In the principle of recursion page, it says:
"Break the problem down into smaller scopes, such as "x0, ∈ X,x1 ∈ X,...,xn ∈ X;"

Generally, I would just brush off and say yeah, ok, I get the idea and move on. However, recursion is one of my weakest topic, I really-really want to understand it.

Say, if X is the superset (input set). When we break down to "x0" which is a subset of "∈ X,x1" or how do we read that?

Given that in "X,x1" there is already a superset "X" and wouldn't adding "x1" be an extra thing in the superset?

Thank you so much in advance.