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!

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jibal 8 hours ago | parent [-]

That's just saying that you can pick and use rational numbers (which are a subset of the reals.)

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skulk 5 hours ago | parent [-]

Not 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 2 hours ago \| parent [-]
		No, it isn't ... an infinite expansion isn't possible.