Is there such a thing in math the inverse of a sequence?Is the sequence $u_n=sum_p=0^n(arctanfracx2^p)^2$ convergent?Does there exist a convergent sequence $a_n$ such that $n d(a_n+1,a_n)$ is not bounded?Show that the sequence $left(frac2^nn!right)$ has a limit.Which is the function that this sequence of functions convergesA convergent / divergent sequence of positive numbers such that $lim fracs_n+1s_n=1$Proof that every bounded sequence in the real numbers has a convergent subsequenceSuch thing as inverse/undo “search” or “filter” operatorConfusion arising from the 'infiniteness' of a sequence.Every sequence of the real numbers has a monotone subsequence.Showing the difference of an unbounded sequence and a convergent sequence is unbounded
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Is there such a thing in math the inverse of a sequence?
Is the sequence $u_n=sum_p=0^n(arctanfracx2^p)^2$ convergent?Does there exist a convergent sequence $a_n$ such that $n d(a_n+1,a_n)$ is not bounded?Show that the sequence $left(frac2^nn!right)$ has a limit.Which is the function that this sequence of functions convergesA convergent / divergent sequence of positive numbers such that $lim fracs_n+1s_n=1$Proof that every bounded sequence in the real numbers has a convergent subsequenceSuch thing as inverse/undo “search” or “filter” operatorConfusion arising from the 'infiniteness' of a sequence.Every sequence of the real numbers has a monotone subsequence.Showing the difference of an unbounded sequence and a convergent sequence is unbounded
$begingroup$
Such as can I construct a sequence by reversing the order of the approximating sequence of $frac13$? So such inverse would look like $left….,0.333333333,0.3333333,0.333333,...0.3right$.
I had this question when I was constructing a sequence that is bounded between 0 and 1/2 and not convergent to 0 for a homework question.
real-analysis sequences-and-series inverse
asked Mar 8 at 1:40
user917099user917099
1616
$endgroup$
add a comment |
$begingroup$
Such as can I construct a sequence by reversing the order of the approximating sequence of $frac13$? So such inverse would look like $left….,0.333333333,0.3333333,0.333333,...0.3right$.
I had this question when I was constructing a sequence that is bounded between 0 and 1/2 and not convergent to 0 for a homework question.
real-analysis sequences-and-series inverse
asked Mar 8 at 1:40
user917099user917099
1616
$endgroup$
$begingroup$
You can't, imagine if the first element has $n$ three's but in the original sequence the element with $n+1$ three's come after the one with $n$ three's hence in the new sequence it should be before the first element, a contradiction.
$endgroup$
– kingW3
Mar 8 at 1:50
1
$begingroup$
And no, there is a difference between stupid and bad questions, in your case the votes have matchedvso your question divides opinion. Giving enough context helps when you are asking a "stupid" question, i.e. mentioning that you heard it in class or in conversation with a friend or online on some webpage helps. Also mention what was the broad topic if the conversation, so that others will be able to address concerns relating to that in the answer as well.
$endgroup$
– астон вілла олоф мэллбэрг
Mar 8 at 3:44
$begingroup$
This is a good question. In several cases, a sequence makes sense for negative values of the index. For example, the Fibonacci numbers $0,1,1,2,3,5,dots$ can be exteneded to negative indices as $dots,5,-3,2,-1,1$. I encounter this kind of thing in the OEIS many time.
$endgroup$
– Somos
Mar 8 at 5:45
add a comment |
$begingroup$
Such as can I construct a sequence by reversing the order of the approximating sequence of $frac13$? So such inverse would look like $left….,0.333333333,0.3333333,0.333333,...0.3right$.
I had this question when I was constructing a sequence that is bounded between 0 and 1/2 and not convergent to 0 for a homework question.
real-analysis sequences-and-series inverse
asked Mar 8 at 1:40
user917099user917099
1616
$endgroup$
Such as can I construct a sequence by reversing the order of the approximating sequence of $frac13$? So such inverse would look like $left….,0.333333333,0.3333333,0.333333,...0.3right$.
