Question

Give an example of a countable collection of finite sets whose union is not finite. Provide an example meeting the specified criteria.

Answer 1

An example of a countable collection of finite sets whose union is not finite is the sequence of sets {1}, {1,2}, {1,2,3}, {1,2,3,4}, and so on. Each set in the sequence is finite and countable, but the union of all these sets is the set of all positive integers, which is infinite.

Step-by-step explanation:

In mathematics, a countable collection of finite sets whose union is not finite can be illustrated by the sequence of sets {1}, {1,2}, {1,2,3}, {1,2,3,4}, and so on. Each set in the sequence is finite and countable, but when we take the union of all these sets, the resulting set is the set of all positive integers, which is infinite. So, the union of this countable collection of finite sets is not finite.