set theory – Denote a set that contains all possible combinations of the input

I want to create a set that contains all possible combinations of integers, such that I can say x in a set of possible combinations integers.

x could be ({0}, {1}, {1,2}, {-1}, {1,2,2,4}..}

How can I describe this mathematically and what rules apply. do sets relate to the rules of Combinations and Permutations