I felt initially kind of wrong in thinking this. however wikipedia also comes to my direction: "Axiomatic probability theory deliberately avoids a definition of a random sequence.[2] Traditional probability theory does not state if a specific sequence is random, but generally proceeds to discuss the properties of random variables and stochastic sequences assuming some definition of randomness. The Bourbaki school considered the statement "let us consider a random sequence" an abuse of language.[3]"
The same Wikipedia explains very clearly which is the state of art of randomness concept but, for a more interested reader, the educational review paper by Volchan [4], is certainly interesting and informative.
I report from Wikipedia the current state of art for the extractions of random sequences: 
"Three basic paradigms for dealing with random sequences have now emerged:[5]