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Exactly right. You can pick and use real numbers, as long as they are only queried to finite precision. There are lots of super cool algorithms for doing this!
by markusde 9mo ago
Exactly right. You can pick and use real numbers, as long as they are only queried to finite precision. There are lots of super cool algorithms for doing this!
- jibal 9mo agoThat's just saying that you can pick and use rational numbers (which are a subset of the reals.)
- skulk 9mo agoNot really. You can simulate a probability of 1/x by expanding 1/x in binary and flipping a coin repeatedly, once for each digit, until the coin matches the digit (assign heads and tails to 0 and 1 consistently). If the match happened on 1, then it's a positive result, otherwise negative. This only requires arbitrary but finite precision but the probability is exactly equal to 1/x which isn't rational.
- jibal 9mo agoNo, it isn't ... an infinite expansion isn't possible.
- markusde 9mo agoKind of, but you're not just picking rationals, you're picking rationals that are known to converge to a real number with some continuous property. You might be interested in this paper [1] which builds on top of this approach to simulate arbitrarily precise samples from the continuous normal distribution. [1] https://dl.acm.org/doi/10.1145/2710016 https://dl.acm.org/doi/10.1145/2710016