9.1.3. Question 3

Try these first

1. 1.

   Define an infinite set with an example.

   Hint

   Think of a set you can count with no upper limit.

2. 2.

   What does countably infinite mean?

   Hint

   Which set can be written in list form?

3. 3.

   What type of set does not have a finite number of elements?

   • A finite set
   • An infinite set
   • A countable set

   Hint

   Think of sets like natural numbers or integers.

4. 4.

   True or False: Any infinite set contains a countably infinite subset.

   • True
   • False

   Hint

   Remember the sequence of removed elements.

5. 5.

   Given the set of all real numbers, demonstrate the extraction of a countably infinite subset through iterations of element removal.

   Hint

   How many elements can you remove from a set before it runs out?

6. 6.

   Take any uncountable set and outline the process of finding a countably infinite subset.

   Hint

   Use the idea of iteration and remember that infinite sets never truly run out.