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real_number [2014/04/04 15:58] nikolaj |
real_number [2015/09/30 22:45] nikolaj |
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| | @#55EE55: postulate | @#55EE55: $ \neg\ \exists (b\in r).\ \forall (a\in r).\ a<_{\mathbb Q}b $ | | | @#55EE55: postulate | @#55EE55: $ \neg\ \exists (b\in r).\ \forall (a\in r).\ a<_{\mathbb Q}b $ | | ||
| - | ==== Discussion ==== | + | ----- |
| + | === Discussion === | ||
| + | {{ are you for reals.jpg?X250}} | ||
| Remark: We distinguish between "$\subset$" and "$\subseteq$", i.e. the above definition implies $ r\neq \mathbb Q $. | Remark: We distinguish between "$\subset$" and "$\subseteq$", i.e. the above definition implies $ r\neq \mathbb Q $. | ||
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| === Reference === | === Reference === | ||
| Wikipedia: [[http://en.wikipedia.org/wiki/Real_number|Real number]], [[http://en.wikipedia.org/wiki/Construction_of_the_real_numbers|Construction of the real numbers]], [[http://en.wikipedia.org/wiki/Dedekind_cut|Dedekind cut]] | Wikipedia: [[http://en.wikipedia.org/wiki/Real_number|Real number]], [[http://en.wikipedia.org/wiki/Construction_of_the_real_numbers|Construction of the real numbers]], [[http://en.wikipedia.org/wiki/Dedekind_cut|Dedekind cut]] | ||
| - | ==== Parents ==== | + | |
| + | ----- | ||
| === Subset of === | === Subset of === | ||
| [[Complex number]], [[Extended real number line]], [[Real coordinate space]] | [[Complex number]], [[Extended real number line]], [[Real coordinate space]] | ||
| === Context === | === Context === | ||
| [[Rational number]] | [[Rational number]] | ||
