===== Real coordinate space =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $ n\in \mathbb N $ |
| @#FFBB00: definiendum | @#FFBB00: $\mathbb R^n$ |

==== Discussion ====
Explicitly,

$ \mathbb R^1=\mathbb R $
$ \mathbb R^p=\mathbb R^{p-1}\times \mathbb R, \hspace{1cm}$

| @#DDDDDD: range       | @#DDDDDD: $1\le i\le p$ |

| @#EEEE55: predicate   | @#EEEE55: $ a< b \equiv \forall i.\ a_i< b_i$ |
| @#EEEE55: predicate   | @#EEEE55: $ a> b \equiv \forall i.\ a_i> b_i$ |
| @#EEEE55: predicate   | @#EEEE55: $ a\le b \equiv \forall i.\ a_i\le b_i$ |
| @#EEEE55: predicate   | @#EEEE55: $ a\ge b \equiv \forall i.\ a_i\ge b_i$ |

>todo: define the following in a seperate entry:

$ [a,b]\equiv\{x\ |\ \forall i.\ a_i\le x_i\le 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 ===
Wikipedia: [[http://en.wikipedia.org/wiki/Real_coordinate_space|Real coordinate space]]

==== Parents ====
=== Subset of ===
[[Cartesian product]]
=== Requirements ===
[[Real number]]