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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 is one of the common notions presented in Elements?**
**(a)** "Things with are equal have an inverse that is equal." **(b)** "Points with equal values can be connected with a line of equal value." **(c)** "The inverse of a line makes a circle." **(d)** "Things which are equal to the same thing are also equal to each other."

**2. What great theorem is presented by Dunham in this chapter?**
**(a)** An improvement on Leibniz's caluclus as presented by Jakob Bernoulli. **(b)** A theorem on finite series developed by Johann Bernoulli. **(c)** A theorem on series developed by Jakob and published by Johann Bernoulli. **(d)** A theorem on infinite series published by Jakob Bernoulli.

**3. How did Euler prove if the number 4,294,967,297 was prime or composite?**
**(a)** He divided it by 2. **(b)** He used Newton's calulus methods. **(c)** He used his own rule of squares. **(d)** He factored it.

**4. What did Cantor define as the continuum?**
**(a)** All imaginary numbers. **(b)** Real numbers between 0 and 1. **(c)** All imaginary and real numbers. **(d)** The square root of any real number.

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

## Short Answer Questions

**1.** Where did Euler study at the age of 20?

**2.** Which of the following was NOT one of Gauss' discoveries?

**3.** In what time period did mathematicians find a solution to cubic equations?

**4.** Who was Euler's teacher?

**5.** What sum did Euler find for the series?

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