Did you ever think you could compute pi to whatever digit you like? Given a computer, there is no algorithm that can infinitely print out the next digit of pi for ever. Any and all algorithms will eventually run out of memory and break. Sorry. Because your computer is a finite machine with a finite amount of states, eventually your algorithm must repeat itself and pi doesn’t. When I thought this up I was like “holy shit” at first but then I calmed down after realizing knowing pi to any digit was only for people with OCD’s anyway…

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But what if you print it out on (infinite) paper, and purge whatever you calculated already from memory?

If you cannot seek through the paper then the answer stays. If you’re saying I have an infinite memory space then that’s kind of cheating…