Converting an infinite space of random wave levels to a hash of 8?

Question

Mathematics

Is it possible, from the point of view of higher mathematics, to prove that by applying a randomly selected algorithm of mathematical transformation, a finite space of pseudo-random values ​​of the graph (of an economic nature) into one of 8 possible combinatorial patterns of system behavior. This process actually transforms a finite set of values ​​with an infinite number of possible structures into a hash function 8 ?

Answer 1

If it’s higher mathematics, then if we take the summation algorithm, then with sets of 1.2 and 3.0, the result will be 3. This means that the random algorithm will not hash.