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*Dirk Schlimm*

**Set theory.**(5 points)Read handout #16.

- Explain the proof of the theorem:
*The interval of all real numbers between 0 and 1 is not denumerable*, on pages 259-261, so that your fellow students who have not read the handout can understand it. - State in one or two sentences the key idea behind this proof.
- State in one or two sentences what the importance of this proof is.

- Explain the proof of the theorem:
**Reflections.**(5 points)Imagine you are on the phone with your little brother, who is a freshman in high school. He asked you what you were doing and you told him that you were studying for the course on the nature of mathematical reasoning. "Wow", he says, "you have been through high school and you still need to take a course like that?

*What have you learned so far that you didn't know before already?*"- What would you answer him? (Your answer should be at least half a page long.)

In order to answer this question, please don't just write down a few sentences from the top of your head, but carefully go through your portfolio and reflect on what you've learned in this course. Keep track of what was new to you, and what you found interesting. This is a good opportunity to check the contents of your portfolio and bring them up to date (remember, it has to be handed in on May 6).

In doing this you might come across issues that are not yet fully clear to you. Keep track of those, too and bring your questions to the review sessions.