Does there exist a proper open subset of $mathbb{R}$ that contains the irrationals? [closed]
-1
$begingroup$
I was wondering if such a set can exist?
analysis
asked Jan 22 at 23:03
EcotisticianEcotistician
32018
$endgroup$
closed as off-topic by Rob Arthan, Travis, amWhy, John Douma, Shailesh Jan 23 at 0:06
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Travis, amWhy, John Douma
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
-1
$begingroup$
I was wondering if such a set can exist?
analysis
asked Jan 22 at 23:03
EcotisticianEcotistician
32018
$endgroup$
closed as off-topic by Rob Arthan, Travis, amWhy, John Douma, Shailesh Jan 23 at 0:06
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Travis, amWhy, John Douma
If this question can be reworded to fit the rules in the help center, please edit the question.
$begingroup$
@RobArthan It was more like a question spawned from a homework problem( folland chapter 4 exercise 4) that I mistakenly thought was interesting. I did the problem already before asking this question, I know how MSE works, I'm not trying to be spoon fed answer by copy and pasting a homework question on here. I genuinely forgot about the trivial examples provided below.
$endgroup$
– Ecotistician
Jan 25 at 8:07
$begingroup$
The background you've given in your comment would have done the trick: "I solved this problem ... and it led me to wondering whether this conjecture ... is true but I don't see how to go about proving it" is a template for a good question. No hard feelings, I hope.
$endgroup$
– Rob Arthan
Jan 25 at 21:11
$begingroup$
I agree, more background would have helped avoid the suspicion in this case, alternatively I could have at least shown what I have tried to disprove the existence of such a set in my futile attempts. No hard feelings, I just want to make it clear I'm not an abuser of the MSE community.
$endgroup$
– Ecotistician
Jan 25 at 23:11
add a comment |
-1
-1
-1
$begingroup$
I was wondering if such a set can exist?
analysis
asked Jan 22 at 23:03
EcotisticianEcotistician
32018
$endgroup$
I was wondering if such a set can exist?
analysis
analysis
asked Jan 22 at 23:03
EcotisticianEcotistician
32018
asked Jan 22 at 23:03
EcotisticianEcotistician
32018
asked Jan 22 at 23:03
EcotisticianEcotistician
32018
asked Jan 22 at 23:03
EcotisticianEcotistician
32018
asked Jan 22 at 23:03
EcotisticianEcotistician
32018
32018
closed as off-topic by Rob Arthan, Travis, amWhy, John Douma, Shailesh Jan 23 at 0:06
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Travis, amWhy, John Douma
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Rob Arthan, Travis, amWhy, John Douma, Shailesh Jan 23 at 0:06
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Travis, amWhy, John Douma
If this question can be reworded to fit the rules in the help center, please edit the question.
$begingroup$
@RobArthan It was more like a question spawned from a homework problem( folland chapter 4 exercise 4) that I mistakenly thought was interesting. I did the problem already before asking this question, I know how MSE works, I'm not trying to be spoon fed answer by copy and pasting a homework question on here. I genuinely forgot about the trivial examples provided below.
$endgroup$
– Ecotistician
Jan 25 at 8:07
$begingroup$
The background you've given in your comment would have done the trick: "I solved this problem ... and it led me to wondering whether this conjecture ... is true but I don't see how to go about proving it" is a template for a good question. No hard feelings, I hope.
$endgroup$
– Rob Arthan
Jan 25 at 21:11
$begingroup$
I agree, more background would have helped avoid the suspicion in this case, alternatively I could have at least shown what I have tried to disprove the existence of such a set in my futile attempts. No hard feelings, I just want to make it clear I'm not an abuser of the MSE community.
$endgroup$
– Ecotistician
Jan 25 at 23:11
add a comment |
$begingroup$
@RobArthan It was more like a question spawned from a homework problem( folland chapter 4 exercise 4) that I mistakenly thought was interesting. I did the problem already before asking this question, I know how MSE works, I'm not trying to be spoon fed answer by copy and pasting a homework question on here. I genuinely forgot about the trivial examples provided below.
$endgroup$
– Ecotistician
Jan 25 at 8:07
$begingroup$
The background you've given in your comment would have done the trick: "I solved this problem ... and it led me to wondering whether this conjecture ... is true but I don't see how to go about proving it" is a template for a good question. No hard feelings, I hope.
$endgroup$
– Rob Arthan
Jan 25 at 21:11
$begingroup$
I agree, more background would have helped avoid the suspicion in this case, alternatively I could have at least shown what I have tried to disprove the existence of such a set in my futile attempts. No hard feelings, I just want to make it clear I'm not an abuser of the MSE community.
