Mathematical proof of mapping between 2 spaces [closed]

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I have 2 spaces. The first space is $s_1=1,2,3,4,5$, the second space is the positive real numbers up to $N$. Both spaces are related to the preference degree of some users, the higher the number, the stronger the preference.



How can I proof mathematically that a function that maps between these two sets always exists? Is there such a proof?




elementary-set-theory




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closed as unclear what you're asking by Jendrik Stelzner, Jyrki Lahtonen, amWhy, Robert Wolfe, Key Flex Aug 22 at 2:50


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.














  • This is not clear. Of course there are functions between these...as there are between any two sets. Presumably you want those functions to have special properties. What properties did you want?
    – lulu
    Aug 21 at 10:43










  • Of course there are functions between these...as there are between any two sets. is there a mathematical proof that ensures that at least that function exists? How can I know for sure? intuitively, it looks there exists, but I don't know if there is a proof for that. In terms of the properties, my knowledge about spaces is limited. Ideally, I would like to find the map between these two spaces, we are looking at conditional probability + Kernel density estimation or calibration. But first we would like to make sure that the function exists
    – Miguel Gonzalez-Fierro
    Aug 21 at 10:47







  • 1




    @MiguelGonzalez-Fierro Of course at least one function exists. For example, the function that maps everything to 0.
    – Jack M
    Aug 21 at 10:53











  • ok thanks @JackM
    – Miguel Gonzalez-Fierro
    Aug 21 at 10:59










  • I'm sure you have some properties in mind. I doubt, for example, that constant functions help you here. What properties were you looking for?
    – lulu
    Aug 21 at 11:02














up vote
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I have 2 spaces. The first space is $s_1=1,2,3,4,5$, the second space is the positive real numbers up to $N$. Both spaces are related to the preference degree of some users, the higher the number, the stronger the preference.



How can I proof mathematically that a function that maps between these two sets always exists? Is there such a proof?




elementary-set-theory




share|cite|improve this question














closed as unclear what you're asking by Jendrik Stelzner, Jyrki Lahtonen, amWhy, Robert Wolfe, Key Flex Aug 22 at 2:50


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.














  • This is not clear. Of course there are functions between these...as there are between any two sets. Presumably you want those functions to have special properties. What properties did you want?
    – lulu
    Aug 21 at 10:43










  • Of course there are functions between these...as there are between any two sets. is there a mathematical proof that ensures that at least that function exists? How can I know for sure? intuitively, it looks there exists, but I don't know if there is a proof for that. In terms of the properties, my knowledge about spaces is limited. Ideally, I would like to find the map between these two spaces, we are looking at conditional probability + Kernel density estimation or calibration. But first we would like to make sure that the function exists
    – Miguel Gonzalez-Fierro
    Aug 21 at 10:47







  • 1




    @MiguelGonzalez-Fierro Of course at least one function exists. For example, the function that maps everything to 0.
    – Jack M
    Aug 21 at 10:53











  • ok thanks @JackM
    – Miguel Gonzalez-Fierro
    Aug 21 at 10:59










  • I'm sure you have some properties in mind. I doubt, for example, that constant functions help you here. What properties were you looking for?
    – lulu
    Aug 21 at 11:02












up vote
0
down vote

favorite









up vote
0
down vote

favorite











I have 2 spaces. The first space is $s_1=1,2,3,4,5$, the second space is the positive real numbers up to $N$. Both spaces are related to the preference degree of some users, the higher the number, the stronger the preference.



How can I proof mathematically that a function that maps between these two sets always exists? Is there such a proof?




elementary-set-theory




share|cite|improve this question














I have 2 spaces. The first space is $s_1=1,2,3,4,5$, the second space is the positive real numbers up to $N$. Both spaces are related to the preference degree of some users, the higher the number, the stronger the preference.



How can I proof mathematically that a function that maps between these two sets always exists? Is there such a proof?





elementary-set-theory





share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Aug 21 at 11:20









Andrés E. Caicedo

63.3k7152237




63.3k7152237










asked Aug 21 at 10:41









Miguel Gonzalez-Fierro

1063




1063




closed as unclear what you're asking by Jendrik Stelzner, Jyrki Lahtonen, amWhy, Robert Wolfe, Key Flex Aug 22 at 2:50


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 Jendrik Stelzner, Jyrki Lahtonen, amWhy, Robert Wolfe, Key Flex Aug 22 at 2:50


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.













