When Emily makes the decision to exclude the even numbers from her threeven list she establishes her method to ensure that all her lists have unique elements. If we consider each list (even, threeven, fiven, seven’n etc.) to be a set then we can say that they are all disjoint.
She starts with a single, infinite set of positive integers with the prime numbers scattered throughout.
By applying her method, Emily creates an infinite number of infinite sets each with just one prime number as its first element (and one finite set containing just the number one).