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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?**
**(a)** 1. **(b)** The sum was infinite. **(c)** 2. **(d)** π²/6

**3. What is the sum of the series 1 + 1/2³ + 1/3³ + 1/4³ ... 1/k³ . . .?**
**(a)** Infinity. **(b)** Nobody has determined the sum. **(c)** 0. **(d)** 2.

**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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