Is ∅ ∈ { {∅} } true?












1












$begingroup$


If $ {emptyset} ∈ {emptyset,{emptyset}} $ is true, does it mean this $ emptyset in {{emptyset}} $ true ? If it is not, why it is false?



Also, does $ {{emptyset}}$ mean ${emptyset,{emptyset,{emptyset}}}$ ?






elementary-set-theory







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    1












    $begingroup$


    If $ {emptyset} ∈ {emptyset,{emptyset}} $ is true, does it mean this $ emptyset in {{emptyset}} $ true ? If it is not, why it is false?



    Also, does $ {{emptyset}}$ mean ${emptyset,{emptyset,{emptyset}}}$ ?






    elementary-set-theory







    share|cite|improve this question









    New contributor




    J.S is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.







    $endgroup$















      1












      1








      1





      $begingroup$


      If $ {emptyset} ∈ {emptyset,{emptyset}} $ is true, does it mean this $ emptyset in {{emptyset}} $ true ? If it is not, why it is false?



      Also, does $ {{emptyset}}$ mean ${emptyset,{emptyset,{emptyset}}}$ ?






      elementary-set-theory







      share|cite|improve this question









      New contributor




      J.S is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.







      $endgroup$




      If $ {emptyset} ∈ {emptyset,{emptyset}} $ is true, does it mean this $ emptyset in {{emptyset}} $ true ? If it is not, why it is false?



      Also, does $ {{emptyset}}$ mean ${emptyset,{emptyset,{emptyset}}}$ ?






      elementary-set-theory




      elementary-set-theory






      share|cite|improve this question









      New contributor




      J.S is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.











      share|cite|improve this question









      New contributor




      J.S is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.









      share|cite|improve this question




      share|cite|improve this question








      edited 1 hour ago









      user549397

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      asked 2 hours ago









      J.SJ.S

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          1 Answer
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          $begingroup$

          The notation $a in A$ says that among the elements of $A$ there is one element that is exactly equal to $a.$



          The notation ${emptyset, {emptyset}}$ describes a set with exactly two elements.



          The first element is $emptyset.$ The second element is ${emptyset}.$
          Is one of those two elements exactly equal to ${emptyset}$?



          The notation ${ {emptyset}}$ describes a set with one element.
          That element is ${emptyset}.$



          Which element of ${ {emptyset}}$ do you think is exactly equal to $emptyset$?
          Hint: there's only one element you have to check.



          The notation ${emptyset, {emptyset, {emptyset}}}$ again describes a set with two elements.
          One element is $emptyset$ and the other is
          ${emptyset, {emptyset}}.$
          So this is definitely not the same thing as any set that has only one element.






          share|cite|improve this answer









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            8












            $begingroup$

            The notation $a in A$ says that among the elements of $A$ there is one element that is exactly equal to $a.$



            The notation ${emptyset, {emptyset}}$ describes a set with exactly two elements.



            The first element is $emptyset.$ The second element is ${emptyset}.$
            Is one of those two elements exactly equal to ${emptyset}$?



            The notation ${ {emptyset}}$ describes a set with one element.
            That element is ${emptyset}.$



            Which element of ${ {emptyset}}$ do you think is exactly equal to $emptyset$?
            Hint: there's only one element you have to check.



            The notation ${emptyset, {emptyset, {emptyset}}}$ again describes a set with two elements.
            One element is $emptyset$ and the other is
            ${emptyset, {emptyset}}.$
            So this is definitely not the same thing as any set that has only one element.






            share|cite|improve this answer









            $endgroup$


















              8












              $begingroup$

              The notation $a in A$ says that among the elements of $A$ there is one element that is exactly equal to $a.$



              The notation ${emptyset, {emptyset}}$ describes a set with exactly two elements.



              The first element is $emptyset.$ The second element is ${emptyset}.$
              Is one of those two elements exactly equal to ${emptyset}$?



              The notation ${ {emptyset}}$ describes a set with one element.
              That element is ${emptyset}.$



              Which element of ${ {emptyset}}$ do you think is exactly equal to $emptyset$?
              Hint: there's only one element you have to check.



              The notation ${emptyset, {emptyset, {emptyset}}}$ again describes a set with two elements.
              One element is $emptyset$ and the other is
              ${emptyset, {emptyset}}.$
              So this is definitely not the same thing as any set that has only one element.






              share|cite|improve this answer









              $endgroup$
















                8












                8








                8





                $begingroup$

                The notation $a in A$ says that among the elements of $A$ there is one element that is exactly equal to $a.$



                The notation ${emptyset, {emptyset}}$ describes a set with exactly two elements.



                The first element is $emptyset.$ The second element is ${emptyset}.$
                Is one of those two elements exactly equal to ${emptyset}$?



                The notation ${ {emptyset}}$ describes a set with one element.
                That element is ${emptyset}.$



                Which element of ${ {emptyset}}$ do you think is exactly equal to $emptyset$?
                Hint: there's only one element you have to check.



                The notation ${emptyset, {emptyset, {emptyset}}}$ again describes a set with two elements.
                One element is $emptyset$ and the other is
                ${emptyset, {emptyset}}.$
                So this is definitely not the same thing as any set that has only one element.






                share|cite|improve this answer









                $endgroup$



                The notation $a in A$ says that among the elements of $A$ there is one element that is exactly equal to $a.$



                The notation ${emptyset, {emptyset}}$ describes a set with exactly two elements.



                The first element is $emptyset.$ The second element is ${emptyset}.$
                Is one of those two elements exactly equal to ${emptyset}$?



                The notation ${ {emptyset}}$ describes a set with one element.
                That element is ${emptyset}.$



                Which element of ${ {emptyset}}$ do you think is exactly equal to $emptyset$?
                Hint: there's only one element you have to check.



                The notation ${emptyset, {emptyset, {emptyset}}}$ again describes a set with two elements.
                One element is $emptyset$ and the other is
                ${emptyset, {emptyset}}.$
                So this is definitely not the same thing as any set that has only one element.







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered 1 hour ago









                David KDavid K

                53.4k341115




                53.4k341115






















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