$endgroup$
– Ecotistician
Jan 25 at 23:11
$begingroup$
@RobArthan It was more like a question spawned from a homework problem( folland chapter 4 exercise 4) that I mistakenly thought was interesting. I did the problem already before asking this question, I know how MSE works, I'm not trying to be spoon fed answer by copy and pasting a homework question on here. I genuinely forgot about the trivial examples provided below.
$endgroup$
– Ecotistician
Jan 25 at 8:07
$begingroup$
@RobArthan It was more like a question spawned from a homework problem( folland chapter 4 exercise 4) that I mistakenly thought was interesting. I did the problem already before asking this question, I know how MSE works, I'm not trying to be spoon fed answer by copy and pasting a homework question on here. I genuinely forgot about the trivial examples provided below.
$endgroup$
– Ecotistician
Jan 25 at 8:07
$begingroup$
The background you've given in your comment would have done the trick: "I solved this problem ... and it led me to wondering whether this conjecture ... is true but I don't see how to go about proving it" is a template for a good question. No hard feelings, I hope.
$endgroup$
– Rob Arthan
Jan 25 at 21:11
$begingroup$
The background you've given in your comment would have done the trick: "I solved this problem ... and it led me to wondering whether this conjecture ... is true but I don't see how to go about proving it" is a template for a good question. No hard feelings, I hope.
$endgroup$
– Rob Arthan
Jan 25 at 21:11
$begingroup$
I agree, more background would have helped avoid the suspicion in this case, alternatively I could have at least shown what I have tried to disprove the existence of such a set in my futile attempts. No hard feelings, I just want to make it clear I'm not an abuser of the MSE community.
$endgroup$
– Ecotistician
Jan 25 at 23:11
$begingroup$
I agree, more background would have helped avoid the suspicion in this case, alternatively I could have at least shown what I have tried to disprove the existence of such a set in my futile attempts. No hard feelings, I just want to make it clear I'm not an abuser of the MSE community.
$endgroup$
– Ecotistician
Jan 25 at 23:11
add a comment |
3 Answers
3
active
oldest
votes
2
$begingroup$
$$Rsmallsetminus{0}$$ is open and contains all irrationals
edited Jan 22 at 23:10
Bernard
122k740116
answered Jan 22 at 23:09
Rohan NuckchadyRohan Nuckchady
1111
$endgroup$
add a comment |
2
$begingroup$
Yes, the set $(-infty,0) cup (0, infty)$
answered Jan 22 at 23:06
AcccumulationAcccumulation
7,0372619
$endgroup$
$begingroup$
@Bernard Oops, got mixed up between rationals and irrationals.
$endgroup$
– Acccumulation
Jan 22 at 23:18
add a comment |
1
$begingroup$
Yes, and it's trivially easy to build one. Let $S$ be any nonempty finite set of rational numbers. Then $mathbb{R}setminus S$ is open and contains all irrationals.
answered Jan 22 at 23:06
jmerryjmerry
11.3k1426
$endgroup$
add a comment |
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
2
$begingroup$
$$Rsmallsetminus{0}$$ is open and contains all irrationals
edited Jan 22 at 23:10
Bernard
122k740116
answered Jan 22 at 23:09
Rohan NuckchadyRohan Nuckchady
1111
$endgroup$
add a comment |
2
$begingroup$
$$Rsmallsetminus{0}$$ is open and contains all irrationals
edited Jan 22 at 23:10
Bernard
122k740116
answered Jan 22 at 23:09
Rohan NuckchadyRohan Nuckchady
1111
$endgroup$
add a comment |
2
2
2
$begingroup$
$$Rsmallsetminus{0}$$ is open and contains all irrationals
edited Jan 22 at 23:10
Bernard
122k740116
answered Jan 22 at 23:09
Rohan NuckchadyRohan Nuckchady
1111
$endgroup$
$$Rsmallsetminus{0}$$ is open and contains all irrationals
edited Jan 22 at 23:10
Bernard
122k740116
answered Jan 22 at 23:09
Rohan NuckchadyRohan Nuckchady
1111
edited Jan 22 at 23:10
Bernard
122k740116
edited Jan 22 at 23:10
Bernard
122k740116
edited Jan 22 at 23:10
Bernard
122k740116
122k740116
answered Jan 22 at 23:09
Rohan NuckchadyRohan Nuckchady
1111
answered Jan 22 at 23:09
Rohan NuckchadyRohan Nuckchady
1111
answered Jan 22 at 23:09
Rohan NuckchadyRohan Nuckchady
1111
1111
add a comment |
add a comment |
2
$begingroup$
Yes, the set $(-infty,0) cup (0, infty)$
answered Jan 22 at 23:06
AcccumulationAcccumulation
7,0372619
$endgroup$
$begingroup$
@Bernard Oops, got mixed up between rationals and irrationals.
