Real coordinate space
Set
| context | $ n\in \mathbb N $ |
| definiendum | $\mathbb R^n$ |
Discussion
Explicitly,
$ \mathbb R^1=\mathbb R $ $ \mathbb R^p=\mathbb R^{p-1}\times \mathbb R, \hspace{1cm}$
| range | $1\le i\le p$ |
| predicate | $ a< b \equiv \forall i.\ a_i< b_i$ |
| predicate | $ a> b \equiv \forall i.\ a_i> b_i$ |
| predicate | $ a\le b \equiv \forall i.\ a_i\le b_i$ |
| predicate | $ 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: Real coordinate space
Parents
Subset of
Requirements
