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ordinal_number [2013/09/05 02:00] nikolaj |
ordinal_number [2014/12/05 11:07] nikolaj |
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| ===== Ordinal number ===== | ===== Ordinal number ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#FFBB00: $\alpha\in \mathrm{Ord}$ | | + | | @#FFBB00: definiendum | @#FFBB00: $\alpha\in \mathrm{Ord}$ | |
| - | + | | @#AAFFAA: inclusion | @#AAFFAA: $\alpha$...transitive | | |
| - | | @#88DDEE: $\alpha$...transitive | | + | | @#FFFDDD: for all | @#FFFDDD: $\beta,\gamma\in\alpha$ | |
| - | + | | @#55EE55: postulate | @#55EE55: $ (\beta\in\gamma)\ \lor\ (\gamma\in\beta)\ \lor\ (\beta=\gamma) $ | | |
| - | | $\beta,\gamma\in\alpha$ | | + | |
| - | + | ||
| - | | @#55EE55: $ (\beta\in\gamma)\ \lor\ (\gamma\in\beta)\ \lor\ (\beta=\gamma) $ | | + | |
| ==== Discussion ==== | ==== Discussion ==== | ||
| Line 17: | Line 14: | ||
| For any two ordinals $\in$ gives an ordering $<$ via | For any two ordinals $\in$ gives an ordering $<$ via | ||
| - | | @#EEEE55: $\beta<\gamma\equiv \beta\in\gamma$ | | + | | @#EEEE55: predicate | @#EEEE55: $\beta<\gamma\equiv \beta\in\gamma$ | |
| === Reference === | === Reference === | ||
| Wikipedia: [[http://en.wikipedia.org/wiki/Ordinal_number|Ordinal number]] | Wikipedia: [[http://en.wikipedia.org/wiki/Ordinal_number|Ordinal number]] | ||
| - | ==== Context ==== | + | ==== Parents ==== |
| - | === Parents === | + | === Requirements === |
| + | [[Transitive relation]] | ||
| + | === Related === | ||
| [[Trichotomous relation]] | [[Trichotomous relation]] | ||
