How to identify a subset using a specific label

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Given a set 1,2,3,4,5, could we use a combination of some labels, for example the sum of elements in the subset or the average or anything else, to build a bijection between the subset and the combination of labels? I tried to use the sum of elements in subsets, the number of elements and the median number to build the bijection but failed. Because in 1,2,3,4,5 if we want to identify 1,3,5 using (9,3,3), it can be also referred to 2,3,4.










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    What is the ultimate goal? With five labels you could give all information.
    – Marc
    Sep 4 at 8:02










  • Actually, I want to find the minimal combination, which means using the minimal number of labels to identify for all sizes of sets.
    – Sooner
    Sep 4 at 8:03






  • 1




    Does $sum_ninmathbb S 2^n$ suit your needs?
    – celtschk
    Sep 4 at 12:02










  • Here is the problem. Given $sum_ninmathbb S 2^n$, can you reconstruct the subset?
    – Sooner
    Sep 4 at 13:42















up vote
0
down vote

favorite












Given a set 1,2,3,4,5, could we use a combination of some labels, for example the sum of elements in the subset or the average or anything else, to build a bijection between the subset and the combination of labels? I tried to use the sum of elements in subsets, the number of elements and the median number to build the bijection but failed. Because in 1,2,3,4,5 if we want to identify 1,3,5 using (9,3,3), it can be also referred to 2,3,4.










share|cite|improve this question



















  • 1




    What is the ultimate goal? With five labels you could give all information.
    – Marc
    Sep 4 at 8:02










  • Actually, I want to find the minimal combination, which means using the minimal number of labels to identify for all sizes of sets.
    – Sooner
    Sep 4 at 8:03






  • 1




    Does $sum_ninmathbb S 2^n$ suit your needs?
    – celtschk
    Sep 4 at 12:02










  • Here is the problem. Given $sum_ninmathbb S 2^n$, can you reconstruct the subset?
    – Sooner
    Sep 4 at 13:42













up vote
0
down vote

favorite









up vote
0
down vote

favorite











Given a set 1,2,3,4,5, could we use a combination of some labels, for example the sum of elements in the subset or the average or anything else, to build a bijection between the subset and the combination of labels? I tried to use the sum of elements in subsets, the number of elements and the median number to build the bijection but failed. Because in 1,2,3,4,5 if we want to identify 1,3,5 using (9,3,3), it can be also referred to 2,3,4.










share|cite|improve this question















Given a set 1,2,3,4,5, could we use a combination of some labels, for example the sum of elements in the subset or the average or anything else, to build a bijection between the subset and the combination of labels? I tried to use the sum of elements in subsets, the number of elements and the median number to build the bijection but failed. Because in 1,2,3,4,5 if we want to identify 1,3,5 using (9,3,3), it can be also referred to 2,3,4.







elementary-set-theory






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edited Sep 4 at 11:48









Andrés E. Caicedo

63.4k7154238




63.4k7154238










asked Sep 4 at 7:54









Sooner

196




196







  • 1




    What is the ultimate goal? With five labels you could give all information.
    – Marc
    Sep 4 at 8:02










  • Actually, I want to find the minimal combination, which means using the minimal number of labels to identify for all sizes of sets.
    – Sooner
    Sep 4 at 8:03






  • 1




    Does $sum_ninmathbb S 2^n$ suit your needs?
    – celtschk
    Sep 4 at 12:02










  • Here is the problem. Given $sum_ninmathbb S 2^n$, can you reconstruct the subset?
    – Sooner
    Sep 4 at 13:42













  • 1




    What is the ultimate goal? With five labels you could give all information.
    – Marc
    Sep 4 at 8:02










  • Actually, I want to find the minimal combination, which means using the minimal number of labels to identify for all sizes of sets.
    – Sooner
    Sep 4 at 8:03






  • 1




    Does $sum_ninmathbb S 2^n$ suit your needs?
    – celtschk
    Sep 4 at 12:02










  • Here is the problem. Given $sum_ninmathbb S 2^n$, can you reconstruct the subset?
    – Sooner
    Sep 4 at 13:42








1




1




What is the ultimate goal? With five labels you could give all information.
– Marc
Sep 4 at 8:02




What is the ultimate goal? With five labels you could give all information.
– Marc
Sep 4 at 8:02












Actually, I want to find the minimal combination, which means using the minimal number of labels to identify for all sizes of sets.
– Sooner
Sep 4 at 8:03




Actually, I want to find the minimal combination, which means using the minimal number of labels to identify for all sizes of sets.
– Sooner
Sep 4 at 8:03




1




1




Does $sum_ninmathbb S 2^n$ suit your needs?
– celtschk
Sep 4 at 12:02




Does $sum_ninmathbb S 2^n$ suit your needs?
– celtschk
Sep 4 at 12:02












Here is the problem. Given $sum_ninmathbb S 2^n$, can you reconstruct the subset?
– Sooner
Sep 4 at 13:42





Here is the problem. Given $sum_ninmathbb S 2^n$, can you reconstruct the subset?
– Sooner
Sep 4 at 13:42
















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