My thought is we can never generate a true random number by any means at all. Even if you start with something as random as a stream of white noise, you still have the problem of collecting something randomly out of it. How do you select a true random moment to dive in and make your collection?
The collecting action itself would need to be random as well as the stream the collecting is done from.
Maybe crashing two random streams together will cause something random to fall out, but how do you choose what to collect of the fallout and when?
I think it can get very deeply philosophical and even touch on the whole argument about free will and determinism.
Then again, I am probably over thinking it. If the experiment cannot cause a repetition of the number for the duration of the experiment, it should be random enough for any practical usage, I would think.
According to me true randomness would allow for duplication of some numbers, but without any predictive algorithm .....
A series with numbers 1 to n with mutually exclusive non-repetitive elements does introduce randomness at each element level but there is a rule that acts over the whole series and introduces non-randomness.
Edited by petrushkagoogol, 13 September 2017 - 11:22 PM.