9.1.5. Question 5

Try these first

1. 1.

   Provide an example of two uncountable sets intersecting at a finite point.

   Hint

   Think of intervals in the real numbers.

2. 2.

   What characterizes a countably infinite set?

   Hint

   Consider how you could count them.

3. 3.

   Are the sets A = [0, 1] and B = [1, 2] uncountable?

   • True
   • False

   Hint

   Think about real number intervals.

4. 4.

   What is the intersection of the integers and any other uncountable set?

   Hint

   Consider what elements both sets share.

5. 5.

   Create a situation with two uncountable sets that intersect both finitely and uncountably.

   Hint

   Think about how rationals align within reals.

6. 6.

   Prove that any two infinite sets can yield different intersection properties.

   Hint

   Explore cases with excludable elements.