  • This is not clear. Of course there are functions between these...as there are between any two sets. Presumably you want those functions to have special properties. What properties did you want?
    – lulu
    Aug 21 at 10:43










  • Of course there are functions between these...as there are between any two sets. is there a mathematical proof that ensures that at least that function exists? How can I know for sure? intuitively, it looks there exists, but I don't know if there is a proof for that. In terms of the properties, my knowledge about spaces is limited. Ideally, I would like to find the map between these two spaces, we are looking at conditional probability + Kernel density estimation or calibration. But first we would like to make sure that the function exists
    – Miguel Gonzalez-Fierro
    Aug 21 at 10:47







  • 1




    @MiguelGonzalez-Fierro Of course at least one function exists. For example, the function that maps everything to 0.
    – Jack M
    Aug 21 at 10:53











  • ok thanks @JackM
    – Miguel Gonzalez-Fierro
    Aug 21 at 10:59










  • I'm sure you have some properties in mind. I doubt, for example, that constant functions help you here. What properties were you looking for?
    – lulu
    Aug 21 at 11:02
















  • This is not clear. Of course there are functions between these...as there are between any two sets. Presumably you want those functions to have special properties. What properties did you want?
    – lulu
    Aug 21 at 10:43










  • Of course there are functions between these...as there are between any two sets. is there a mathematical proof that ensures that at least that function exists? How can I know for sure? intuitively, it looks there exists, but I don't know if there is a proof for that. In terms of the properties, my knowledge about spaces is limited. Ideally, I would like to find the map between these two spaces, we are looking at conditional probability + Kernel density estimation or calibration. But first we would like to make sure that the function exists
    – Miguel Gonzalez-Fierro
    Aug 21 at 10:47







  • 1




    @MiguelGonzalez-Fierro Of course at least one function exists. For example, the function that maps everything to 0.
    – Jack M
    Aug 21 at 10:53











  • ok thanks @JackM
    – Miguel Gonzalez-Fierro
    Aug 21 at 10:59










  • I'm sure you have some properties in mind. I doubt, for example, that constant functions help you here. What properties were you looking for?
    – lulu
    Aug 21 at 11:02















This is not clear. Of course there are functions between these...as there are between any two sets. Presumably you want those functions to have special properties. What properties did you want?
– lulu
Aug 21 at 10:43




This is not clear. Of course there are functions between these...as there are between any two sets. Presumably you want those functions to have special properties. What properties did you want?
– lulu
Aug 21 at 10:43












Of course there are functions between these...as there are between any two sets. is there a mathematical proof that ensures that at least that function exists? How can I know for sure? intuitively, it looks there exists, but I don't know if there is a proof for that. In terms of the properties, my knowledge about spaces is limited. Ideally, I would like to find the map between these two spaces, we are looking at conditional probability + Kernel density estimation or calibration. But first we would like to make sure that the function exists
– Miguel Gonzalez-Fierro
Aug 21 at 10:47





Of course there are functions between these...as there are between any two sets. is there a mathematical proof that ensures that at least that function exists? How can I know for sure? intuitively, it looks there exists, but I don't know if there is a proof for that. In terms of the properties, my knowledge about spaces is limited. Ideally, I would like to find the map between these two spaces, we are looking at conditional probability + Kernel density estimation or calibration. But first we would like to make sure that the function exists
– Miguel Gonzalez-Fierro
Aug 21 at 10:47





1




1




@MiguelGonzalez-Fierro Of course at least one function exists. For example, the function that maps everything to 0.
– Jack M
Aug 21 at 10:53





@MiguelGonzalez-Fierro Of course at least one function exists. For example, the function that maps everything to 0.
– Jack M
Aug 21 at 10:53













ok thanks @JackM
– Miguel Gonzalez-Fierro
Aug 21 at 10:59




ok thanks @JackM
– Miguel Gonzalez-Fierro
Aug 21 at 10:59












I'm sure you have some properties in mind. I doubt, for example, that constant functions help you here. What properties were you looking for?
– lulu
Aug 21 at 11:02




I'm sure you have some properties in mind. I doubt, for example, that constant functions help you here. What properties were you looking for?
– lulu
Aug 21 at 11:02










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Given two non-empty sets $A$ and $B$, there is always a function from $A$ to $B$, since we can pick some element $b$ out of $B$ and map every element of $A$ to $b$. If you want to get super philosophical, we can probably start talking about set theory axioms, but there's not much point other than just for the sake of it.






share|cite|improve this answer



























    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    1
    down vote



    accepted










    Given two non-empty sets $A$ and $B$, there is always a function from $A$ to $B$, since we can pick some element $b$ out of $B$ and map every element of $A$ to $b$. If you want to get super philosophical, we can probably start talking about set theory axioms, but there's not much point other than just for the sake of it.






    share|cite|improve this answer
























      up vote
      1
      down vote



      accepted










      Given two non-empty sets $A$ and $B$, there is always a function from $A$ to $B$, since we can pick some element $b$ out of $B$ and map every element of $A$ to $b$. If you want to get super philosophical, we can probably start talking about set theory axioms, but there's not much point other than just for the sake of it.






      share|cite|improve this answer






















        up vote
        1
        down vote



        accepted







        up vote
        1
        down vote



        accepted






        Given two non-empty sets $A$ and $B$, there is always a function from $A$ to $B$, since we can pick some element $b$ out of $B$ and map every element of $A$ to $b$. If you want to get super philosophical, we can probably start talking about set theory axioms, but there's not much point other than just for the sake of it.






        share|cite|improve this answer












        Given two non-empty sets $A$ and $B$, there is always a function from $A$ to $B$, since we can pick some element $b$ out of $B$ and map every element of $A$ to $b$. If you want to get super philosophical, we can probably start talking about set theory axioms, but there's not much point other than just for the sake of it.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Aug 21 at 11:01









        Jack M

        17.4k33473




        17.4k33473












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