I had this question when I was constructing a sequence that is bounded between 0 and 1/2 and not convergent to 0 for a homework question.
real-analysis sequences-and-series inverse
real-analysis sequences-and-series inverse
asked Mar 8 at 1:40
user917099user917099
1616
asked Mar 8 at 1:40
user917099user917099
1616
edited Mar 8 at 5:47
user917099
asked Mar 8 at 1:40
user917099user917099
1616
asked Mar 8 at 1:40
user917099user917099
1616
asked Mar 8 at 1:40
user917099user917099
1616
1616
$begingroup$
You can't, imagine if the first element has $n$ three's but in the original sequence the element with $n+1$ three's come after the one with $n$ three's hence in the new sequence it should be before the first element, a contradiction.
$endgroup$
– kingW3
Mar 8 at 1:50
1
$begingroup$
And no, there is a difference between stupid and bad questions, in your case the votes have matchedvso your question divides opinion. Giving enough context helps when you are asking a "stupid" question, i.e. mentioning that you heard it in class or in conversation with a friend or online on some webpage helps. Also mention what was the broad topic if the conversation, so that others will be able to address concerns relating to that in the answer as well.
$endgroup$
– астон вілла олоф мэллбэрг
Mar 8 at 3:44
$begingroup$
This is a good question. In several cases, a sequence makes sense for negative values of the index. For example, the Fibonacci numbers $0,1,1,2,3,5,dots$ can be exteneded to negative indices as $dots,5,-3,2,-1,1$. I encounter this kind of thing in the OEIS many time.
$endgroup$
– Somos
Mar 8 at 5:45
add a comment |
$begingroup$
You can't, imagine if the first element has $n$ three's but in the original sequence the element with $n+1$ three's come after the one with $n$ three's hence in the new sequence it should be before the first element, a contradiction.
$endgroup$
– kingW3
Mar 8 at 1:50
1
$begingroup$
And no, there is a difference between stupid and bad questions, in your case the votes have matchedvso your question divides opinion. Giving enough context helps when you are asking a "stupid" question, i.e. mentioning that you heard it in class or in conversation with a friend or online on some webpage helps. Also mention what was the broad topic if the conversation, so that others will be able to address concerns relating to that in the answer as well.
$endgroup$
– астон вілла олоф мэллбэрг
Mar 8 at 3:44
$begingroup$
This is a good question. In several cases, a sequence makes sense for negative values of the index. For example, the Fibonacci numbers $0,1,1,2,3,5,dots$ can be exteneded to negative indices as $dots,5,-3,2,-1,1$. I encounter this kind of thing in the OEIS many time.
$endgroup$
– Somos
Mar 8 at 5:45
$begingroup$
You can't, imagine if the first element has $n$ three's but in the original sequence the element with $n+1$ three's come after the one with $n$ three's hence in the new sequence it should be before the first element, a contradiction.
$endgroup$
– kingW3
Mar 8 at 1:50
$begingroup$
You can't, imagine if the first element has $n$ three's but in the original sequence the element with $n+1$ three's come after the one with $n$ three's hence in the new sequence it should be before the first element, a contradiction.
$endgroup$
– kingW3
Mar 8 at 1:50
1
1
$begingroup$
And no, there is a difference between stupid and bad questions, in your case the votes have matchedvso your question divides opinion. Giving enough context helps when you are asking a "stupid" question, i.e. mentioning that you heard it in class or in conversation with a friend or online on some webpage helps. Also mention what was the broad topic if the conversation, so that others will be able to address concerns relating to that in the answer as well.
$endgroup$
– астон вілла олоф мэллбэрг
Mar 8 at 3:44
$begingroup$
And no, there is a difference between stupid and bad questions, in your case the votes have matchedvso your question divides opinion. Giving enough context helps when you are asking a "stupid" question, i.e. mentioning that you heard it in class or in conversation with a friend or online on some webpage helps. Also mention what was the broad topic if the conversation, so that others will be able to address concerns relating to that in the answer as well.
