Corollary: Circular References Of Self-Contained Sets Are Forbidden

(related to Axiom: Axiom of Foundation)

A chain of $n\ge 0$ sets being contained in each other in the form $X_0\in X_1\in\ldots X_{n-1}\in X_n\in X_0$ is not possible.

Proofs: 1

Motivations: 1


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References

Bibliography

  1. Hoffmann, Dirk W.: "Grenzen der Mathematik - Eine Reise durch die Kerngebiete der mathematischen Logik", Spektrum Akademischer Verlag, 2011
  2. Ebbinghaus, H.-D.: "Einf├╝hrung in die Mengenlehre", BI Wisschenschaftsverlag, 1994, 3th Edition