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As you recall from the historical development, Cantor’s naive set definition also allowed constructing a “set of all sets”. With the axiom of separation, such a set cannot exist.

Corollary: There is no set of all sets

There is no such set $X$ which contains the set $\{z\in X\mid z\not\in z\}$ as an element. In other words, a “set of all sets” does not exist.

| | | | | created: 2019-01-08 23:22:32 | modified: 2019-01-08 23:30:23 | by: bookofproofs | references: [656], [983]

1.Proof: (related to "There is no set of all sets")

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Bibliography (further reading)

[983] Ebbinghaus, H.-D.: “Einf├╝hrung in die Mengenlehre”, BI Wisschenschaftsverlag, 1994, 3

[656] Hoffmann, Dirk W.: “Grenzen der Mathematik – Eine Reise durch die Kerngebiete der mathematischen Logik”, Spektrum Akademischer Verlag, 2011

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