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The previous different but equivalent notions of ordinals reveal a major property of all ordinal numbers.

Proposition: Ordinals Are Downward Closed

Let $X$ be an ordinal number. Then each element \(w \in X \) is also an ordinal number.

Table of Contents

Proofs: 1

Mentioned in:

Definitions: 1
Lemmas: 2
Motivations: 3
Proofs: 4

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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