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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?
This section contains 306 words
(approx. 2 pages at 300 words per page)