Proof

(related to Corollary: Minimal Inductive Set Is Subset Of All Inductive Sets)

By the axiom of foundation, we have to show that every element of the minimal inductive set $\omega$ is also an element of any given inductive set $X$. From this, it will follow immediately that $\omega\subseteq X.$


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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