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Proof

(related to Lemma: Properties of Ordinal Numbers)

According to the properties of transitive sets, all elements of the sets \(\bigcup X\), \(\bigcap X\), are transitive sets. Following the definition of ordinal numbers thy must be themselves ordinal numbers.

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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