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Name: _________________________ | Period: ___________________ |

This test consists of 15 multiple choice questions and 5 short answer questions.

## Multiple Choice Questions

**1. What did George Cantor discover?**
**(a)** A way to compare the relative sizes of infinite sets. **(b)** A way to determine the accuracy of a calculation. **(c)** A method to measure infinity. **(d)** A method to measure a curved area.

**2. Who was Euler's teacher?**
**(a)** Isaac Newton. **(b)** Gottfried Leibniz. **(c)** Jakob Bernoulli. **(d)** Johann Bernoulli.

**3. Where was Euler born?**
**(a)** Switzerland. **(b)** Germany. **(c)** Finland. **(d)** Denmark.

**4. What is true about real numbers between 0 and 1?**
**(a)** There is no set for these numbers. **(b)** They are denumerable, **(c)** No sum can be determined. **(d)** They are not denumerable.

**5. What hindered Euler's work as he grew older?**
**(a)** His increasing blindness. **(b)** His hearing was getting worse. **(c)** He had very bad arthritis. **(d)** He had a stroke.

**6. What were the two types of transfinite cardinals defined by Cantor?**
**(a)** 1 and pi. **(b)** Ã—ÂÃ¢â€šâ€™ and c. **(c)** pi and Ã—ÂÃ¢â€šâ€™. **(d)** c and pi.

**7. Who eventually solved the sum of the successive squared denominator series?**
**(a)** John Napier. **(b)** Jakob Bernoulli. **(c)** Leonhard Euler. **(d)** Johann Bernoulli.

**8. What did Cantor develop?**
**(a)** A method to factor very large composite numbers. **(b)** A system to compare relative sizes of cardinal numbers. **(c)** A method to find the sum of a geometric series. **(d)** A system to identify prime numbers of very large size.

**9. What did Cantor find after extending the continuum between 0 and 1 into two dimensions?**
**(a)** That the set is infinite. **(b)** That the series is infinite. **(c)** That the set is equal to 1. **(d)** That the set is still equal to c.

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

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

**12. Which word best describes Newton's childhood?**
**(a)** Simple. **(b)** Hard. **(c)** Troubled. **(d)** Cold.

**13. What did Dunham describe as the same between artistic movements and mathematical studies in the 19th century?**
**(a)** They are both fascinated on artificial images, such as photography. **(b)** They are both less concern with reality. **(c)** They are both focused on realism. **(d)** They are both becoming less abstract.

**14. What were the main technique(s) that Euler used to find the sum of the series?**
**(a)** Cubic equations. **(b)** Quadratic sums, **(c)** Trigonometry and basic algebra. **(d)** Calculus methods.

**15. What did Cantor's beliefs lead him to think?**
**(a)** That he was seeing God when he worked on equations. **(b)** That he was tapping into the nature of God by delving into the infinite. **(c)** That he was learning about the origins of God. **(d)** That he was God.

## Short Answer Questions

**1.** What was the same about the series proposed by Leibniz and the series proposed by Bernoulli?

**2.** What did British scholars accuse Leibniz of?

**3.** Which of the following is a series that the Bernoullis proposed did not converge on a finite sum?

**4.** What did Cantor struggle with later in his life?

**5.** What did Euler prove about 2²ⁿ + 1?

This section contains 521 words(approx. 2 pages at 300 words per page) |