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Unformatted text preview: Hw 27 1 Marks: 1 George Cantor believed that there could be no set whose cardinality was greater than the cardinality of N but less than the cardinality of R. He couldn't prove it, but he believed it, and he wrote it down as a statement for others to settle as true or false. What is the name of the statement? a. The cardinality hypotenuse. b. The cardinality hypothesis. c. The continuum hypothesis. d. The continuing hypothesis. Choose one answer. Correct Marks for this submission: 1/1. Question 2 Marks: 1 Explain why aleph nought + 3 = aleph nought. Choose the best answer. Choose one answer. a. Aleph nought means infinity and infinity plus 3 is still infinity. b. The set N is the union of the set A = {1, 2, 3} and the set B = {4, 5, 6, 7,...}, and A and B have no elements in common. So N = A + B = 3 + aleph nought since B can be put into onetoone correspondence with N. Thus aleph nought = 3 + aleph nought. c. Huh? d. What in the world does aleph nought mean? Correct Marks for this submission: 1/1. Question 3 Marks: 1 How many "basic symbols" are used to write a number in binary notation ? Choose one answer. a. Two. The "basic symbols" are 0, 1. They are called "bits" which is a shortened form of "binary digit" . b. five c. I showed this question to my dog, and he bit me. So the answer is "ouch!" d. ten Correct Marks for this submission: 1/1. Question 4 Marks: 1 Use sets to explain why aleph nought + aleph nought = aleph nought. Choose one answer. a. This is wrong. Anything plus itself is two times that thing, as in x + x = 2x. And two times anything is bigger that that thing alone. b. If I'm infinitely wealthy and I gain another infinite fortune, then I have more than I had at the beginning. c. The set N is the union of the subset E of all even nataural numbers and the set O of all odd natural numbers, and E and O have no element in common. So N = E + O which gives aleph nought = aleph nought + aleph nought, d. If I wanted to learn about aleph, I would have registered for a Hebrew class. Correct Marks for this submission: 1/1. Question 5 Marks: 1 Gloria Marie has submitted five recipies to her church's cookbook committee. She anxiously awaits the news as to whether the committee will choose none, one, several, or all of her recipes. How many different decisions can the committee make about Gloria Marie's recipes?...
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 Spring '10
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