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I am a non-math person and have a question about randomness: When generating elements from a finite set using some algorithm, it is clear what it means when saying that elements should be randomly generated. How about for infinite sets? For example if I want to generate real numbers randomly, what does it mean to be random? In general, how is random defined in Euclidean n-space? How about for subsets of n-space, eg. generating random points on the (n-1) unit sphere? Thanks.

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    To answer your question, "how is random defined in Euclidean n-space?", you might want to check out algorithmic randomness.2011-06-19

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