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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 Cantor's cardinal numbers represent?
(a) Series of prime numbers.
(b) Infinite sets.
(c) Finite series.
(d) Sets of all imaginary numbers.

2. What did Archimedes manage to prove using Euclid's ideas?
(a) That the value of pi is proportional to the area of the circle.
(b) That the area of a circle and the square of its diameter is really the same as the relationship of diameter to circumference.
(c) That the relationship of area to circumference is really the same as the relationship of radius to diameter.
(d) That the square of a diameter is equal to pi.

3. What concept did Dunham end his book with?
(a) Heron's triangulated area.
(b) Cantor and his voyage into the infinite.
(c) Newton's method of calculus.
(d) Archimedes and the infinite series.

4. Which of the following is a series that the Bernoullis proposed did not converge on a finite sum?
(a) 1 + 1/2 + 1/3 + 1/4 + 1/5 . . . 1/1000 . . .
(b) 1 + 2 + 3 + 4 + 5. . .
(c) 1 + 1/2 + 1/6 + 1/10 + 1/15 . . .
(d) 1 + 1/2 + 3/4 + 4/5 . . .

5. Which of the following was one of Euclid's great theorems?
(a) There exists an finite number of prime numbers.
(b) There exists only infinite and whole numbers.
(c) Prime numbers are more comples than discrete numbers.
(d) There exists an infinite number of prime numbers.

Short Answer Questions

1. In the Bernoulli's time, what was the current definition of a series?

2. Who were Johann and Jakob Bernoulli?

3. Which is one of the common notions presented in Elements?

4. Who acted as the gate keepers of knowledge?

5. In his later life, what position did Isaac Newton hold?

(see the answer key)

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