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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.

| | | | | created: 2014-06-30 21:06:09 | modified: 2019-03-08 12:55:56 | by: bookofproofs | references: [656]

1.Proof: (related to "Ordinals Are Downward Closed")

Edit or AddNotationAxiomatic Method

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Bibliography (further reading)

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