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arithmetic_structure_of_real_numbers [2013/09/08 14:24] nikolaj |
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| - | ===== Arithmetic structure of real numbers ===== | ||
| - | ==== Definition ==== | ||
| - | | @#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: $ ... $ | | ||
| - | | @#55EE55: $ ... $ | | ||
| - | | @#55EE55: $ ... $ | | ||
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| - | The operations $+_\mathbb{Q}$ and $\cdot_\mathbb{Q}$ on the right hand sides are these of [[arithmetic structure of rational numbers]]. | ||
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| - | >todo: | ||
| - | > | ||
| - | > http://en.wikipedia.org/wiki/Construction_of_the_real_numbers#Construction_by_Dedekind_cuts | ||
| - | |||
| - | ==== Discussion ==== | ||
| - | === 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]] | ||
| - | ==== Parents ==== | ||
| - | === Requirements === | ||
| - | [[Real number]] | ||
| - | === Element of === | ||
| - | [[Field]] | ||
