In Cantor set, at every step, the intervals are divided into other 3 intervals and the middle interval is taken out.
Give examples of numbers which are in Cantor set. There is an infinity of such numbers.
I found 0 and 1.
2006-07-10 06:41:57 · 8 answers · asked by Theta40 7 in Science & Mathematics ➔ Mathematics
we start with [0,1]
2006-07-10 06:54:58 · update #1
the link gave by spyder is very clear
thx
2006-07-10 07:04:02 · update #2
1/4 = 0.0202020202.....
1/3 = 0.0101010101.....
the link below may help
2006-07-10 06:50:25 · answer #1 · answered by Spyder 2 · 2⤊ 0⤋
If you start with the closed interval [0,1], then on your first interation, (1/3) and (2/3) would be in the set since you take out the middle third.
2006-07-10 06:50:55 · answer #2 · answered by kooshman38 3 · 0⤊ 0⤋
0, 1. (no intervals removed)
1/3, 2/3. (first interval removed)
1/9, 2/9, 7/9, 8/9. (second intervals removed)
Just keep removing middle thirds of each segment while leaving the endpoints of the intervals that are removed. If you keep doing this you will be left with uncountably many points. Furthermore, you will have no intervals left, only points.
2006-07-10 07:12:16 · answer #3 · answered by random.oracle_23 2 · 0⤊ 0⤋
At the end you are left with numbers, having a base 3 expansion of the form:
0. a_1 a_2 a_3 a_4 ... a_n ...
where a_i is either 0 or 2.
2006-07-10 13:34:08 · answer #4 · answered by AnyMouse 3 · 0⤊ 0⤋
Depends on the start and end points of the set.
2006-07-10 06:47:28 · answer #5 · answered by ag_iitkgp 7 · 0⤊ 0⤋
It helps us to learn calculus, logic and distinctive different application. this question is fairly vast. In calculus OR diagnosis set thought is used to coach various theorems of sequences.
2016-12-08 17:56:05 · answer #6 · answered by ? 3 · 0⤊ 0⤋
are the intervals open or closed ?
2006-07-10 06:46:34 · answer #7 · answered by gjmb1960 7 · 0⤊ 0⤋
http://mathworld.wolfram.com/CantorSet.html
2006-07-10 06:47:12 · answer #8 · answered by kanajlo 5 · 0⤊ 0⤋