Expressing the truth set of x≤0

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Say I have the following predicate which is in the domain of the integers (Z):



$P(x) : x leqslant 0$



Would the truth set be expressed as:



$x inBbb Z : xleqslant 0$



or



$x inBbb Z : x<0 lor x=0$



or



$x inBbb Z : x inBbb Z^- cup 0$







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  • Which one would you suspect is correct? And why?
    – esotechnica
    Aug 19 at 8:26














up vote
-3
down vote

favorite












Say I have the following predicate which is in the domain of the integers (Z):



$P(x) : x leqslant 0$



Would the truth set be expressed as:



$x inBbb Z : xleqslant 0$



or



$x inBbb Z : x<0 lor x=0$



or



$x inBbb Z : x inBbb Z^- cup 0$







share|cite|improve this question






















  • Which one would you suspect is correct? And why?
    – esotechnica
    Aug 19 at 8:26












up vote
-3
down vote

favorite









up vote
-3
down vote

favorite











Say I have the following predicate which is in the domain of the integers (Z):



$P(x) : x leqslant 0$



Would the truth set be expressed as:



$x inBbb Z : xleqslant 0$



or



$x inBbb Z : x<0 lor x=0$



or



$x inBbb Z : x inBbb Z^- cup 0$







share|cite|improve this question














Say I have the following predicate which is in the domain of the integers (Z):



$P(x) : x leqslant 0$



Would the truth set be expressed as:



$x inBbb Z : xleqslant 0$



or



$x inBbb Z : x<0 lor x=0$



or



$x inBbb Z : x inBbb Z^- cup 0$









share|cite|improve this question













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edited Aug 19 at 8:24









Graham Kemp

80.5k43275




80.5k43275










asked Aug 19 at 8:20









R. Lee

1




1











  • Which one would you suspect is correct? And why?
    – esotechnica
    Aug 19 at 8:26
















  • Which one would you suspect is correct? And why?
    – esotechnica
    Aug 19 at 8:26















Which one would you suspect is correct? And why?
– esotechnica
Aug 19 at 8:26




Which one would you suspect is correct? And why?
– esotechnica
Aug 19 at 8:26










2 Answers
2






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0
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Yes.   Those sets are equivalent and represent the set of integers which satisfy the given predicate.



Indeed, they can be simply represented as: $~~Bbb Z^-cup0$






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    down vote













    Fact is that under $P(x) : x leqslant 0$ and $mathbb Z^-:=xinmathbb Zmid x<0$ the following expressions are notations for exactly the same set:



    • $xinmathbb Zmid P(x)$

    • $x inBbb Z : xleqslant 0$

    • $x inBbb Z : x<0 lor x=0$

    • $x inBbb Z : x inBbb Z^- cup 0$





    share|cite|improve this answer




















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      2 Answers
      2






      active

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      2 Answers
      2






      active

      oldest

      votes









      active

      oldest

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      active

      oldest

      votes








      up vote
      0
      down vote













      Yes.   Those sets are equivalent and represent the set of integers which satisfy the given predicate.



      Indeed, they can be simply represented as: $~~Bbb Z^-cup0$






      share|cite|improve this answer
























        up vote
        0
        down vote













        Yes.   Those sets are equivalent and represent the set of integers which satisfy the given predicate.



        Indeed, they can be simply represented as: $~~Bbb Z^-cup0$






        share|cite|improve this answer






















          up vote
          0
          down vote










          up vote
          0
          down vote









          Yes.   Those sets are equivalent and represent the set of integers which satisfy the given predicate.



          Indeed, they can be simply represented as: $~~Bbb Z^-cup0$






          share|cite|improve this answer












          Yes.   Those sets are equivalent and represent the set of integers which satisfy the given predicate.



          Indeed, they can be simply represented as: $~~Bbb Z^-cup0$







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Aug 19 at 8:28









          Graham Kemp

          80.5k43275




          80.5k43275




















              up vote
              0
              down vote













              Fact is that under $P(x) : x leqslant 0$ and $mathbb Z^-:=xinmathbb Zmid x<0$ the following expressions are notations for exactly the same set:



              • $xinmathbb Zmid P(x)$

              • $x inBbb Z : xleqslant 0$

              • $x inBbb Z : x<0 lor x=0$

              • $x inBbb Z : x inBbb Z^- cup 0$





              share|cite|improve this answer
























                up vote
                0
                down vote













                Fact is that under $P(x) : x leqslant 0$ and $mathbb Z^-:=xinmathbb Zmid x<0$ the following expressions are notations for exactly the same set:



                • $xinmathbb Zmid P(x)$

                • $x inBbb Z : xleqslant 0$

                • $x inBbb Z : x<0 lor x=0$

                • $x inBbb Z : x inBbb Z^- cup 0$





                share|cite|improve this answer






















                  up vote
                  0
                  down vote










                  up vote
                  0
                  down vote









                  Fact is that under $P(x) : x leqslant 0$ and $mathbb Z^-:=xinmathbb Zmid x<0$ the following expressions are notations for exactly the same set:



                  • $xinmathbb Zmid P(x)$

                  • $x inBbb Z : xleqslant 0$

                  • $x inBbb Z : x<0 lor x=0$

                  • $x inBbb Z : x inBbb Z^- cup 0$





                  share|cite|improve this answer












                  Fact is that under $P(x) : x leqslant 0$ and $mathbb Z^-:=xinmathbb Zmid x<0$ the following expressions are notations for exactly the same set:



                  • $xinmathbb Zmid P(x)$

                  • $x inBbb Z : xleqslant 0$

                  • $x inBbb Z : x<0 lor x=0$

                  • $x inBbb Z : x inBbb Z^- cup 0$






                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered Aug 19 at 8:50









                  drhab

                  87.7k541119




                  87.7k541119






















                       

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