9.1.4. Question 4

Try these first

1. 1.

   Define a countable set with an example.

   Hint

   Think of listing elements in a sequence.

2. 2.

   What is the significance of the union of two countable sets?

   Hint

   Consider the definition of countability.

3. 3.

   What is a countable set?

   • A set with infinite elements
   • A set that can be listed with natural numbers
   • A finite set only

   Hint

   Consider how lists of elements are structured.

4. 4.

   The union of two countable sets is what type of set?

   • True
   • False

   Hint

   Remember the definitions discussed.

5. 5.

   If you have three countable sets, S₁, S₂, and S₃, how can you show their union remains countable?

   Hint

   Think about how each element can be represented by its indices.

6. 6.

   Provide a counterexample to show that the union of an uncountable set with a countable set is uncountable.

   Hint

   Reflect on the definitions of countable versus uncountable.