Differences
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metric [2013/09/13 17:38] nikolaj |
metric [2014/11/20 13:00] nikolaj |
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| ===== Metric ===== | ===== Metric ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $ X $ | | + | | @#55CCEE: context | @#55CCEE: $ X $ | |
| - | + | | @#FFBB00: definiendum | @#FFBB00: $d\in$ it | | |
| - | | @#FFBB00: $d\in \text{Metric}(X)$ | | + | | @#55EE55: postulate | @#55EE55: $d:X\times X \to \mathbb{R}_+$ | |
| - | + | | @#55EE55: postulate | @#55EE55: $ d(x,y)=0 \implies x=y$ | | |
| - | | @#55EE55: $d:X\times X \to \mathbb{R}_+$ | | + | | @#55EE55: postulate | @#55EE55: $ d(x,y)=d(y,x)$ | |
| - | + | | @#55EE55: postulate | @#55EE55: $ d(x,y)\le d(x,p)+d(p,y)$ | | |
| - | | @#55EE55: $ d(x,y)=0 \implies x=y$ | | + | |
| - | | @#55EE55: $ d(x,y)=d(y,x)$ | | + | |
| - | | @#55EE55: $ d(x,y)\le d(x,p)+d(p,y)$ | | + | |
| ==== Discussion ==== | ==== Discussion ==== | ||
| Line 19: | Line 16: | ||
| === Equivalent to === | === Equivalent to === | ||
| [[Metric space]] | [[Metric space]] | ||
| - | === Requirements === | + | === Context === |
| [[Non-negative real number]] | [[Non-negative real number]] | ||
