A set S is countably infinite if it is in bijective correspondence withN, the natural numbers. An enumeration of an infinite set S is a listt(1), t(2), . . . , t(n), . . . in which each element of T occurs exactly once.Part A. Let S be a countable, infinite set and f : N → S is a bijection.Provide an enumeration of S (suggestion: use f (x) and its bijectivity) andbriefly explain why it is indeed an enumeration of S

Part A: Since S is a countable, infinite set, there exists a bijection f: N → S. This means that each natural number n in N is associated with exactly one element in S, and each element in S is associated with exactly one natural number in N.

We can use this bijection to enumerate S. The enumeration would look like this: f(1), f(2), f(3), ..., f(n), ... . This is a list of elements of S, where each element appears exactly once.

This is indeed an enumeration of S because of the properties of the bijection. Since f is a bijection, it is both injective (one-to-one) and surjective (onto).

Being injective ensures that no two natural numbers map to the same element of S, so each element of S appears only once in the enumeration.

Being surjective ensures that every element of S is associated with some natural number, so every element of S appears in the enumeration.

Therefore, the function f provides a valid enumeration of the set S.