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# 80-110 Nature of Mathematical Reasoning

Spring 2002

Dirk Schlimm

Homework 4

Wednesday, February 6

Due Monday, February 11

1. Kinds of proofs (3 points)

a) List the proofs you've seen in class so far and classify them as direct, negation introduction, or reductio ad absurdum (RAA).

- Are they `on the same level' as direct proofs?
- If you could prove a theorem directly or using an indirect argument, which one would you choose, and why?
2. Socratic method and Euclid's definitions (2 points)

The following questions refer to Handout #3, Proofs (Glymour).

a) Describe the Socratic method.
b) Answer study question 1, on page 15.
c) Answer study question 2, on page 15.

3. Definitions (2 points)

a) Find a definition in any textbook you like, copy it and determine its primitive terms.
b) Discuss in a few sentences whether you think your example is a good definition or not.

4. A somewhat difficult problem (3 points)

Try to solve the following problem: Write numbers, using each of the ten digits (0,1,2,3,4,5,6,7,8,9) exactly once, so that the sum of the numbers is exactly 100.

An example for a possible solution would be: 19+28+30+7+6+5+4. Here all ten digits are used exactly once, but unfortunately the sum is only 99, instead of 100. Thus, this isn't a solution to the problem!

Write a paragraph describing your experiences in solving this problem addressing the following issues:
- Did you employ inductive or deductive reasoning?
- Did you find a solution, how?