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euclidean_space [2014/03/21 11:11] 127.0.0.1 external edit |
euclidean_space [2014/10/29 20:28] nikolaj |
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| ==== Set ==== | ==== Set ==== | ||
| | @#55CCEE: context | @#55CCEE: $ n\in \mathbb N $ | | | @#55CCEE: context | @#55CCEE: $ n\in \mathbb N $ | | ||
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| | @#FFBB00: definiendum | @#FFBB00: $\mathbb E^n \equiv \langle d,\mathbb R^n\rangle $ | | | @#FFBB00: definiendum | @#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:\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: postulate | @#55EE55: $d(x,y):=\left( \sum_{j=1}^n (x_j-y_j)^2 \right)^\frac{1}{2} $ | | ||
