Sequence with infinite range and 3 accumulation points
I have a task about limits and accumulation points, but I'm a little bit confused about it. The task is the following:
I'm asked to find a sequence with 3 accumulation points, but with an infinite range. Also, for each accumulation point, I should find a monotone subsequence converging to that point.
I have an assumption that such sequence can be described as Sn = {2, 1, 0, 4, 2, 1, 0, 6, 2, 1, 0, ...}
and the subsequences are like {4, 2, 1, 0}, {4, 2, 1}, {4, 2}, since 2, 1 and 0 are accumulation points.
Am I right or I completely miss a point of task?
real-analysis sequences-and-series
asked Nov 18 at 23:01
Sergey Malinov
154
add a comment |
I have a task about limits and accumulation points, but I'm a little bit confused about it. The task is the following:
I'm asked to find a sequence with 3 accumulation points, but with an infinite range. Also, for each accumulation point, I should find a monotone subsequence converging to that point.
I have an assumption that such sequence can be described as Sn = {2, 1, 0, 4, 2, 1, 0, 6, 2, 1, 0, ...}
and the subsequences are like {4, 2, 1, 0}, {4, 2, 1}, {4, 2}, since 2, 1 and 0 are accumulation points.
Am I right or I completely miss a point of task?
real-analysis sequences-and-series
asked Nov 18 at 23:01
Sergey Malinov
154
The subsequences will be ${4,4,4,4,dots}$, ${2,2,2,2,dots}$, and so on.
– steven gregory
Nov 18 at 23:14
add a comment |
I have a task about limits and accumulation points, but I'm a little bit confused about it. The task is the following:
I'm asked to find a sequence with 3 accumulation points, but with an infinite range. Also, for each accumulation point, I should find a monotone subsequence converging to that point.
I have an assumption that such sequence can be described as Sn = {2, 1, 0, 4, 2, 1, 0, 6, 2, 1, 0, ...}
and the subsequences are like {4, 2, 1, 0}, {4, 2, 1}, {4, 2}, since 2, 1 and 0 are accumulation points.
Am I right or I completely miss a point of task?
real-analysis sequences-and-series
asked Nov 18 at 23:01
Sergey Malinov
154
I have a task about limits and accumulation points, but I'm a little bit confused about it. The task is the following:
I'm asked to find a sequence with 3 accumulation points, but with an infinite range. Also, for each accumulation point, I should find a monotone subsequence converging to that point.
I have an assumption that such sequence can be described as Sn = {2, 1, 0, 4, 2, 1, 0, 6, 2, 1, 0, ...}
and the subsequences are like {4, 2, 1, 0}, {4, 2, 1}, {4, 2}, since 2, 1 and 0 are accumulation points.
Am I right or I completely miss a point of task?
real-analysis sequences-and-series
real-analysis sequences-and-series
asked Nov 18 at 23:01
Sergey Malinov
154
asked Nov 18 at 23:01
Sergey Malinov
154
asked Nov 18 at 23:01
Sergey Malinov
154
asked Nov 18 at 23:01
Sergey Malinov
154
asked Nov 18 at 23:01
Sergey Malinov
154
154
The subsequences will be ${4,4,4,4,dots}$, ${2,2,2,2,dots}$, and so on.
– steven gregory
Nov 18 at 23:14
add a comment |
The subsequences will be ${4,4,4,4,dots}$, ${2,2,2,2,dots}$, and so on.
– steven gregory
Nov 18 at 23:14
The subsequences will be ${4,4,4,4,dots}$, ${2,2,2,2,dots}$, and so on.
– steven gregory
Nov 18 at 23:14
The subsequences will be ${4,4,4,4,dots}$, ${2,2,2,2,dots}$, and so on.
– steven gregory
Nov 18 at 23:14
add a comment |
1 Answer
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Your accumulation points are correct.
Your sun sequences are the constant subsequences $$ 0,0,0,...$$,$$1,1,1,....$$ and $$2,2,2,.....$$,
answered Nov 18 at 23:19
Mohammad Riazi-Kermani
40.8k42059
add a comment |
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1 Answer
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1 Answer
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active
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Your accumulation points are correct.
Your sun sequences are the constant subsequences $$ 0,0,0,...$$,$$1,1,1,....$$ and $$2,2,2,.....$$,
answered Nov 18 at 23:19
Mohammad Riazi-Kermani
40.8k42059
add a comment |
Your accumulation points are correct.
Your sun sequences are the constant subsequences $$ 0,0,0,...$$,$$1,1,1,....$$ and $$2,2,2,.....$$,
answered Nov 18 at 23:19
Mohammad Riazi-Kermani
40.8k42059
add a comment |
Your accumulation points are correct.
Your sun sequences are the constant subsequences $$ 0,0,0,...$$,$$1,1,1,....$$ and $$2,2,2,.....$$,
answered Nov 18 at 23:19
Mohammad Riazi-Kermani
40.8k42059
Your accumulation points are correct.
Your sun sequences are the constant subsequences $$ 0,0,0,...$$,$$1,1,1,....$$ and $$2,2,2,.....$$,
answered Nov 18 at 23:19
Mohammad Riazi-Kermani
40.8k42059
answered Nov 18 at 23:19
Mohammad Riazi-Kermani
40.8k42059
answered Nov 18 at 23:19
Mohammad Riazi-Kermani
40.8k42059
answered Nov 18 at 23:19
Mohammad Riazi-Kermani
40.8k42059
40.8k42059
add a comment |
add a comment |
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The subsequences will be ${4,4,4,4,dots}$, ${2,2,2,2,dots}$, and so on.
– steven gregory
Nov 18 at 23:14