Previous | Next |

*Dirk Schlimm*

**Nested quantifiers.**(2 points)Read carefully FOL, pages 154-168 (Sections 6.1-6.5) Do the following problem:

- Page 164, Problem 21 (Filename: 6-21.sen).

**Mathematical induction.**(3 points)Read FOL, pages 227-232 (Section 9.1) and pages 235-237 (Section 9.3). Do problems:

- Page 232, Problem 1. (1 point)
- Page 233, Problem 7. (2 points)

**Mathematical induction.**(2 points)Choose one of the claims on Handout #14,

*Mathematical induction problems*and prove it as carefully and detailed as possible.**Reflections.**(3 points)Imagine you were at home over spring break and you met your older sister who is a graduate student of physics at MIT. After you told her that you are attending a course on the nature of mathematical reasoning, she says: "Well, I know what the nature of mathematical reasoning is: it's calculating. The Greeks started it 500 years ago with simple equations, and now we have differential equations and computer programs like Maple or Mathematica to solve them. It has become a zillion times more complex, but basically it's still the same thing." What would you reply to her? Write a few paragraphs.