Notice that wherever you stop, you have a partial sum that is less than 1/3. But the infinite decimal expansion does not have to be calculated in some sense: it already exists as complete.)
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