i'm not sure if this should be obvious, but it surprised me to find that both are equal to πpic.twitter.com/973xR17ilx
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Plot of the error between the integral and the sum as a function of the limits of integration/sum.pic.twitter.com/jP9zq7vr6u
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This feels strictly... not true? The sum of a function over a domain only approaches its Riemann sum when the rectangle widths vanish relative to the characteristic scale on which the function varies. This simply doesn't happen here. Unless I'm missing something..?
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It seems to be a way of suggesting that the law of large numbers is the same in both the smallest infinity and the second smallest infinity. Definitely did not seem like a foregone conclusion though
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I'm curious. Which tools did you use to create the plot, along with the animation?
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Just mathematica!
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interesting, I wonder if these are points from a function like a.sin(bx)/x^c
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I find it intuitive (just naively, but kind of Shannon sampling theorem?) that the two equal, but not intuitive at all that it sums to Pi.
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