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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. Which of the following was an important proposition given by Euclid's number theory?
(a) Any even number is divisible by 3.
(b) Any composite number is divisible by some prime number.
(c) Numbers from one to ten are only divisible by composite numbers.
(d) Any perfect number is divisible by some composite number.
2. What sum did Euler find for the series?
(b) The sum was infinite.
3. What is the sum of the series 1 + 1/2³ + 1/3³ + 1/4³ ... 1/k³ . . .?
(b) Nobody has determined the sum.
4. Which of the following is a series that the Bernoullis proposed did not converge on a finite sum?
(a) 1 + 1/2 + 3/4 + 4/5 . . .
(b) 1 + 1/2 + 1/3 + 1/4 + 1/5 . . . 1/1000 . . .
(c) 1 + 1/2 + 1/6 + 1/10 + 1/15 . . .
(d) 1 + 2 + 3 + 4 + 5. . .
5. What were the main technique(s) that Euler used to find the sum of the series?
(a) Quadratic sums,
(b) Cubic equations.
(c) Trigonometry and basic algebra.
(d) Calculus methods.
Short Answer Questions
1. To how many decimal places did Newton determine the number for pi?
2. Which of the following was true about Cardano, according to Dunham?
3. How many definitions were stated in Elements?
4. Besides being a mathematician, what else other work was Archimedes famous for?
5. What was true when Euler used n = 5 in the statement 2²ⁿ + 1?
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