Differences

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

Link to this comparison view

Both sides previous revision Previous revision
Next revision
Previous revision
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] (current)
Line 1: Line 1:
 ===== Arithmetic structure of rational numbers ===== ===== Arithmetic structure of rational numbers =====
-==== Definition ​==== +==== Set ==== 
-| @#FFBB00: $\langle \mathbb Q,​+_\mathbb{Q},​\cdot_\mathbb{Q} \rangle$ |+| @#FFBB00: definiendum ​| @#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: postulate ​  | @#55EE55: $[\langle a,​b\rangle]+_\mathbb{Q}[\langle m,​n\rangle]=[\langle a\ n+b\ m,b\ n\rangle]$ | 
-| @#55EE55: $[\langle a,​b\rangle]\cdot_\mathbb{Q}[\langle m,​n\rangle]=[\langle a\ m,b\ n\rangle]$ |+| @#55EE55: postulate ​  | @#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]]. The operations $+$ and $\cdot$ on the right hand sides are these of [[arithmetic structure of integers]].
Line 15: Line 15:
 We'll also often omit the multiplication sign. We'll also often omit the multiplication sign.
  
->We can also introduce numerator and denominator:​ +We can also introduce numerator and denominator:​ 
-> + 
->$ \mathrm{num}\frac{a}{b}\equiv a $ +$ \mathrm{num}\frac{a}{b}\equiv a $ ^ 
->$ \mathrm{den}\frac{a}{b}\equiv b $+$ \mathrm{den}\frac{a}{b}\equiv b $ ^
  
 === Theorems === === Theorems ===
Line 27: Line 27:
 Wikipedia: [[http://​en.wikipedia.org/​wiki/​Rational_number|Rational number]] Wikipedia: [[http://​en.wikipedia.org/​wiki/​Rational_number|Rational number]]
 ==== Parents ==== ==== Parents ====
-=== Requirements ​===+=== Context ​===
 [[Rational number]] [[Rational number]]
 === Element of === === Element of ===
 [[Field]] [[Field]]
Link to graph
Log In
Improvements of the human condition