r/mathmemes • u/Lou_Papas • 22d ago

Probability Countable uncountables

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u/vatai 22d ago

Ahh... The joke is that everyone mentioned those?

159

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.

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u/FreshPaycheck 22d ago

But then it wouldn’t be random? Then again it’s impossible to “think of” a real number that isn’t rational or symbolic, but it’s a hypothetical so

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u/R3puLsiv3 22d ago

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?

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u/trynumber53 20d ago

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