Blairbash.org

Quote #12734 

#12734

66

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

⚐ Report
//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