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If someone gives me a list of numbers and says they are entirely and completely random, how I can I verify this?

EDIT: Let's suppose that a well-known string theorist told me he can produce a list of numbers that is truly, genuinely random. If I can't prove that they're really random, then who am I supposed to believe: him, or the mathematicians?

(Don't hurt me; I'm just trying to learn.)

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    You can’t. For any finite sequence of numbers $\langle x_1,\dots,x_n\rangle$ there is a polynomial $p$ of degree $n-1$ such that $p(k)=x_k$ for $k=1,\dots,n$.2012-12-08
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    Possible duplicate of [The pseudoness of pseudorandom number generators](http://math.stackexchange.com/q/6196/856), [How do you check if a sequence of numbers is truly random?](http://math.stackexchange.com/q/26563/856), [How do we check Randomness?](http://math.stackexchange.com/q/75005/856), [How to check that a sequence of numbers is random?](http://math.stackexchange.com/q/204003/856)2012-12-08
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    Wait, it's not quite a duplicate. I need to get some answers first and then I'll add an edit to my post. But I don't want to influence the answers I get with additional information.2012-12-08
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    "I don't want to influence the answers I get with additional information." That sounds like a really bad idea. Why would anyone want to answer if (a) they don't know what you're looking for that's different from the already existing previous questions and answers, and (b) after they've put in all the effort to write a nice answer, you might change the question rendering their answer irrelevant? Tell us what your question really is, please.2012-12-08
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    See my edit above.2012-12-08
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    There are many randomness tests, big field. Quite useful in detecting invented experimental "data." Poor cheaters don't have enough runs of identical digits, tend to avoid things like $12.20$ in favour of $12.37$, and so on. Easily detected. If you plan to cheat, use a pseudo-random number generator.2012-12-08
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    This isn't *exactly* an answer to your question, but you may find [Benford's Law](http://en.wikipedia.org/wiki/Benford's_law) interesting.2012-12-08
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    If you explore the concept of a "normal number" (e.g. Hardy and Wright) you will discover that any infinite "random" sequence [defined according to this concept] contains any finite sequence an infinite number of times (in asymptotically the exact proportion you would expect by chance).2014-04-11
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    Do you think that $640$, $231$, $100$, $91$ and $1003$ are random?2014-04-11

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