If a set is a member of itself, then it is called an Abnormal set. One such example would be: Let S be a set such that S contains all sets. Then S itself is a member of S. Is this the only example of an abnormal set? Are there other sets that are abnormal?
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2What set theory are you working with? Under $\mathsf{ZFC}$, no such sets can exist. – JunderscoreH Sep 23 '20 at 05:12
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Treatments of set theory often include an axiom (Mirimanoff's) designed to prohibit "abnormal" sets. In the absence of such an axiom, the equation $x={x}$ could have a vast number of solutions. – bof Sep 23 '20 at 05:14