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arithmetic_structure_of_rational_numbers [2013/09/06 22:04]
127.0.0.1 external edit
arithmetic_structure_of_rational_numbers [2014/03/21 11:11]
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-===== Arithmetic structure of rational numbers ===== 
-==== Definition ==== 
-| @#FFBB00: $\langle \mathbb Q,​+_\mathbb{Q},​\cdot_\mathbb{Q} \rangle$ | 
  
-| @#55EE55: $[\langle a,​b\rangle]+_\mathbb{Q}[\langle m,​n\rangle]=[\langle a\ n+b\ m,b\ n\rangle]$ | 
-| @#55EE55: $[\langle a,​b\rangle]\cdot_\mathbb{Q}[\langle m,​n\rangle]=[\langle a\ m,b\ n\rangle]$ | 
- 
-The operations $+$ and $\cdot$ on the right hand sides are these of [[arithmetic structure of integers]]. 
- 
-==== Discussion ==== 
-We'll generally use the notation introduced in [[integer]] as well as 
- 
-$\frac{a}{b}\equiv\langle a,b\rangle$ 
- 
-We'll also often omit the multiplication sign. 
- 
->We can also introduce numerator and denominator:​ 
-> 
->$ \mathrm{num}\frac{a}{b}\equiv a $ 
->$ \mathrm{den}\frac{a}{b}\equiv b $ 
- 
-=== Theorems === 
-Division or rational numbers is given by 
- 
-$\frac{[\langle a,​b\rangle]}{[\langle m,​n\rangle]}=[\langle a\ m,b\ m\rangle]$ 
-=== Reference === 
-Wikipedia: [[http://​en.wikipedia.org/​wiki/​Rational_number|Rational number]] 
-==== Parents ==== 
-=== Requirements === 
-[[Rational number]] 
-=== Element of === 
-[[Field]] 
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