Every subset equal to original set?












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Is there any set whose every subset is equal to the set itself? It seems like this isn't possible, but maybe something similar is possible.






elementary-set-theory







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    $begingroup$


    Is there any set whose every subset is equal to the set itself? It seems like this isn't possible, but maybe something similar is possible.






    elementary-set-theory







    share|cite|improve this question









    $endgroup$















      1












      1








      1





      $begingroup$


      Is there any set whose every subset is equal to the set itself? It seems like this isn't possible, but maybe something similar is possible.






      elementary-set-theory







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      $endgroup$




      Is there any set whose every subset is equal to the set itself? It seems like this isn't possible, but maybe something similar is possible.






      elementary-set-theory




      elementary-set-theory






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      asked 39 mins ago









      lthompsonlthompson

      1169




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          $begingroup$

          In standard foundations (by which I mean ZF, or ZFC) the empty set works:
          If $Ssubset emptyset$, then $S = emptyset$.



          If you wish to do so otherwise, you’d violate the Axiom of Extensionality.






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            3












            $begingroup$

            The empty set has only itself as a subset. This is the only example because every set has the empty set as a subset.






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              3












              $begingroup$

              In standard foundations (by which I mean ZF, or ZFC) the empty set works:
              If $Ssubset emptyset$, then $S = emptyset$.



              If you wish to do so otherwise, you’d violate the Axiom of Extensionality.






              share|cite|improve this answer









              $endgroup$


















                3












                $begingroup$

                In standard foundations (by which I mean ZF, or ZFC) the empty set works:
                If $Ssubset emptyset$, then $S = emptyset$.



                If you wish to do so otherwise, you’d violate the Axiom of Extensionality.






                share|cite|improve this answer









                $endgroup$
















                  3












                  3








                  3





                  $begingroup$

                  In standard foundations (by which I mean ZF, or ZFC) the empty set works:
                  If $Ssubset emptyset$, then $S = emptyset$.



                  If you wish to do so otherwise, you’d violate the Axiom of Extensionality.






                  share|cite|improve this answer









                  $endgroup$



                  In standard foundations (by which I mean ZF, or ZFC) the empty set works:
                  If $Ssubset emptyset$, then $S = emptyset$.



                  If you wish to do so otherwise, you’d violate the Axiom of Extensionality.







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered 33 mins ago









                  user458276user458276

                  743212




                  743212























                      3












                      $begingroup$

                      The empty set has only itself as a subset. This is the only example because every set has the empty set as a subset.






                      share|cite|improve this answer









                      $endgroup$


















                        3












                        $begingroup$

                        The empty set has only itself as a subset. This is the only example because every set has the empty set as a subset.






                        share|cite|improve this answer









                        $endgroup$
















                          3












                          3








                          3





                          $begingroup$

                          The empty set has only itself as a subset. This is the only example because every set has the empty set as a subset.






                          share|cite|improve this answer









                          $endgroup$



                          The empty set has only itself as a subset. This is the only example because every set has the empty set as a subset.







                          share|cite|improve this answer












                          share|cite|improve this answer



                          share|cite|improve this answer










                          answered 33 mins ago









                          Ross MillikanRoss Millikan

                          298k24200373




                          298k24200373






























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