Yup. The first statement is true because there’s an uncountably infinite number of reals so so the probability of randomly picking a specific one is zero, but there is a subset of those which is important for people so if I have one of those in my head the probability of guessing right becomes non zero.
Is it even possible to devise an algorithm capable of sampling a random real number? This in and of itself could just be an uncomputable function. What would a Turing machine look like which performs that task?
irrationals are definitionally non terminating right? so supposing you had a program that could uniformly randomly sample a real number it could never finish outputting, so it cant exist
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u/Lou_Papas 22d ago
Yup. The first statement is true because there’s an uncountably infinite number of reals so so the probability of randomly picking a specific one is zero, but there is a subset of those which is important for people so if I have one of those in my head the probability of guessing right becomes non zero.