How to formalize the following statement: “for all integers, n, n^2 is even.” [on hold]

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I am trying to formalize the statement "for all integers $n$, $n^2$ is even" by using mathematical quantifiers but I am not sure if I am on the right track.
I'd be grateful if someone could shed light on it.




calculus




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put on hold as off-topic by M. Winter, Lord Shark the Unknown, Jyrki Lahtonen, John Ma, José Carlos Santos 2 days ago


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." – M. Winter, Lord Shark the Unknown, Jyrki Lahtonen, John Ma, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.








  • 6




    $forall nin mathbbN, exists kin mathbbN | n^2=2k$ (note that this statement is false: $3^2=9$).
    – Suzet
    Aug 4 at 1:41










  • I would recommend that you always include what you already have worked out yourself, or you face the danger that your question becomes closed.
    – M. Winter
    Aug 4 at 2:25














up vote
0
down vote

favorite












I am trying to formalize the statement "for all integers $n$, $n^2$ is even" by using mathematical quantifiers but I am not sure if I am on the right track.
I'd be grateful if someone could shed light on it.




calculus




share|cite|improve this question













put on hold as off-topic by M. Winter, Lord Shark the Unknown, Jyrki Lahtonen, John Ma, José Carlos Santos 2 days ago


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." – M. Winter, Lord Shark the Unknown, Jyrki Lahtonen, John Ma, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.








  • 6




    $forall nin mathbbN, exists kin mathbbN | n^2=2k$ (note that this statement is false: $3^2=9$).
    – Suzet
    Aug 4 at 1:41










  • I would recommend that you always include what you already have worked out yourself, or you face the danger that your question becomes closed.
    – M. Winter
    Aug 4 at 2:25












up vote
0
down vote

favorite









up vote
0
down vote

favorite











I am trying to formalize the statement "for all integers $n$, $n^2$ is even" by using mathematical quantifiers but I am not sure if I am on the right track.
I'd be grateful if someone could shed light on it.




calculus




share|cite|improve this question













I am trying to formalize the statement "for all integers $n$, $n^2$ is even" by using mathematical quantifiers but I am not sure if I am on the right track.
I'd be grateful if someone could shed light on it.





calculus





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Aug 4 at 1:49









Hans Hüttel

3,0142819




3,0142819









asked Aug 4 at 1:39









Susan mohammad.k

31




31




put on hold as off-topic by M. Winter, Lord Shark the Unknown, Jyrki Lahtonen, John Ma, José Carlos Santos 2 days ago


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." – M. Winter, Lord Shark the Unknown, Jyrki Lahtonen, John Ma, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.




put on hold as off-topic by M. Winter, Lord Shark the Unknown, Jyrki Lahtonen, John Ma, José Carlos Santos 2 days ago


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." – M. Winter, Lord Shark the Unknown, Jyrki Lahtonen, John Ma, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.







  • 6




    $forall nin mathbbN, exists kin mathbbN | n^2=2k$ (note that this statement is false: $3^2=9$).
    – Suzet
    Aug 4 at 1:41










  • I would recommend that you always include what you already have worked out yourself, or you face the danger that your question becomes closed.
    – M. Winter
    Aug 4 at 2:25












  • 6




    $forall nin mathbbN, exists kin mathbbN | n^2=2k$ (note that this statement is false: $3^2=9$).
    – Suzet
    Aug 4 at 1:41










  • I would recommend that you always include what you already have worked out yourself, or you face the danger that your question becomes closed.
    – M. Winter
    Aug 4 at 2:25







6




6




$forall nin mathbbN, exists kin mathbbN | n^2=2k$ (note that this statement is false: $3^2=9$).
– Suzet
Aug 4 at 1:41




$forall nin mathbbN, exists kin mathbbN | n^2=2k$ (note that this statement is false: $3^2=9$).
– Suzet
Aug 4 at 1:41












I would recommend that you always include what you already have worked out yourself, or you face the danger that your question becomes closed.
– M. Winter
Aug 4 at 2:25




I would recommend that you always include what you already have worked out yourself, or you face the danger that your question becomes closed.
– M. Winter
Aug 4 at 2:25










1 Answer
1






active

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votes

















up vote
1
down vote



accepted










Note that $mathbbN$ stands for natural numbers.



Since you want to state for all integers, you need to modify $$forall nin mathbbN, exists kin mathbbN | n^2=2k$$ to



$$forall nin mathbbZ, exists kin mathbbZ | n^2=2k$$






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










    Note that $mathbbN$ stands for natural numbers.



    Since you want to state for all integers, you need to modify $$forall nin mathbbN, exists kin mathbbN | n^2=2k$$ to



    $$forall nin mathbbZ, exists kin mathbbZ | n^2=2k$$






    share|cite|improve this answer

























      up vote
      1
      down vote



      accepted










      Note that $mathbbN$ stands for natural numbers.



      Since you want to state for all integers, you need to modify $$forall nin mathbbN, exists kin mathbbN | n^2=2k$$ to



      $$forall nin mathbbZ, exists kin mathbbZ | n^2=2k$$






      share|cite|improve this answer























        up vote
        1
        down vote



        accepted







        up vote
        1
        down vote



        accepted






        Note that $mathbbN$ stands for natural numbers.



        Since you want to state for all integers, you need to modify $$forall nin mathbbN, exists kin mathbbN | n^2=2k$$ to



        $$forall nin mathbbZ, exists kin mathbbZ | n^2=2k$$






        share|cite|improve this answer













        Note that $mathbbN$ stands for natural numbers.



        Since you want to state for all integers, you need to modify $$forall nin mathbbN, exists kin mathbbN | n^2=2k$$ to



        $$forall nin mathbbZ, exists kin mathbbZ | n^2=2k$$







        share|cite|improve this answer













        share|cite|improve this answer



        share|cite|improve this answer











        answered Aug 4 at 2:23









        Mohammad Riazi-Kermani

        27k41850




        27k41850












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