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seen Jan 30 '13 at 0:09

Jan
29
comment Countability of “center” points of line segments in complement of Cantor set
Alright, I'm no longer confused. I'm actually not entirely clear on what I was thinking before.
Jan
29
comment Countability of “center” points of line segments in complement of Cantor set
You can visualize it as a binary tree with 1/2 on the first level, 1/4 and 3/4 on the second, k/2^n for all k in {1,...,2^n-1} on the nth level/iteration etc. So I'm mapping between points in S and number in R that way. Sorry if that's unclear. Also I'm sure I'm just missing something really obvious here.
Jan
29
comment Countability of “center” points of line segments in complement of Cantor set
OK but I'm still confused about something. What happens to the points in S as the number of iterations approaches infinity? In other words, if I said that the "first" element of S maps to 1/2, and the next 2 to 1/4 and 3/4, etc. what would happen if I tried to map, say pi/4 to a point in S by following this pattern, going left if that element of S was greater than pi/4 or right otherwise? I would presumably either not be able to complete this or end up on a point in C, right?
Jan
29
comment Countability of “center” points of line segments in complement of Cantor set
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Jan
29
awarded  Scholar
Jan
29
accepted Countability of “center” points of line segments in complement of Cantor set
Jan
29
awarded  Student
Jan
29
asked Countability of “center” points of line segments in complement of Cantor set