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If $x_minmathbbR$, $y_n$ is the n'th rational number in $x_m$, and $z_n$ is the n'th irrational number in $x_m$ then [closed]
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If $x_minmathbbR$, $y_n$ is the n'th rational number in $x_m$, and $z_n$ is the n'th irrational number in $x_m$ then
- both $y$ and $z$ are the subsequence of $x$
- at least one of them is the subsequence of$ x$
- Neither $y$ nor $z$ is the subsequence of$x$
I am taking the example the sequence $x(n)=n^1/2$ here both $y$ and $z$ are subsequence of $x$ but I don't know this is true or not in general ....Plz help me
real-analysis real-numbers
edited Jul 31 at 8:18
user529760
511216
asked Jul 31 at 5:50
abhay pratap singh
12
closed as unclear what you're asking by Did, Adrian Keister, Lord Shark the Unknown, Shailesh, Isaac Browne Jul 31 at 16:47
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
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If $x_minmathbbR$, $y_n$ is the n'th rational number in $x_m$, and $z_n$ is the n'th irrational number in $x_m$ then
- both $y$ and $z$ are the subsequence of $x$
- at least one of them is the subsequence of$ x$
- Neither $y$ nor $z$ is the subsequence of$x$
I am taking the example the sequence $x(n)=n^1/2$ here both $y$ and $z$ are subsequence of $x$ but I don't know this is true or not in general ....Plz help me
real-analysis real-numbers
edited Jul 31 at 8:18
user529760
511216
asked Jul 31 at 5:50
abhay pratap singh
12
closed as unclear what you're asking by Did, Adrian Keister, Lord Shark the Unknown, Shailesh, Isaac Browne Jul 31 at 16:47
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
Yes it is true in general. Since you are constructing $y,z$ from $x$.
– Piyush Divyanakar
Jul 31 at 5:58
The problem is that $y_n$ and $z_n$ need not even be sequences! For example, if you take a sequence of ratonal numbers, like $1,1,1,1,1$, then $z_n$ is not well defined, for example what would $z_1$ be? If the sequence $x_n$ has infinitely many rational and irrational terms, then one can conclude that $y$ and $z$ are both subsequences of $x$.
– Ã°ÑÂтþý òіûûð þûþф üÑÂûûñÑÂрó
Jul 31 at 8:18
add a comment |Â
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
If $x_minmathbbR$, $y_n$ is the n'th rational number in $x_m$, and $z_n$ is the n'th irrational number in $x_m$ then
- both $y$ and $z$ are the subsequence of $x$
- at least one of them is the subsequence of$ x$
- Neither $y$ nor $z$ is the subsequence of$x$
I am taking the example the sequence $x(n)=n^1/2$ here both $y$ and $z$ are subsequence of $x$ but I don't know this is true or not in general ....Plz help me
real-analysis real-numbers
edited Jul 31 at 8:18
user529760
511216
asked Jul 31 at 5:50
abhay pratap singh
12
If $x_minmathbbR$, $y_n$ is the n'th rational number in $x_m$, and $z_n$ is the n'th irrational number in $x_m$ then
- both $y$ and $z$ are the subsequence of $x$
- at least one of them is the subsequence of$ x$
- Neither $y$ nor $z$ is the subsequence of$x$
I am taking the example the sequence $x(n)=n^1/2$ here both $y$ and $z$ are subsequence of $x$ but I don't know this is true or not in general ....Plz help me
real-analysis real-numbers
edited Jul 31 at 8:18
user529760
511216
asked Jul 31 at 5:50
abhay pratap singh
12
edited Jul 31 at 8:18
user529760
511216
edited Jul 31 at 8:18
user529760
511216
edited Jul 31 at 8:18
user529760
511216
511216
asked Jul 31 at 5:50
abhay pratap singh
12
asked Jul 31 at 5:50
abhay pratap singh
12
asked Jul 31 at 5:50
abhay pratap singh
12
12
closed as unclear what you're asking by Did, Adrian Keister, Lord Shark the Unknown, Shailesh, Isaac Browne Jul 31 at 16:47
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as unclear what you're asking by Did, Adrian Keister, Lord Shark the Unknown, Shailesh, Isaac Browne Jul 31 at 16:47
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
Yes it is true in general. Since you are constructing $y,z$ from $x$.
– Piyush Divyanakar
Jul 31 at 5:58
The problem is that $y_n$ and $z_n$ need not even be sequences! For example, if you take a sequence of ratonal numbers, like $1,1,1,1,1$, then $z_n$ is not well defined, for example what would $z_1$ be? If the sequence $x_n$ has infinitely many rational and irrational terms, then one can conclude that $y$ and $z$ are both subsequences of $x$.
– Ã°ÑÂтþý òіûûð þûþф üÑÂûûñÑÂрó
Jul 31 at 8:18
add a comment |Â
Yes it is true in general. Since you are constructing $y,z$ from $x$.
– Piyush Divyanakar
Jul 31 at 5:58
The problem is that $y_n$ and $z_n$ need not even be sequences! For example, if you take a sequence of ratonal numbers, like $1,1,1,1,1$, then $z_n$ is not well defined, for example what would $z_1$ be? If the sequence $x_n$ has infinitely many rational and irrational terms, then one can conclude that $y$ and $z$ are both subsequences of $x$.
– Ã°ÑÂтþý òіûûð þûþф üÑÂûûñÑÂрó
Jul 31 at 8:18
Yes it is true in general. Since you are constructing $y,z$ from $x$.
– Piyush Divyanakar
Jul 31 at 5:58
Yes it is true in general. Since you are constructing $y,z$ from $x$.
– Piyush Divyanakar
Jul 31 at 5:58
The problem is that $y_n$ and $z_n$ need not even be sequences! For example, if you take a sequence of ratonal numbers, like $1,1,1,1,1$, then $z_n$ is not well defined, for example what would $z_1$ be? If the sequence $x_n$ has infinitely many rational and irrational terms, then one can conclude that $y$ and $z$ are both subsequences of $x$.
– Ã°ÑÂтþý òіûûð þûþф üÑÂûûñÑÂрó
Jul 31 at 8:18
The problem is that $y_n$ and $z_n$ need not even be sequences! For example, if you take a sequence of ratonal numbers, like $1,1,1,1,1$, then $z_n$ is not well defined, for example what would $z_1$ be? If the sequence $x_n$ has infinitely many rational and irrational terms, then one can conclude that $y$ and $z$ are both subsequences of $x$.
– Ã°ÑÂтþý òіûûð þûþф üÑÂûûñÑÂрó
Jul 31 at 8:18
add a comment |Â
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Yes it is true in general. Since you are constructing $y,z$ from $x$.
– Piyush Divyanakar
Jul 31 at 5:58
The problem is that $y_n$ and $z_n$ need not even be sequences! For example, if you take a sequence of ratonal numbers, like $1,1,1,1,1$, then $z_n$ is not well defined, for example what would $z_1$ be? If the sequence $x_n$ has infinitely many rational and irrational terms, then one can conclude that $y$ and $z$ are both subsequences of $x$.
– Ã°ÑÂтþý òіûûð þûþф üÑÂûûñÑÂрó
Jul 31 at 8:18