Differences

This shows you the differences between two versions of the page.

--- arithmetic_structure_of_real_numbers [2013/09/08 14:40]
nikolaj
+++ arithmetic_structure_of_real_numbers [2013/09/08 14:40]
nikolaj
@@ Line 7: / Line 7: @@
 | @#55EE55: $ -_{\mathbb R}r = \{q-_\mathbb{Q}p\ |\ q<0\land p\in \mathbb Q\setminus r\} $ |
-| @#55EE55: $ r\ge 0\land s\ge 0\implies r\cdot_\mathbb{R}s = \{q\cdot_\mathbb{Q}p\ |\ q\in r\land p\in s\land q,p\ge 0\}\cup\{q\ |\ q\in\mathbb Q\land q<0\}  $ |
+| @#55EE55: $ r\ge 0\land s\ge 0\implies r\cdot_\mathbb{R}s = \{q\cdot_\mathbb{Q}p\ |\ (q\in r)\land (p\in s)\land (q,p\ge 0)\}\cup\{q\ |\ (q\in\mathbb Q)\land (q<0)\}  $ |
 | @#55EE55: $ r\ge 0\land s <  0\implies r\cdot_\mathbb{R}s = -(r\cdot_\mathbb{R}(-s))  $ |
 | @#55EE55: $ r  < 0\land s\ge 0\implies r\cdot_\mathbb{R}s = -((-r)\cdot_\mathbb{R}s)  $ |
 | @#55EE55: $ r  < 0\land s <  0\implies r\cdot_\mathbb{R}s = (-r)\cdot_\mathbb{R}(-s)  $ |
-| @#55EE55: $ r\ge 0\land s >  0\implies r/_\mathbb{R}s = \{q/_\mathbb{Q}p\ |\ q\in r\land p\in \mathbb Q\setminus s\} $ |
+| @#55EE55: $ r\ge 0\land s >  0\implies r/_\mathbb{R}s = \{q/_\mathbb{Q}p\ |\ (q\in r)\land (p\in \mathbb Q\setminus s)\} $ |
 | @#55EE55: $ r\ge 0\land s <  0\implies r/_\mathbb{R}s = -(r/_\mathbb{R}(-s))  $ |
 | @#55EE55: $ r  < 0\land s > 0\implies r/_\mathbb{R}s = -((-r)/_\mathbb{R}s)  $ |