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arithmetic_structure_of_real_numbers [2013/09/08 14:23] nikolaj |
arithmetic_structure_of_real_numbers [2013/09/08 14:24] nikolaj |
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| @#FFBB00: $\langle \mathbb R,+_\mathbb{R},\cdot_\mathbb{R} \rangle$ | | | @#FFBB00: $\langle \mathbb R,+_\mathbb{R},\cdot_\mathbb{R} \rangle$ | | ||
- | | @#55EE55: $r +_\mathbb{R} s = {q+_\mathbb{Q}p\ |\ q\in r\land s\in p}$ | | + | | @#55EE55: $ r +_\mathbb{R} s = \{q+_\mathbb{Q}p\ |\ q\in r\land s\in p\} $ | |
+ | | @#55EE55: $ ... $ | | ||
+ | | @#55EE55: $ ... $ | | ||
+ | | @#55EE55: $ ... $ | | ||
The operations $+_\mathbb{Q}$ and $\cdot_\mathbb{Q}$ on the right hand sides are these of [[arithmetic structure of rational numbers]]. | The operations $+_\mathbb{Q}$ and $\cdot_\mathbb{Q}$ on the right hand sides are these of [[arithmetic structure of rational numbers]]. | ||
- | >todo: http://en.wikipedia.org/wiki/Construction_of_the_real_numbers#Construction_by_Dedekind_cuts | + | >todo: |
+ | > | ||
+ | > http://en.wikipedia.org/wiki/Construction_of_the_real_numbers#Construction_by_Dedekind_cuts | ||
==== Discussion ==== | ==== Discussion ==== |