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J_Taylor comments on Open Thread, June 16-30, 2013 - Less Wrong
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Writing down only every arithmetic fact you know, assuming you have basic knowledge of math, would, in theory, take an infinite amount of time. In practice, the universe would end first.
Your mind doesn't have an infinite amount of memory so that can't be the case. You could use your mind to generate an infinite amount of arithmetic facts, but just recording the knowledge already there would be much faster. And if you are doing this for practical purposes, I imagine you would limit yourself to just relevant or interesting facts or beliefs, and not literally everything.