How to describe formula as "for each" over some set?

Question

What are the math symbols used to describe an operation that simply transforms each element in some input set?

For example, the operation takes each element, squares it, and subtracts itself.

function someOperation(set) {
   return set.forEach((element) => {
      return element * element - element;
   });
}

Answer 1

There is a way to specify using set notation along the lines of $\{i^2-i, \text{for }i \in A\}$. Often, you'll see the word for replaced by a colon $\{i^2-i : i \in A\}$