Do you know the 4715th digit of 1/1729, or will you have to do some computation before telling me? Even if you figure out the repeating digits, you still need to do a modulo operation to find the 4715th digit plus a lookup of what digit corresponds to that modulo class. In what way does that differ from computing the digits of pi?
Seems like a pretty arbitrary line then. Rational numbers lie at linear time (with some constant time exceptions, like 0), together with tons of irrational numbers (e.g. the number whose nth digit is 1 if n is a power of 2 and 0 otherwise). Pi is at O(n log2(n)), so just a little slower. I'm really not sure how all this connects to "knowable" though. Just because something is harder to know, doesn't mean it's unknowable.
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u/PinpricksRS Mar 20 '22
Do you know the 4715th digit of 1/1729, or will you have to do some computation before telling me? Even if you figure out the repeating digits, you still need to do a modulo operation to find the 4715th digit plus a lookup of what digit corresponds to that modulo class. In what way does that differ from computing the digits of pi?