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first_infinite_von_neumann_ordinal [2014/12/27 19:42] nikolaj |
first_infinite_von_neumann_ordinal [2015/10/26 21:04] nikolaj |
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| | @#55EE55: postulate | @#55EE55: $ m = \emptyset\ \lor\ \exists (k\in\omega_{\mathcal N}).\ m = {\mathrm{succ}}\ k $ | | | @#55EE55: postulate | @#55EE55: $ m = \emptyset\ \lor\ \exists (k\in\omega_{\mathcal N}).\ m = {\mathrm{succ}}\ k $ | | ||
| + | ----- | ||
| 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 $\omega_{\mathcal N}$. | ||
| - | ==== Discussion ==== | + | {{Infinite_Jest.jpg?X800}} |
| === Idea === | === Idea === | ||
| This is probably the most straightforward way to set up a countably infinite set. | This is probably the most straightforward way to set up a countably infinite set. | ||
| Line 36: | Line 38: | ||
| [[https://en.wikipedia.org/wiki/Axiom_of_infinity|Axiom of infinity]], | [[https://en.wikipedia.org/wiki/Axiom_of_infinity|Axiom of infinity]], | ||
| [[https://en.wikipedia.org/wiki/Set-theoretic_definition_of_natural_numbers|Set-theoretic definition of natural numbers]] | [[https://en.wikipedia.org/wiki/Set-theoretic_definition_of_natural_numbers|Set-theoretic definition of natural numbers]] | ||
| - | ==== Parents ==== | + | |
| + | ----- | ||
| === Requirements === | === Requirements === | ||
| [[Empty set]], [[Successor set]] | [[Empty set]], [[Successor set]] | ||
