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The error here is that the associative law cannot be applied freely to an infinite sum unless the sum is absolutely convergent.
We can say that the sum of Grandi's series is Na N.' is the square root of -1, for b 0.
In short, Na N is not really a number but a symbol that represents a numerical quantity whose magnitude cannot be determined by the operating system.
But if a graph of such numbers is markedly different from the one predicted by Benford's Law, he said, "I think I'd call someone in for a detailed audit".=0! is also used in statistics when dealing with 5-business day weeks.
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Imaginary numbers (and complex numbers in general) are essential for describing physical reality and have concrete applications in: electromagnetism, signal processing, control theory, quantum mechanics, cryptology, and cartography...
The difference between 3, 30 and 300 is only some extra zeros, but those little circles are actually one of the world's greatest inventions! C., Hindu scholars were working with nine oddly shaped symbols and a dot that eventually would bring order out of a world of mathematical chaos.
In fact, if you treat this series like a telescoping series and/or use different bracketing procedures to sum it, you may obtain contradictory results...