9.3. Claim 2

Try these first

1. 1.

   Define the term 'cardinality'.

   Hint

   It's about counting elements.

2. 2.

   How many elements are in the set of positive integers?

   Hint

   Think about the positive integers themselves.

3. 3.

   What does cardinality refer to?

   Hint

   It's about counting how many items are there.

4. 4.

   True or False: All infinite sets have the same cardinality.

   • True
   • False

   Hint

   Think about the countable versus uncountable expanses.

5. 5.

   Prove that the set of all rational numbers cannot be uncountable.

   Hint

   Remember, rational numbers can be expressed in m/n format.

6. 6.

   Show that the union of countable sets is countable using diagonalization.

   Hint

   Check how elements can be indexed systematically.