I don't know whether you meant to do this on purpose, but your post makes it sound like (-1)^(-i) - pi = 19.999999... (that is, repeating nines), when in fact it's something like 19.999129...etc. It's not much of a coincidence. "e^(pi * i) + 1 = 0" is actually better at demonstrating deep mathematical unity, since it involves all five of what for lack of a better term you might say are the deep constants of mathematics: 0, 1, pi, e, and i.
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I don't know whether you meant to do this on purpose, but your post makes it sound like (-1)^(-i) - pi = 19.999999... (that is, repeating nines), when in fact it's something like 19.999129...etc. It's not much of a coincidence. "e^(pi * i) + 1 = 0" is actually better at demonstrating deep mathematical unity, since it involves all five of what for lack of a better term you might say are the deep constants of mathematics: 0, 1, pi, e, and i.
If I really meant repeating 9's, surely I'd just write "20", wouldn't I?
I did intend, however, to make people wonder if there were any more 9's in the expansion.
Sorry, on rereading, that reply sounds kind of snotty. I didn't intend it that way but I apologise, because it sure reads that way.
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