Math 145 Test 2 Chapters 3 and 4 Study Sheet
In class portion
Your second test will consist of (2) questions from homework, and (3) essay questions
You will not know in advance which homework problems will appear on the test. Three
of these short essay questions will appear on the test. You may bring one 3x5 card with
notes.
Possible essay questions:
.
1. Given a finite set of cardinality 4, define its power set and state the cardinality of
the power set. If an additional element was added to the original set, how many
sets would be added to the power set? Justify your statement with logic.
Generalize your discussion to a rule about power sets.
2. Use an example to explain Cantor’s diagonal method of showing that that the
cardinality of the reals must be greater than the cardinality of the natural numbers.
Be sure to build on the ides of one-to-oneness.
3. Compare and contrast a “cube” in zero dimensions, one dimension, two
dimensions, three dimensions, and 4th dimension. Include a discussion of the idea
of a “slide.” Include sketches. Discuss the advantages of a 3-d person examining
a 2- world and the disadvantages of a 3-d person examining a 4-d world.
4. Describe the method used to construct a golden rectangle. Based on your method
prove that the small rectangle within the original golden rectangle is also golden.
Explain why it is golden. Briefly discuss how golden rectangles relate to
Fibonacci numbers.
5. Explain two geometric proofs of th Pythagorean theorem.
