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I don't really have a deep mathematics background so even if there isn't a specific answer I would be really grateful if you could point me in the right direction.

If for a particular set of input data (a1,a2,a3,...) a system generates the corresponding output (b1,b2,b3,...)

Is there any way, I can construct a function that describes the behavior of the system? Assuming that there is no constraint on the kind of function the system can implement(linear, polynomial, non-linear etc)

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  • $\begingroup$ well it really depends on the input data and output data, without knowledge of the data there can not be an answer! $\endgroup$
    – Wanderer
    Commented Sep 23, 2015 at 10:40
  • $\begingroup$ @Dimitri C Ok, supposing both the input and output data set are natural numbers what forms could the function take. Or better yet, if you could give me an idea of what the function would be in a couple of scenarios (when the data set is other than natural numbers), I think I'd understand better $\endgroup$
    – Savvy
    Commented Sep 23, 2015 at 11:32

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Provided that there is no overlap in your a values, you can always express it as a polynomial. You can put it into a matrix and solve, or use substitution to work out a general formula for a fixed number of points (would not recommend).

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