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You are in a state of sin :-) Don't talk about random sequences, talk about random generators. There's an unambiguous definition of "true random number generator" in terms of probabilities, joint probabilities etc., but there's no way to determine if a given string of numbers is random, and in fact no definition of a "random string of numbers" other than "the output of a random number generator".

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I am reminded of Borges's "Pierre Menard, Author of the Quixote" (http://www.coldbacon.com/writing/borges-quixote.html) (and what do you know, Borges even slips George Boole into it).

"He did not want to compose another Quixote —which is easy— but the Quixote itself. Needless to say, he never contemplated a mechanical transcription of the original; he did not propose to copy it. His admirable intention was to produce a few pages which would coincide—word for word and line for line—with those of Miguel de Cervantes."

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