Question about finding choice function [closed]

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This is a question of munkres topology ch 1 of section axiom of choice and choice function. From help by lattice I understood that how to find it for set of integers. But for set of Rationals, I am not able to find how to define such a function.
QUESTION IS-



Find, if possible a choice function for the collection of nonempty subsets of Rational numbers.



Please help me as I don't have help from teachers or fellow classmates.




axiom-of-choice




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closed as off-topic by user223391, Peter, José Carlos Santos, amWhy, Adrian Keister Aug 2 at 14:15


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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Community, amWhy, Adrian Keister
If this question can be reworded to fit the rules in the help center, please edit the question.












  • Please, provide more information about the context of your question.
    – Taroccoesbrocco
    Aug 2 at 14:02










  • It is a question from munkres topology section 9 ( axiom of choice. Choice function). It asks on finding a choice function, if possible, for the collection of non empty subsets of integers. Please help me.
    – A D
    Aug 2 at 14:10










  • You could set $Amapsto a$ where $a$ is the element of $A$ having the smallest absolute value (possibly there are two such elements, then choose $a$ for instance to be the positive one). The axiom of choice is not needed here since the considered sets are subsets of a space which has enough "structure" to make a choice for an arbitrary set possible. In particular there is some distinguished element $0$ and some relation/order on the set of integers making that choice possible. It seems to me that this question aims to show that the axiom of choice is not always needed.
    – lattice
    Aug 2 at 14:21










  • Thank you very much lattice. Can you please tell me in which conditions on set B (whose subcollection we want to take) choice function doesn't exists.
    – A D
    Aug 2 at 15:11










  • In particular if it exists for collection of nonempty subsets of Rational numbers.
    – A D
    Aug 2 at 15:13














up vote
-4
down vote

favorite
1












I am sorry, if someone were not clear with my question.
Actually I am new to this site.



This is a question of munkres topology ch 1 of section axiom of choice and choice function. From help by lattice I understood that how to find it for set of integers. But for set of Rationals, I am not able to find how to define such a function.
QUESTION IS-



Find, if possible a choice function for the collection of nonempty subsets of Rational numbers.



Please help me as I don't have help from teachers or fellow classmates.




axiom-of-choice




share|cite|improve this question













closed as off-topic by user223391, Peter, José Carlos Santos, amWhy, Adrian Keister Aug 2 at 14:15


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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Community, amWhy, Adrian Keister
If this question can be reworded to fit the rules in the help center, please edit the question.












  • Please, provide more information about the context of your question.
    – Taroccoesbrocco
    Aug 2 at 14:02










  • It is a question from munkres topology section 9 ( axiom of choice. Choice function). It asks on finding a choice function, if possible, for the collection of non empty subsets of integers. Please help me.
    – A D
    Aug 2 at 14:10










  • You could set $Amapsto a$ where $a$ is the element of $A$ having the smallest absolute value (possibly there are two such elements, then choose $a$ for instance to be the positive one). The axiom of choice is not needed here since the considered sets are subsets of a space which has enough "structure" to make a choice for an arbitrary set possible. In particular there is some distinguished element $0$ and some relation/order on the set of integers making that choice possible. It seems to me that this question aims to show that the axiom of choice is not always needed.
    – lattice
    Aug 2 at 14:21










  • Thank you very much lattice. Can you please tell me in which conditions on set B (whose subcollection we want to take) choice function doesn't exists.
    – A D
    Aug 2 at 15:11










  • In particular if it exists for collection of nonempty subsets of Rational numbers.
    – A D
    Aug 2 at 15:13












up vote
-4
down vote

favorite
1









up vote
-4
down vote

favorite
1






1





I am sorry, if someone were not clear with my question.
Actually I am new to this site.



This is a question of munkres topology ch 1 of section axiom of choice and choice function. From help by lattice I understood that how to find it for set of integers. But for set of Rationals, I am not able to find how to define such a function.
QUESTION IS-



Find, if possible a choice function for the collection of nonempty subsets of Rational numbers.



Please help me as I don't have help from teachers or fellow classmates.




axiom-of-choice




share|cite|improve this question













I am sorry, if someone were not clear with my question.
Actually I am new to this site.



This is a question of munkres topology ch 1 of section axiom of choice and choice function. From help by lattice I understood that how to find it for set of integers. But for set of Rationals, I am not able to find how to define such a function.
QUESTION IS-



Find, if possible a choice function for the collection of nonempty subsets of Rational numbers.



