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real_number [2014/02/07 17:33] nikolaj |
real_number [2014/03/21 11:11] 127.0.0.1 external edit |
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| ===== Real number ===== | ===== Real number ===== | ||
| ==== Set ==== | ==== Set ==== | ||
| - | | @#FFBB00: $ r \in \mathbb R $ | | + | | @#FFBB00: definiendum | @#FFBB00: $ r \in \mathbb R $ | |
| | $x,y\in \mathbb Q$ | | | $x,y\in \mathbb Q$ | | ||
| - | | @#55EE55: $ r\subset \mathbb Q $ | | + | | @#55EE55: postulate | @#55EE55: $ r\subset \mathbb Q $ | |
| - | | @#55EE55: $ r\neq \emptyset $ | | + | | @#55EE55: postulate | @#55EE55: $ r\neq \emptyset $ | |
| - | | @#55EE55: $ y\in r\implies x\in r $ | | + | | @#55EE55: postulate | @#55EE55: $ y\in r\implies x\in r $ | |
| - | | @#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 $ | |
| 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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| === Subset of === | === Subset of === | ||
| [[Complex number]], [[Extended real number line]], [[Real coordinate space]] | [[Complex number]], [[Extended real number line]], [[Real coordinate space]] | ||
| - | === Requirements === | + | === Context === |
| [[Rational number]] | [[Rational number]] | ||
