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Real coordinate space
Set
| context | $ n\in \mathbb N $ |
| definiendum | $\mathbb R^n$ |
Recursive definition:
| $ p\in \mathbb N $ | $ p>1 $ |
| postulate | $ \mathbb R^1=\mathbb R $ |
| postulate | $ \mathbb R^p=\mathbb R^{p-1}\times \mathbb R, \hspace{1cm}$ |
Discussion
| 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$ |
| definiendum | $ [a,b]\equiv\{x\ |\ \forall i.\ a_i\le x_i\le b_i\}$ |
| definiendum | $ ]a,b]\equiv\{x\ |\ \forall i.\ a_i<x_i\le b_i\}$ |
| definiendum | $ [a,b[\ \equiv\{x\ |\ \forall i.\ a_i\le x_i<b_i\}$ |
| definiendum | $ ]a,b[\ \equiv\{x\ |\ \forall i.\ a_i<x_i<b_i\}$ |
Reference
Parents
Subset of
Context
