English is not my native language.
Hello everybody.
If I have a finite set of natural numbers. It is always possible to find an algorithm that generates it (and of course not the trivial one that only repeat each number of the set) , or could exist a set that is not possible to generate?
Thank you
What you're asking appears essentially to be a question of Kolmogorov complexity, in which case the answer is that the majority of such sets cannot be generated by an algorithm better than the trivial one. This is easily shown by a counting argument in the case of arbitrary sequences of bits; your sets can be transformed into arbitrary sequences of bits by sorting them to get sequences and then difference-encoding the sequences.