Please help me as I don't have help from teachers or fellow classmates.





axiom-of-choice





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Aug 4 at 3:22
























asked Aug 2 at 13:54









A D

62




62




closed as off-topic by user223391, Peter, José Carlos Santos, amWhy, Adrian Keister Aug 2 at 14:15


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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Community, amWhy, Adrian Keister
If this question can be reworded to fit the rules in the help center, please edit the question.




closed as off-topic by user223391, Peter, José Carlos Santos, amWhy, Adrian Keister Aug 2 at 14:15


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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Community, amWhy, Adrian Keister
If this question can be reworded to fit the rules in the help center, please edit the question.











  • Please, provide more information about the context of your question.
    – Taroccoesbrocco
    Aug 2 at 14:02










  • It is a question from munkres topology section 9 ( axiom of choice. Choice function). It asks on finding a choice function, if possible, for the collection of non empty subsets of integers. Please help me.
    – A D
    Aug 2 at 14:10










  • You could set $Amapsto a$ where $a$ is the element of $A$ having the smallest absolute value (possibly there are two such elements, then choose $a$ for instance to be the positive one). The axiom of choice is not needed here since the considered sets are subsets of a space which has enough "structure" to make a choice for an arbitrary set possible. In particular there is some distinguished element $0$ and some relation/order on the set of integers making that choice possible. It seems to me that this question aims to show that the axiom of choice is not always needed.
    – lattice
    Aug 2 at 14:21










  • Thank you very much lattice. Can you please tell me in which conditions on set B (whose subcollection we want to take) choice function doesn't exists.
    – A D
    Aug 2 at 15:11










  • In particular if it exists for collection of nonempty subsets of Rational numbers.
    – A D
    Aug 2 at 15:13
















  • Please, provide more information about the context of your question.
    – Taroccoesbrocco
    Aug 2 at 14:02










  • It is a question from munkres topology section 9 ( axiom of choice. Choice function). It asks on finding a choice function, if possible, for the collection of non empty subsets of integers. Please help me.
    – A D
    Aug 2 at 14:10










  • You could set $Amapsto a$ where $a$ is the element of $A$ having the smallest absolute value (possibly there are two such elements, then choose $a$ for instance to be the positive one). The axiom of choice is not needed here since the considered sets are subsets of a space which has enough "structure" to make a choice for an arbitrary set possible. In particular there is some distinguished element $0$ and some relation/order on the set of integers making that choice possible. It seems to me that this question aims to show that the axiom of choice is not always needed.
    – lattice
    Aug 2 at 14:21










  • Thank you very much lattice. Can you please tell me in which conditions on set B (whose subcollection we want to take) choice function doesn't exists.
    – A D
    Aug 2 at 15:11










  • In particular if it exists for collection of nonempty subsets of Rational numbers.
    – A D
    Aug 2 at 15:13















Please, provide more information about the context of your question.
– Taroccoesbrocco
Aug 2 at 14:02




Please, provide more information about the context of your question.
– Taroccoesbrocco
Aug 2 at 14:02












It is a question from munkres topology section 9 ( axiom of choice. Choice function). It asks on finding a choice function, if possible, for the collection of non empty subsets of integers. Please help me.
– A D
Aug 2 at 14:10




It is a question from munkres topology section 9 ( axiom of choice. Choice function). It asks on finding a choice function, if possible, for the collection of non empty subsets of integers. Please help me.
– A D
Aug 2 at 14:10












You could set $Amapsto a$ where $a$ is the element of $A$ having the smallest absolute value (possibly there are two such elements, then choose $a$ for instance to be the positive one). The axiom of choice is not needed here since the considered sets are subsets of a space which has enough "structure" to make a choice for an arbitrary set possible. In particular there is some distinguished element $0$ and some relation/order on the set of integers making that choice possible. It seems to me that this question aims to show that the axiom of choice is not always needed.
– lattice
Aug 2 at 14:21




You could set $Amapsto a$ where $a$ is the element of $A$ having the smallest absolute value (possibly there are two such elements, then choose $a$ for instance to be the positive one). The axiom of choice is not needed here since the considered sets are subsets of a space which has enough "structure" to make a choice for an arbitrary set possible. In particular there is some distinguished element $0$ and some relation/order on the set of integers making that choice possible. It seems to me that this question aims to show that the axiom of choice is not always needed.
– lattice
Aug 2 at 14:21












Thank you very much lattice. Can you please tell me in which conditions on set B (whose subcollection we want to take) choice function doesn't exists.
– A D
Aug 2 at 15:11




Thank you very much lattice. Can you please tell me in which conditions on set B (whose subcollection we want to take) choice function doesn't exists.
– A D
Aug 2 at 15:11












In particular if it exists for collection of nonempty subsets of Rational numbers.
– A D
Aug 2 at 15:13




In particular if it exists for collection of nonempty subsets of Rational numbers.
– A D
Aug 2 at 15:13















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