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first_infinite_von_neumann_ordinal [2015/10/26 21:04] nikolaj |
first_infinite_von_neumann_ordinal [2020/05/20 14:23] (current) nikolaj |
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==== Set ==== | ==== Set ==== | ||
| @#FFBB00: definiendum | @#FFBB00: $ \omega_{\mathcal N}$ | | | @#FFBB00: definiendum | @#FFBB00: $ \omega_{\mathcal N}$ | | ||
- | | @#55EE55: postulate | @#55EE55: $ \emptyset\in\omega_{\mathcal N}$ | | + | |
- | | @#FFFDDD: for all | @#FFFDDD: $ n\in\omega_{\mathcal N}$ | | + | ... |
- | | @#55EE55: postulate | @#55EE55: $ n = \emptyset\ \lor\ \exists (k\in\omega_{\mathcal N}).\ n = {\mathrm{succ}}\ k $ | | + | |
- | | @#FFFDDD: for all | @#FFFDDD: $ m\in n $ | | + | |
- | | @#55EE55: postulate | @#55EE55: $ m = \emptyset\ \lor\ \exists (k\in\omega_{\mathcal N}).\ m = {\mathrm{succ}}\ k $ | | + | |
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As is common, I'll also use the symbol $\mathbb N$ to denote the set theoretic object $\omega_{\mathcal N}$. | As is common, I'll also use the symbol $\mathbb N$ to denote the set theoretic object $\omega_{\mathcal N}$. | ||
- | {{Infinite_Jest.jpg?X800}} | + | {{Infinite_Jest.jpg?X700}} /* Nikolaj Kuntner 2015 */ |
=== Idea === | === Idea === |