$endgroup$
– Acccumulation
Jan 22 at 23:18
add a comment |
2
$begingroup$
Yes, the set $(-infty,0) cup (0, infty)$
answered Jan 22 at 23:06
AcccumulationAcccumulation
7,0372619
$endgroup$
$begingroup$
@Bernard Oops, got mixed up between rationals and irrationals.
$endgroup$
– Acccumulation
Jan 22 at 23:18
add a comment |
2
2
2
$begingroup$
Yes, the set $(-infty,0) cup (0, infty)$
answered Jan 22 at 23:06
AcccumulationAcccumulation
7,0372619
$endgroup$
Yes, the set $(-infty,0) cup (0, infty)$
answered Jan 22 at 23:06
AcccumulationAcccumulation
7,0372619
edited Jan 22 at 23:18
answered Jan 22 at 23:06
AcccumulationAcccumulation
7,0372619
answered Jan 22 at 23:06
AcccumulationAcccumulation
7,0372619
answered Jan 22 at 23:06
AcccumulationAcccumulation
7,0372619
7,0372619
$begingroup$
@Bernard Oops, got mixed up between rationals and irrationals.
$endgroup$
– Acccumulation
Jan 22 at 23:18
add a comment |
$begingroup$
@Bernard Oops, got mixed up between rationals and irrationals.
$endgroup$
– Acccumulation
Jan 22 at 23:18
$begingroup$
@Bernard Oops, got mixed up between rationals and irrationals.
$endgroup$
– Acccumulation
Jan 22 at 23:18
$begingroup$
@Bernard Oops, got mixed up between rationals and irrationals.
$endgroup$
– Acccumulation
Jan 22 at 23:18
add a comment |
1
$begingroup$
Yes, and it's trivially easy to build one. Let $S$ be any nonempty finite set of rational numbers. Then $mathbb{R}setminus S$ is open and contains all irrationals.
answered Jan 22 at 23:06
jmerryjmerry
11.3k1426
$endgroup$
add a comment |
1
$begingroup$
Yes, and it's trivially easy to build one. Let $S$ be any nonempty finite set of rational numbers. Then $mathbb{R}setminus S$ is open and contains all irrationals.
answered Jan 22 at 23:06
jmerryjmerry
11.3k1426
$endgroup$
add a comment |
1
1
1
$begingroup$
Yes, and it's trivially easy to build one. Let $S$ be any nonempty finite set of rational numbers. Then $mathbb{R}setminus S$ is open and contains all irrationals.
answered Jan 22 at 23:06
jmerryjmerry
11.3k1426
$endgroup$
Yes, and it's trivially easy to build one. Let $S$ be any nonempty finite set of rational numbers. Then $mathbb{R}setminus S$ is open and contains all irrationals.
answered Jan 22 at 23:06
jmerryjmerry
11.3k1426
answered Jan 22 at 23:06
jmerryjmerry
11.3k1426
answered Jan 22 at 23:06
jmerryjmerry
11.3k1426
answered Jan 22 at 23:06
jmerryjmerry
11.3k1426
11.3k1426
add a comment |
add a comment |
$begingroup$
@RobArthan It was more like a question spawned from a homework problem( folland chapter 4 exercise 4) that I mistakenly thought was interesting. I did the problem already before asking this question, I know how MSE works, I'm not trying to be spoon fed answer by copy and pasting a homework question on here. I genuinely forgot about the trivial examples provided below.
$endgroup$
– Ecotistician
Jan 25 at 8:07
$begingroup$
The background you've given in your comment would have done the trick: "I solved this problem ... and it led me to wondering whether this conjecture ... is true but I don't see how to go about proving it" is a template for a good question. No hard feelings, I hope.
$endgroup$
– Rob Arthan
Jan 25 at 21:11
$begingroup$
I agree, more background would have helped avoid the suspicion in this case, alternatively I could have at least shown what I have tried to disprove the existence of such a set in my futile attempts. No hard feelings, I just want to make it clear I'm not an abuser of the MSE community.
$endgroup$
– Ecotistician
Jan 25 at 23:11