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This test consists of 5 multiple choice questions, 5 short answer questions, and 10 short essay questions.

Multiple Choice Questions

1. What did George Cantor determine to be true of a set of rational numbers?
(a) They are all composite numbers.
(b) They are non-denumerable.
(c) They are all prime numbers.
(d) They are denumerable.

2. What did Cantor develop?
(a) A system to identify prime numbers of very large size.
(b) A method to find the sum of a geometric series.
(c) A system to compare relative sizes of cardinal numbers.
(d) A method to factor very large composite numbers.

3. What is true about real numbers between 0 and 1?
(a) There is no set for these numbers.
(b) They are not denumerable.
(c) No sum can be determined.
(d) They are denumerable,

4. Who, in modern day, is given credit for the calculus method?
(a) Newton,
(b) Both Newton and Leibniz.
(c) Leibniz.
(d) Johann Bernoulli.

5. Where was George Cantor born?
(a) Germany.
(b) Switzerland.
(c) Britian.
(d) Russia.

Short Answer Questions

1. Which of the following demonstrates the successive squared denominator series?

2. What did Cantor find after extending the continuum between 0 and 1 into two dimensions?

3. What did mathematicians want to perfect in the mid-19th century?

4. What did Cantor's beliefs lead him to think?

5. Which name does NOT belong?

Short Essay Questions

1. Describe Cantor's difficult personal life.

2. Describe what the Bernoullis discovered about series, and give an example.

3. What was the great theorem of this chapter? Describe it briefly.

4. Describe who were Jakob and Johann Bernoulli.

5. What was Euler able to prove about 2²ⁿ + 1? Why was this a great accomplishment?

6. Describe the controversy that Newton was caught in with his publication of his calculus methods.

7. Who was Georg Cantor, and what was significant about his work in mathematics?

8. What was Gauss's major unpublished achievement in geometry?

9. Describe some of Gauss's work.

10. Describe Newton's days in Cambridge and what he eventually came to discover.

(see the answer keys)

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