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#12734

66

Dec. 14, 2023, 5:43 p.m.

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//after explaining uncountability of the real numbers Rose: If you want to feel even more confused ... //introduces the Cantor ternary set (pathological fractal) Rose: The Cantor set is uncountable. Do you all believe me on that? Katz: I don't believe that. Rose: Okay, Katz. I can prove it to you. You have to consider the ternary representation of the real numbers ... *starts explaining binary and ternary* Katz: Okay, I believe you now. The Cantor set is uncountable. Rose: Will you just play along? *continues proof*

a real number in [0, 1] is in the Cantor set iff it has no 1s in the ternary expansion, so any number in it is an infinite sequence of 0s and 2s, which is equivalent to the set of all real numbers in [0, 1] in binary

logic, infinity, rose, katz

#2244

57

Oct. 2, 2010, 5:17 p.m.

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Student: Infinitive! Student: Infinitive? Student: Infinitive! Student: Infinitive? Student: Infinitive! Student: Infinitive? Student: Infinitive! Student: Infinitive? Giles: This is the dumbest conversation I have ever heard! Both of you be quiet for the rest of class.

#39

55

May 21, 2009, 8:54 p.m.

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If you had to spend an eternity in hell, it would still suck even if you got to spend the first billion years in heaven. ~Mr. Rose, explaining infinity