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This quiz consists of 5 multiple choice and 5 short answer questions through Cantor and the Transfinite Realm.

Multiple Choice Questions

1. What did Gauss do with his best work?
(a) He gave it to his students.
(b) He published it.
(c) He gave it to his son to publish.
(d) He did not publish it.

2. What is true about the successive squared denominator series proposed by the Bernoullis?
(a) The sum diverges into infinity.
(b) The sum converges.
(c) The sum converges to 2.
(d) The sum diverges.

3. What did Gauss set out to prove?
(a) That a right angle is always equal to 90 degrees.
(b) That Euclid's postulate on straight lines was incorrect.
(c) That a circle can have less than 360 degrees.
(d) That the sum of the angles in a triangle is 180 degrees.

4. Which of the following was one of Gauss' early discoveries?
(a) A way to construct a regular 17-sided polygon.
(b) A method to simplify Newton's calulus.
(c) A demonstration of the sum of the series 1 + 1/2³ + 1/3³ + 1/4³ . . . 1/k³ . .
(d) A proof that the Pythagorean Theorem was correct.

5. Heron's work referred to the work of what other famous scholar?
(a) Hippocrates.
(b) Euclid.
(c) Archimedes.
(d) Thales.

Short Answer Questions

1. What did Cantor suspect about transfinite cardinals?

2. What is the sum of the series 1 + 1/2³ + 1/3³ + 1/4³ ... 1/k³ . . .?

3. Which of the following is INCORRECT, and not used in Archimedes proof of his theory?

4. What did Gauss construct?

5. What were the proofs in Elements based on?

(see the answer key)

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