Ordinal: Difference between revisions
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(ZFC not only setting of pure sets. There are also theories with urelements →Von Neumann definition) |
(Foundations other than set theory) |
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In a pure set theory such as ZFC, we need a way to define ordinals as objects of study. The Von Neumann definition of ordinals does this, by associating each ordinal \( \alpha \) is defined as the set of all ordinals less than \( \alpha \). |
In a pure set theory such as ZFC, we need a way to define ordinals as objects of study. The Von Neumann definition of ordinals does this, by associating each ordinal \( \alpha \) is defined as the set of all ordinals less than \( \alpha \). |
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== Equivalence class definition == |
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Another common definition of ordinals, often used in settings not based on set theory, is as equivalence classes of well-orders. |
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