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euclidean_space [2013/09/13 17:39] nikolaj |
euclidean_space [2014/10/29 20:28] nikolaj |
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| ===== Euclidean space ===== | ===== Euclidean space ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $ n\in \mathbb N $ | | + | | @#55CCEE: context | @#55CCEE: $ n\in \mathbb N $ | |
| - | + | | @#FFBB00: definiendum | @#FFBB00: $\mathbb E^n \equiv \langle d,\mathbb R^n\rangle $ | | |
| - | | @#FFBB00: $\mathbb E^n \equiv \langle d,\mathbb R^n\rangle $ | | + | | @#55EE55: postulate | @#55EE55: $d:\mathbb R^n\times \mathbb R^n\to \mathbb R_+ $ | |
| - | + | | @#55EE55: postulate | @#55EE55: $d(x,y):=\left( \sum_{j=1}^n (x_j-y_j)^2 \right)^\frac{1}{2} $ | | |
| - | | @#55EE55: $d:\mathbb R^n\times \mathbb R^n\to \mathbb R_+ $ | | + | |
| - | | @#55EE55: $d(x,y):=\left( \sum_{j=1}^n (x_j-y_j)^2 \right)^\frac{1}{2} $ | | + | |
| ==== Discussion ==== | ==== Discussion ==== | ||
| Line 14: | Line 12: | ||
| === Subset of === | === Subset of === | ||
| [[Metric space]] | [[Metric space]] | ||
| - | === Requirements === | + | === Context === |
| [[Real coordinate space]] | [[Real coordinate space]] | ||
