A finite set S of positive integers is called cardinal if S contains the integer ∣S∣ where ∣S∣ denotes the number of distinct elements in S. Let f be a function from the set of positive integers to itself such that for any cardinal set S, the set f(S) is also cardinal. Here f(S) denotes the set of all integers that can be expressed as f(a) where a∈S. Find all possible values of f(2024)
Proposed by Sutanay Bhattacharya functionalgebracombinatorics