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real_coordinate_space [2014/03/21 11:11]
127.0.0.1 external edit
real_coordinate_space [2014/04/04 16:01] (current)
nikolaj
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 ==== Set ==== ==== Set ====
 | @#55CCEE: context ​    | @#55CCEE: $ n\in \mathbb N $ | | @#55CCEE: context ​    | @#55CCEE: $ n\in \mathbb N $ |
- 
 | @#FFBB00: definiendum | @#FFBB00: $\mathbb R^n$ | | @#FFBB00: definiendum | @#FFBB00: $\mathbb R^n$ |
  
-Recursive definition:+==== Discussion ==== 
 +Explicitly,
  
-p\in \mathbb ​$ p>1 $ |+$ \mathbb R^1=\mathbb ​$ 
 +\mathbb R^p=\mathbb R^{p-1}\times \mathbb R, \hspace{1cm}$
  
-| @#55EE55: postulate ​  | @#55EE55: $ \mathbb R^1=\mathbb R $ | 
-| @#55EE55: postulate ​  | @#55EE55: $ \mathbb R^p=\mathbb R^{p-1}\times \mathbb R, \hspace{1cm}$ | 
- 
-==== Discussion ==== 
 | @#DDDDDD: range       | @#DDDDDD: $1\le i\le p$ | | @#DDDDDD: range       | @#DDDDDD: $1\le i\le p$ |
  
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 | @#EEEE55: predicate ​  | @#EEEE55: $ a\ge b \equiv \forall i.\ a_i\ge b_i$ | | @#EEEE55: predicate ​  | @#EEEE55: $ a\ge b \equiv \forall i.\ a_i\ge b_i$ |
  
-| @#FFBB00definiendum | @#FFBB00: $ [a,​b]\equiv\{x\ |\ \forall i.\ a_i\le x_i\le b_i\}$ ​| +>tododefine the following in a seperate entry: 
-| @#FFBB00: definiendum | @#​FFBB00: ​$ ]a,​b]\equiv\{x\ |\ \forall i.\ a_i<​x_i\le b_i\}$ ​| + 
-| @#FFBB00: definiendum | @#​FFBB00: ​$ [a,b[\ \equiv\{x\ |\ \forall i.\ a_i\le x_i<​b_i\}$ ​| +$ [a,​b]\equiv\{x\ |\ \forall i.\ a_i\le x_i\le b_i\}$ 
-| @#FFBB00: definiendum | @#​FFBB00: ​$ ]a,b[\ \equiv\{x\ |\ \forall i.\ a_i<​x_i<​b_i\}$ ​|+ 
 +$ ]a,​b]\equiv\{x\ |\ \forall i.\ a_i<​x_i\le b_i\}$ 
 + 
 +$ [a,b[\ \equiv\{x\ |\ \forall i.\ a_i\le x_i<​b_i\}$ 
 + 
 +$ ]a,b[\ \equiv\{x\ |\ \forall i.\ a_i<​x_i<​b_i\}$
  
 === Reference === === Reference ===
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 === Subset of === === Subset of ===
 [[Cartesian product]] [[Cartesian product]]
-=== Context ​===+=== Requirements ​===
 [[Real number]] [[Real number]]
  
  
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