$endgroup$
– астон вілла олоф мэллбэрг
Mar 8 at 3:44
$begingroup$
This is a good question. In several cases, a sequence makes sense for negative values of the index. For example, the Fibonacci numbers $0,1,1,2,3,5,dots$ can be exteneded to negative indices as $dots,5,-3,2,-1,1$. I encounter this kind of thing in the OEIS many time.
$endgroup$
– Somos
Mar 8 at 5:45
$begingroup$
This is a good question. In several cases, a sequence makes sense for negative values of the index. For example, the Fibonacci numbers $0,1,1,2,3,5,dots$ can be exteneded to negative indices as $dots,5,-3,2,-1,1$. I encounter this kind of thing in the OEIS many time.
$endgroup$
– Somos
Mar 8 at 5:45
add a comment |
1 Answer
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$begingroup$
A sequence is ultimately a map whose domain is $mathbb N$, but the object that you describe (a) has no first term, and (b) terminates.
If you want, I suppose you could define an object whose indices run from $-infty$ to $0$, but that's not appreciably different from looking at the original sequence while standing on your head.
answered Mar 8 at 1:49
J. MurrayJ. Murray
55017
$endgroup$
add a comment |
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$begingroup$
A sequence is ultimately a map whose domain is $mathbb N$, but the object that you describe (a) has no first term, and (b) terminates.
If you want, I suppose you could define an object whose indices run from $-infty$ to $0$, but that's not appreciably different from looking at the original sequence while standing on your head.
answered Mar 8 at 1:49
J. MurrayJ. Murray
55017
$endgroup$
add a comment |
$begingroup$
A sequence is ultimately a map whose domain is $mathbb N$, but the object that you describe (a) has no first term, and (b) terminates.
If you want, I suppose you could define an object whose indices run from $-infty$ to $0$, but that's not appreciably different from looking at the original sequence while standing on your head.
answered Mar 8 at 1:49
J. MurrayJ. Murray
55017
$endgroup$
add a comment |
$begingroup$
A sequence is ultimately a map whose domain is $mathbb N$, but the object that you describe (a) has no first term, and (b) terminates.
If you want, I suppose you could define an object whose indices run from $-infty$ to $0$, but that's not appreciably different from looking at the original sequence while standing on your head.
answered Mar 8 at 1:49
J. MurrayJ. Murray
55017
$endgroup$
A sequence is ultimately a map whose domain is $mathbb N$, but the object that you describe (a) has no first term, and (b) terminates.
If you want, I suppose you could define an object whose indices run from $-infty$ to $0$, but that's not appreciably different from looking at the original sequence while standing on your head.
answered Mar 8 at 1:49
J. MurrayJ. Murray
55017
edited Mar 8 at 3:27
answered Mar 8 at 1:49
J. MurrayJ. Murray
55017
answered Mar 8 at 1:49
J. MurrayJ. Murray
55017
answered Mar 8 at 1:49
J. MurrayJ. Murray
55017
55017
add a comment |
add a comment |
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$begingroup$
You can't, imagine if the first element has $n$ three's but in the original sequence the element with $n+1$ three's come after the one with $n$ three's hence in the new sequence it should be before the first element, a contradiction.
$endgroup$
– kingW3
Mar 8 at 1:50
1
$begingroup$
And no, there is a difference between stupid and bad questions, in your case the votes have matchedvso your question divides opinion. Giving enough context helps when you are asking a "stupid" question, i.e. mentioning that you heard it in class or in conversation with a friend or online on some webpage helps. Also mention what was the broad topic if the conversation, so that others will be able to address concerns relating to that in the answer as well.
$endgroup$
– астон вілла олоф мэллбэрг
Mar 8 at 3:44
$begingroup$
This is a good question. In several cases, a sequence makes sense for negative values of the index. For example, the Fibonacci numbers $0,1,1,2,3,5,dots$ can be exteneded to negative indices as $dots,5,-3,2,-1,1$. I encounter this kind of thing in the OEIS many time.
$endgroup$
– Somos
Mar 8 at 5:45