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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?

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  • $\begingroup$ The subsequences will be $\{4,4,4,4,\dots\}$, $\{2,2,2,2,\dots\}$, and so on. $\endgroup$ Nov 18, 2018 at 23:14

1 Answer 1

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Your accumulation points are correct.

Your sun sequences are the constant subsequences $$ 0,0,0,...$$,$$1,1,1,....$$ and $$2,2,2,.....$$,

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