Mixing
Sequence with infinite range and 3 accumulation points
up vote
0
down vote
favorite
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 yesterday
Sergey Malinov
51
add a comment |
up vote
0
down vote
favorite
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 yesterday
Sergey Malinov
51
The subsequences will be ${4,4,4,4,dots}$, ${2,2,2,2,dots}$, and so on.
– steven gregory
yesterday
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
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 yesterday
Sergey Malinov
51
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 yesterday
Sergey Malinov
51
asked yesterday
Sergey Malinov
51
asked yesterday
Sergey Malinov
51
asked yesterday
Sergey Malinov
51
asked yesterday
Sergey Malinov
51
51
The subsequences will be ${4,4,4,4,dots}$, ${2,2,2,2,dots}$, and so on.
– steven gregory
yesterday
add a comment |
The subsequences will be ${4,4,4,4,dots}$, ${2,2,2,2,dots}$, and so on.
– steven gregory
yesterday
The subsequences will be ${4,4,4,4,dots}$, ${2,2,2,2,dots}$, and so on.
– steven gregory
yesterday
The subsequences will be ${4,4,4,4,dots}$, ${2,2,2,2,dots}$, and so on.
– steven gregory
yesterday
add a comment |
1 Answer
1
active
oldest
votes
up vote
0
down vote
accepted
Your accumulation points are correct.
Your sun sequences are the constant subsequences $$ 0,0,0,...$$,$$1,1,1,....$$ and $$2,2,2,.....$$,
answered yesterday
Mohammad Riazi-Kermani
40.2k41958
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
accepted
Your accumulation points are correct.
Your sun sequences are the constant subsequences $$ 0,0,0,...$$,$$1,1,1,....$$ and $$2,2,2,.....$$,
answered yesterday
Mohammad Riazi-Kermani
40.2k41958
add a comment |
up vote
0
down vote
accepted
Your accumulation points are correct.
Your sun sequences are the constant subsequences $$ 0,0,0,...$$,$$1,1,1,....$$ and $$2,2,2,.....$$,
answered yesterday
Mohammad Riazi-Kermani
40.2k41958
add a comment |
up vote
0
down vote
accepted
up vote
0
down vote
accepted
Your accumulation points are correct.
Your sun sequences are the constant subsequences $$ 0,0,0,...$$,$$1,1,1,....$$ and $$2,2,2,.....$$,
answered yesterday
Mohammad Riazi-Kermani
40.2k41958
Your accumulation points are correct.
Your sun sequences are the constant subsequences $$ 0,0,0,...$$,$$1,1,1,....$$ and $$2,2,2,.....$$,
answered yesterday
Mohammad Riazi-Kermani
40.2k41958
answered yesterday
Mohammad Riazi-Kermani
40.2k41958
answered yesterday
Mohammad Riazi-Kermani
40.2k41958
answered yesterday
Mohammad Riazi-Kermani
40.2k41958
40.2k41958
add a comment |
add a comment |
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3004253%2fsequence-with-infinite-range-and-3-accumulation-points%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
The subsequences will be ${4,4,4,4,dots}$, ${2,2,2,2,dots}$, and so on.
– steven gregory
yesterday