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I do not have a degree in any field of mathematics; however I would like to get an input perhaps from those who do.

I argued a point with one of my children the other day that if all of the arguments against a system that could generate true random numbers were moot (algorithms, entropy salt, etc), that a given system could in theory produce the same output every time as logically as any other number, because the odds of it ever arriving at that one are both exactly the same as every other number it could produce, and therefore just as likely.

So on said system I could request a purely random number between 1 and 10 and it would consistently produce 5, not in error, so if asked to repeat this ten times 5,5,5,5,5,5,5,5,5,5 or 1,2,3,4,5,6,7,8,9,10 is just as likely as any other outcome.

If this is not correct please correct me. If so, does this theory or law have a name?

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    I have to confess I fail to parse the question.2012-10-09
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    That if a system is truy random, and the quality of that random is not bound by error of say processor architecture, or a flaw in the process creating it. Then the past products of said system have no bearing on what the next could be. getting the sequence 1,1,1 shuld be just as probable as 1,2,3.2012-10-09
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    Thanks for the clarification. I got a better idea at what you were asking from the answer by Michael Boratko.2012-10-09

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